Kaushikee Banerjee

What is current and voltage division?

Voltage and current divider

Current and voltage division are real-life examples of Kirchhoff’s laws. The current division takes place in a parallel circuit, while voltage division occurs in a series circuit.

What are the current divider rule and voltage divider rule?

Current divider rule | Current divider law

What is a current divider?

The current-divider rule is a practical application of Kirchhoff’s current law. It states that,

In a circuit with a parallel combination of resistors, the current gets divided into all the branches having the same voltage across them. Thus a parallel circuit behaves as a current divider.

What is Voltage divider with current source ?

Voltage divider current

A voltage divider with a current source divides the supply voltage in the resistances. The voltagedrop across any resistor is the multiplication of the resistances with the value of current in the circuitry.

Current divider circuit example

Let us take a circuit with a DC voltage source of V volt and two resistors R₁ and R₂, connected in parallel. The total current in the circuit is i,  current through R₁ is i₁, and R₂ is i₂.

What is Current divider theory | Current divider rule definition | Current divider definition ?

Current divider theorem | Current divider principle

The current-divider rule says that the current in any branch of the parallel circuit is equal to the total current in the circuit multiplied by the ratio of the resistance of the opposite branch and the total circuit resistance.

Current divider rule derivation | Formula derivation

Current divider parallel

In the image1, we can see two parallelly connected resistances R₁ and R₂, are joined with a DC voltage V and currents thru them are i₁ and i₂, respectively.

The equivalent resistance of the circuit is

=11

What is Voltage and current divider formula ?

Current divider rule formula

According to the currentdivider rule,

Current in through any resistor = Total current of the network x resistance of other resistor/equivalent resistance of the circuit.

Voltage divider rule

According to the voltage divider rule,

The voltage drop across any resistor = Total current of the network x resistance of that resistor

Current divider equation | Derive current divider equation

For the above circuit, we can see that resistances R₁, R₂, R₃, and R_X are connected in parallel. A voltage source is added to this combination, and current I_T flows through the circuit. The equivalent resistance of R₁, R₂, and R₃ is denoted as R_T, and If the current across resistor R_X is I_X, we can say that,

What is Current divider rule for 2 resistors in parallelly connected ?

Parallel circuit current divider | Current divider formula for parallel circuit

Two resistors R₁ and R₂, are connected in parallel with a DC source V. If the currents i₁ and i₂ flow through them and the total current is I then,

What is the Current divider rule for 3 resistors in parallelly ?

Current divider rule for 3 resistors

Three resistors R₁, R₂, and R₃, are connected in parallel with a voltage source V. Total current in the circuit is I_T and branch currents are i₁, i₂, and i₃, respectively. Therefore,

Current in a voltage divider

As the voltage dividers are series circuits, the current through all the resistors or impedance elements is the same. With the help of the total current, the voltage divider rule is constructed. The voltage drop across any resistor equals the total current multiplied by the resistance of that resistor present in the circuitry.

Current divider applications | Current divider examples

• The main purpose of using a current division is to reduce complexity while solving for current in any circuit. It divides the current into small components.
• Current division is used to protect circuits from overheating. As it divides the total current into fractions, small current components generate, and large current flow is avoided. This allows less heat dissipation and saves the circuits from any damage.

High current voltage divider

A voltage divider that can deliver a high amount of current is difficult to be built with a traditional resistor network. A switching regulator or a buck converter type design can come in handy in this case. For the buck converter approach, its voltage reference can be replaced with a divider derived from the incoming supply.

Series voltage divider with parallel load current

If a load resistance is connected with the voltage divider in parallel, the overall equivalent resistance decreases. Therefore the current in the circuit increases, but the voltage at the divider output drops.

AC current divider

AC circuits function the same as DC. Just the impedances must be written with their phasor representations using the complex quantity j.

Current divider impedance

If we generalize the resistive network equation for elements other than resistance,

Where I_T is the total current, I_X is the current through a particular branch, Z_T is the equivalent impedance of the circuit, and ZX is the impedance of that branch.

To know about Inductors in Series and Parallel click here

How to use the current divider rule? How to apply the current divider rule? | How to divide current in a parallel circuit?

Current divider method

The current division is calculated in the following steps:

• First, find the equivalent resistance R_T of the other circuit elements, excluding the one for which current needs to be calculated (R_X)
• Compute the fraction of this R_T and R_T + R_X
• Multiplying this quantity with the total current would fetch the desired branch current I_X.

What is the difference between voltage divider and current divider ?

Voltage divider and current divider | Current divider vs voltage divider

Current Divider	Voltage Divider
It is constructed through parallel circuits.	It is constructed through series circuits.
The values of current through the resistors are measured.	The values of voltage drop through the resistors are measured.
The voltages in all the resistors are equal, the currents vary.	The currents in all the resistors are equal, the voltages vary.

Low current voltage divider

Voltage divider circuits with low or almost zero current can be used to design switches with an additional transistor.

Voltage divider current limit

There’s no specific limit for current in a voltage divider. However, observed values suggest that currents over 1 amp can be regarded as high for the voltage dividers.

Current divider problems with solutions

Current and voltage divider

Q. Two impedances, Z₁ = 2+j5 and Z₂ = 5+j2, are connected in a parallel circuit. Total current, I = 10 amp. Using the current division, find out the currents through individual impedances.

We know,

Therefore, I₁ = 10 x (5+j2)/ 2+j5+5+j2 = 5(7-j3)/7 amp

I₂ = I – I1 = 10 – 5(7-j3)/7 = 5(7+j3)/7 amp

Current and voltage divider examples | current and voltage divider problems

Q. Three resistors of 6 ohm, 12 ohm, and 18 ohm are connected in series with DC supply voltage 54V, then calculate the voltage drop across all the resistors.

The voltage divider rule says that voltage drop across any resistor in a series circuit = resistance of that resistor x the current.

Now, equivalent resistance of the circuit = 6 + 12 + 18 = 36 ohm

So, net current in the circuit = 54/36 = 1.5 A

Therefore, voltage drop across 6 ohm resistor = 1.5 x 6 = 9 Volt

voltage drop across 12 ohm resistor = 1.5 x 12 = 18 Volt

voltage drop across 18 ohm resistor = 1.5 x 18 = 27 Volt

Current divider rule example problems | Current divider sample problems

Q. 4 resistors with resistances 5 ohm, 10 ohm, 15 ohm, and 20 ohm are connected in parallel with a voltage source. The total current in the circuit is 5A, then compute the current thru the 10Ω resistor.

The equivalent resistance of the circuit = 5 x 10 x 15 x 20 / (50 + 75 + 100 + 150 + 200 + 300) = 17.14 Ohm

Therefore, current through the 10 ohm resistor = 5 x 17.14/10 = 8.57 A

Q. Two resistors of 10 ohm and 20 ohm are connected in parallel with a 200 V DC supply, then compute current thru the 20Ω resistor.

Net resistance in the circuit = 10 x 20/ 30 = 20/3 ohm

Total current in the circuit = 200/(20/3) = 30 A

So the current through 20 ohm resistor = (20/3)/20 x 30 = 10 A

Q. For the network with n resistances shown below, R₁ = R₂ = R₃ = ………= R_n = R. Find the current passing through R_n.

Equivalent resistance of the circuit,

We know the total current in the circuit is I

Therefore, current through R_n = (R/n)/R x I = I/n

Frequently Asked Questions | Short Notes | FAQs

Q. How can we calculate the current division?

Current division occurs in a parallel circuit. The supply current gets divided into branches connected in parallel. The voltage across all the branch resistors is equal to voltage supplied. With the help of Ohm’s law and Kirchhoff’s current law, the current division is calculated. The divided current in one branch is the multiplication of the total current and the ratio of the other branch’s resistance with the sum of all the resistance.

Q. In which condition is the current divider rule applicable?

The currentdivider rule is applicable for any circuit where resistance or other impedance parameters are connected in parallel.

Q. What is the advantage of applying the current-divider rule in a parallel circuitry ?

The basic reason for using the current-divider rule in parallel circuits is to make problem-solving easier. In a parallel circuit, the current gets divided into branches, So calculating current thru the branches becomes less time-consuming if the total current is known.

Q. Does the current division rule disobey Ohm’s law?

The Current-divider rule is based on Ohm’s law itself. The fundamental concept of Ohm’s law is used to calculate the divided currents.

Q. State the difference between a voltage divider and a current divider?

The main difference between a voltage divider and a current-divider is the operating circuit. The Voltage divider rule is applied in series circuits where as the current-divider rule is utilized in parallel circuit.

Q. When can we apply the voltage divider and the current divider rule?

In a series circuit, the voltage divider rule is used to calculate the voltage drop across the resistors. In a parallel circuit, the current-divider rule is used to calculate the branch currents.

Q. What are the voltage dividers?

The voltage dividers are linear circuits where the output voltage is obtained from the fraction of input voltage. The most common example of voltage is a potentiometer.

Q. How to use a rheostat so that it works as a potential divider and current limiter?

A rheostat can be used as a large variable resistor. It has three terminals, two at the ends and one movable contact. By adding voltage sources at the ending terminals, the voltage across the other terminal is obtained. This way the rheostat works as a potential divider, and the terminals work as current limiters.

Q. What are the advantages of a voltage divider?

A voltage divider helps in getting the voltage drop across components from the large supply voltage.

Q. How can we calculate the value of current passing through the resistor R₁ in the circuit?

The current through resistor R₁ is the total current multiplied by the other resistance divided by the sum of all resistance in the circuit.

Q.Why cannot we use the voltage divider method to get a constant current?

The supply voltage keeps fluctuating in a circuit. So we cannot get a constant current.

Q. Three parallel branches with resistances are connected across a DC voltage. What would be the ratio of the branch currents I₁, I₂, and I₃ if the branch resistance ratio is  R₁: R₂ : R₃ = 2 : 4 : 6?

Let us assume that R₁ = 2x ohm, R₂ = 4x ohm and R₃ = 6x ohm

Equivalent resistance of the circuit = 2x x 4x x 6x/ 8×2 + 24×2 + 12×2 = 12x/11 ohm

Therefore, I₁ = I x 12x/11/(2x) = 6I/11 A

I₂ = I x 12x/11/(4x) = 3I/11 A

I₃ = I x 12x/11/(6x) = 2I/11 A

So I₁ : I₂ : I₃ = 6:3:2

Q. Can we apply the voltage divider rule in an ac circuit?

Voltage divider rule is equally applicable for AC circuit calculations, but only if phasor representation is used involving the imaginary quantity ‘j’.

Q. How to obtain zero output voltage using a potential divider?

Zero output voltage can be achieved by keeping a potentiometer in series with a resistance. When this combination is subjected to supply voltage, an end terminal and the middle terminal of the potentiometer fetch output. When the slider terminal is at one end, the voltage is zero.

Q. In a series RC circuitry, the voltage across the capacitor and resistor are 60V & 80V, then What will be total voltage in the circuitry?

By simply applying voltage divider rule, the total voltage is the summation of the voltages across the resistors and the capacitors, So Total voltage = V_R+V_C=60+80=140V.

Q. Current flow is divided between the different branches in a __.

The answer would be parallel circuitry.

Q. Does a voltage divider affect current?

A voltage divider is nothing but a parallel circuit,will not affect the total current of the circuit. However, the branch current values differ according to the branch impedance.

Q. Is current divided in a parallel circuit?

By the rule of current division, we can say that the parallel circuits divide current flowing through them.

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Concept of mutual inductance | Mutual inductance definition

In two adjacent conductor coils, the variation in current in one coil will cause induced emf in the other coil, This phenomenon is called mutual induction. Mutual induction is not a single coil’s property as both/multiple the inductor/inductors are impacted by this property at same time. The primary coil is the coil in which variation of current takes place, and the 2nd coil in which emf is induced named secondary.

Unit of mutual inductance | SI unit of mutual inductance

The unit of mutual inductance is same as inductance, i.e. So SI unit of mutual inductance is Henry(H).

Dimension of mutual inductance

Dimension of mutual inductance = dimension of magnetic flux/dimension of current = [MLT^-2I^-2]

Mutual inductance equation

Mutual induction is the principle that current running through a conductor will generate a magnetic field, and a changing magnetic field will induce a current in another conductor.
From Faraday’s law and Lenz’s law, we can write,

E = -(dφ/dt)

E ∝ dφ/dt

We already know, ? ∝ i [ as B=μ₀ni and ?=nBA]

Therefore, E ∝ di/dt; E =-Mdi/dt [M is proportionality constant]

This M is called the mutual inductance.

M = -E/(di/dt)= emf induced in the secondary coil/rate of change of current in the primary coil

We can also write by comparing that,

-Mdi/dt = dφ/dt

Integrating both sides, we get, ? = Mi

Define Mutual Inductance of 1 Henry

This is the measurement in one coil having 1 m² area, produced 1 V by the variation of the inducing current of 1 Amp/sec in other coil in the existence of 1 T magnetic field.

Derive an expression for mutual inductance

Mutual inductance circuit analysis | Mutual inductance equivalent circuit

Let us consider, two inductor coils with self-inductance, L₁ and L₂, are kept in close contact with each other. Current i₁ flows through the first one, and i₂ flows through the second one. When i₁ changes with time, the magnetic field also varies and leads to a change in magnetic flux linked to the 2nd coil, the EMF is induced in the 2nd coil due to the change in current in the 1st coil and can be expressed as,

E₂₁ = -N₂(dφ₂₁/dt)

Therefore, N₂φ₂₁ ∝ i₁

Or, N₂φ₂₁ = M₂₁i₁

Or, M₂₁= N₂φ₂₁/i₁

This proportionality constant M₂₁ is called the mutual inductance

Similarly we can write, N₁φ₁₂ = M₁₂}i₂ or M₁₂ = N₁φ₁₂ /i₂

M₁₂ is called another mutual inductance

Mutual inductance of a coil
Define mutual inductance between a pair of coils

The mutual inductance of a pair of coils is the ratio of magnetic flux linked with one coil and current passing through another coil.

Where, μ₀=permeability of free space
N₁, N₂ are turns of the coil.
A is the cross-sectional area of the coil.
L is the length of the coil.

Mutual inductance formula | Mutual inductance of two solenoids

Mutual inductance between two coils,

M = μ₀N₁N₂A/L if there’s no core in between two coils

M = μ₀\\μ_rN₁N₂A/L if the soft iron core is placed between the coils

How to find the mutual inductance of two long co-axial solenoid ?

Derivation of mutual inductance of two long coaxial solenoids

Let us assume that two solenoids S₁ and S₂, are placed in close contact with each other. Due to the phenomenon of mutual induction, the current passing through 1st coil will induce EMF in the another coil. Now, we connect S₁ with a battery through a switch and S₂ with a galvanometer. The galvanometer detects the presence of current and its direction.

Due to the flow of current in S₁, magnetic flux is generated in S₂, and a change in magnetic flux causes the current in S₂. Due to this current, the galvanometer needle shows deflection. Therefore we can say current i of S₁ is proportional to ? in S₂.

? ∝ i

? = Mi

Here M is called mutual inductance.

Now, in the case of coaxial solenoids, one coil is placed inside another so that they share the same axis. Suppose S₁ and S₂ have turns N₁, N₂, and areas A₁, A₂ respectively.

Mutual inductance formula derivation

For inner coil S1:

When current i₁ flows through S₁, magnetic field, B₁ =μ₀N₁i₁

Magnetic flux linked with S₂, φ₂₁ = B₁A₁ = μ₀N₁i₁A₁

This is the flux for a single turn. [Though the area of S₂ is A₂, the flux will only generate in the area A₁]

Therefore for N₂ turns φ₂₁ = μ₀N₁i₁A₁ x N₂/L …..(1), where L is the length of the solenoids

We know,
? = Mi
?₂₁ = M₂₁i₁…….(2)

Equating (1) and (2), we get,

M₂₁i₁ = μ₀N₁i₁A₁N₂/L
M₂₁ = μ₀N₁A₁N₂/L

For outer coil S2:

When current i₂ flows through S₂, magnetic field, B₂ = μ₀N₁i₂

Magnetic flux linked with S₁ for N₁ turns, φ₁₂ = N₁/L x B₂A₁ = μ₀N₁N₂i₂A₁/L ….(3)

Similar to the inner coil we can write,
?₁₂ = M₁₂i₂……(4)

Equating (1) and (2), we get,

M₁₂i₂= μ₀N₁N₂i₂A₁/L
M₁₂ = μ₀N₁N₂A₁/L

From the above two findings, we can say that M₁₂=M₂₁ = M. This is the mutual inductance of the system.

Mutual inductance of a coil inside a solenoid | Mutual inductance between two loops

A coil with N₂ bindings is placed inside a long thin solenoid that contains N₁ number of bindings. Let us assume that the bindings of the coil and the solenoid are A₂ and A₁, respectively, and the length of the solenoid is L.

It is known that the magnetic field inside a solenoid due to current i₁ is,

B = μ₀N₁i₁/L

Magnetic flux that passes through the coil due to the solenoid,

?₂₁ = BA₂cos? [? is the angle between the magnetic field vector B and area vector A₂]

φ₂₁ = μ₀N₁i₁/L x A₂ cosθ

Mutual inductance, M = φ₂₁N₂/i₁= μ₀N₁N₂ A₂ cosθ/L

Mutual inductance in parallel

In this circuit 2-inductors having self-inductance L₁ and L₂, are adjoined in parallel, Let us assume the total current is i, the sum of i₁( current through L₁) and i₂(current through L₂) Mutual inductance between considered as M.

i= i₁ + i₂

di/dt = di₁/dt+ di₂/dt

Effective flux through L₁, ?₁ = L₁i₁ + Mi₂

Effective flux through L₂, ?₂ = L₂i₂ + Mi₁

Induced EMF in L₁,

Induced EMF in L2,

We know in case of parallel connection, E₁ = E₂

-L₁(di₁/dt) – Mdi₂/dt = E … (1)
-L₁(di₂/dt) – Mdi₁/dt = E … (2)

Solving the two equations, we get,

di₁/dt = E(M-L₂)/L₁L₂ – M²

di₂/dt = E(M-L)/L₁L₂ – M²

We know, E = -L_eff (di/dt)

Or, L_eff =-E/(di/dt) = L₁L₂ – M²/L₁-L₂-2M

To know more about the Inductors in series and parallel click here

Calculating mutual inductance between circular coils | Mutual inductance of two circular loops

Let us take two circular coils of radii r₁ and r₂ sharing the same axis. The number of turns in the coils are N₁ and N₂.
The total magnetic field in the primary coil due to current i,

B = μ₀N₁i_2r1

Magnetic flux produced in the secondary coil because of B,

We know mutual inductance,

Factors affecting mutual inductance | Mutual inductance M is dependent on what factors

• Material of the core- Air core or Solid core
• No of Turn (N) of the coils
• Length (L) of the coil.
• Cross-sectional area(A).
• Distance(d) between the coils.
• Alignment/Orientation of the coil.

Mutual inductance coupling | Coupling coefficient k

The fraction of the magnetic flux generated in one coil that is linked with another coil is known as the coefficient of coupling. It is denoted by k.
Coefficient of mutual inductance,

• If coils are not coupled, k = 0
• If coils are loosely coupled, k<½ If coils are tightly coupled, k>½
• If coils are perfectly coupled, k = 1

The formula for self-inductance and mutual inductance

Self-inductance L = N?/i = number of turns in the coil x magnetic flux linked with the coil/current flowing through the coil
Mutual inductance M = ?/i = magnetic flux linked with one coil/current passing through another coil

Mutual inductance between two parallel wires

Let us think that two parallel cylindrical wires carrying equal current, each of l length and radius a. Their centers are d distance apart.
The mutual inductance between them is determined with the help of Neumann’s formula.

M = 2l[ln(2d/a) -1 + d/l] (Approximately)

Where, l>>d

What is the difference between self and mutual inductance ?

Self-inductance	Mutual inductance
Self-inductance is the property of an individual coil.	Mutual inductance is shared by both the coils
It is the ratio of the total magnetic flux produced in the coil and the current.	It is the ratio of the total magnetic flux produced in one coil and the current passing through another coil.
If the own current increases, the induced current opposes that.	If the own current of one coil increases, the induced current in the other coil opposes that.

What are the application of self induction and mutual induction ?

Applications of self-inductance

The principle of self-induction is used in the following devices-

• Choke coils.
• Sensors.
• Relays
• DC to AC converter.
• Ac filter.
• Oscillator circuit.

Applications of mutual inductance

The principle of mutual induction is used in the following devices-

• Transformers.
• Metal detector.
• Generators.
• Radio receiver.
• Pacemaker.
• Electric motors.

Mutual inductance circuits | Mutual inductance circuit example

T-circuit:

Three inductors are connected like a T-shape as shown in the figure. The circuit is analyzed with the two-port network concept.

Π-circuit:

Contrarily, two coupled inductors can be created using a π equivalent circuit with optional ideal transformers at each port. The circuit can look complicated initially, but it can further be generalized into circuits that have more than two coupled inductors.

What is the Difference between mutual induction and mutual inductance ?

Mutual induction vs Mutual inductance

Mutual inductance is the property shared by two inductive coils in which varying current in one coil induces EMF in the another one, If mutual induction is the cause, mutual inductance can be said to be its effect.

Mutual inductance dot convention

The relative polarity of the mutually coupled inductors decides whether the induced EMF is additive or subtractive. This relative polarity is expressed with dot convention. It is denoted by a dot sign at the ends of the coil. At any instance, if the current enters a coil through the dotted end, mutually induced EMF on the other coil will have a positive polarity at the dotted end of that coil.

Energy stored in mutually coupled inductors

Let us assume that two mutually coupled inductors have self-inductance values L1 and L2. Currents i1 and i2 travel in them. Initially, the current in both the coils is zero. So the energy is also zero. The value of i1 rises from 0 to I1, while i2 is zero. So the power in inductor one,

So, the energy stored,

Now, if we keep i1 = I1 and increase i2 from zero to I2, the mutually induced EMF in inductor one is M12 di2/dt, while the mutually induced EMF in inductor two is zero since i1 does not change.
So, the power of inductor two due to mutual induction,

Energy stored,

The total energy stored in the inductors when both i1 and i2 have reached constant values is,

w = w₁ + w₂ = 1/2L₁I₁² + 1/2L₂I₂² – MI₁I₂

If we reverse the current increments, that is, increase i2 from zero to I2 first and later increase i1 from zero to I1, the total energy stored in the inductors is,

w = w₁ + w₂ = 1/2L₁I₁² + 1/2L₂I₂² – MI₁I₂

Since, M₁₂ = M₂₁, we can conclude that the total energy of mutually coupled inductors is,

w = w₁ + w₂ = 1/2L₁I₁² + 1₂L₂I₂² + MI₁I₂

This formula is correct only when both the currents enter dotted terminals. If one current enters the dotted terminal and the other leave, the energy stored will be,

w = w₁ + w₂ = 1/2L₁I₁² + 1/2L₂I₂² – MI₁I₂

Mutual inductance devices

Mutual inductance transformer model

An AC voltage can be increased or reduced according to the requirements of any electrical circuit by using a static device. It is called a transformer. It is a four-terminal device that consists of two or more mutually coupled coils.
Transformers follow the principle of mutual induction. They transfer electric energy from one circuit to another when the circuits are not electrically connected.

Linear transformer:

If the coils in the transformer are wound on magnetically linear material, then it is called a linear transformer. Magnetically linear materials have constant permeability.

In a linear transformer, magnetic flux is proportional to the current passing through the windings. The coil that is directly joined to a voltage source is known as the primary coil and the coil adjoined to load impedance is entitled as secondary. If R₁ is connected in the circuit with the voltage source and R₂ is connected in the circuit with the load.

Applying Kirchhoff’s voltage law in two meshes, we can write,

V = (R₁ + jΩL₁)I₁ – jΩMI₂……(1)

-jΩ MI₁ + (R₂ + jΩL₂ + Z_L)I₂ = 0.…..(2)

Input impedance in the primary coil,

Z_in = V/I₁ = R₁+ jΩL₁ + Ω₂M₂/R₂+jΩL₂ + Z_L

The first term (R₁+jωL₁) is called the primary impedance and the other second term is called the reflected impedance Z_R.

Z_R = Ω²M₂/R₂+jΩ L₂ + Z_L

Ideal transformer

A transformer that doesn’t have any type of loss is called an ideal transformer.

Characteristics:

• An ideal transformer has zero primary and secondary winding resistance.
• Permeability of the core is considered as infinite.
• No leakage flux is there in an ideal case.
• Hysteresis does not take place.
• The value of eddy current loss is zero.
• The ideal transformer is said to be 100% efficient.

Mutual inductance of transformer formula-

There’s zero power loss in an ideal transformer. So, the input power = output power

W₁i₁cosφ = W₂i₂cosφ or W₁i₁ = W₂i₂

Therefore, i₁/i₂ = W₂/W₁

Since voltage is directly proportional to the no. of turns in the coil.,
we can write,

V₂/V₁ = W₂/W₁= N₂/N₁ = i₁/i₂

If V₂>V₁, then the transformer is called a step-up transformer.
If V₂<V₁, then the transformer is called a step-down transformer.

Applications of transformer:

• A transformer can electrically isolate two circuits
• The most important application of a transformer is to step up ( increase) or step down (decrease) the voltage. It can raise or lower the value of current and voltage so that if any of the quantities increase or decrease, power remains the same.
• It can also increase or decrease the impedance, capacitance, or inductance values in a circuit. In other words, the transformer can perform impedance matching.
• Transformer will prevent carrying direct current from one circuit to other.
• It is used in mobile chargers to avoid damages caused by high voltage.
• It is used to generate a neutral in three-phase power supply.

Heaviside Mutual Inductance Bridge | Mutual Inductance measurement bridge

We use mutual inductance in various circuits to determine the values of self-inductance, frequency, capacitance, etc. Heaviside bridge is a component where we can measure mutual inductance with the help of a known self-inductance. A modified version of this bridge can be used in performing the reverse application i.e. measuring self-inductance with the help of known mutual inductance.

Operation

Let us take a combination of elements in the form of the bridge circuit shown in the figure. The coil S₁ with mutual inductance M is not the part of the bridge but it is mutually coupled with the coil S₂ in the bridge which has self-inductance L₁. Current passing through S₁ produces flux that is linked with S₂. As per the dot convention, we can say, current i passes through S₁ and further gets divided into i₁ and i₂. The current i₁ passes through S₂.

Under balanced condition,
i₃=i₁; i₄=i₂ ; i=i₁+i₂

As no current passes through the galvanometer, the potential of B is equal to the potential of D.

Therefore we can say, E₁=E₂

Or, (i₁+i₂)jΩM + i₁(R₁+jΩ L₁) = i₂(R₂+jΩ L₂)

i₁R₁+jΩ (L₁i₁+ M(i₁+i₂))= i₂R₂ + jΩ L₂i₂ …..(1)

i₁[R₁+jΩ (L₁+M) = i₂[R₂+jΩ (L₂-M)] ……(2)

Similarly, E₃=E₄

i₃R₃=i₄R₄

Or, i₁R₃=i₂R₄…….(3)

Dividing (1) by (3) we get,

R₁+jΩ (L₁+M)/R₃ = R₂ + jΩ (L₂-M)/R₄

Taking the real parts of both sides, we can write,

R₁/R₃=R₂/R₄

Taking the imaginary parts of both sides, we can write,

L₁+M/R₃=L₂-M/R₄

So, M=R₃L₂-R₄L₁/R₃+R₄

We can conclude from the above equation that the value of L₁ must be known. Now if R₃=R₄,

R₁=R₂ and M = L₂-L_1/2

Or, L₂= L₁+2M

This way we can find out the value of unknown inductance L₂

The bridge that measures the unknown mutual inductance in terms of two known self-inductance L₁ and L₂, is called the mutual inductance measurement bridge or Campbell bridge.

The field-armature mutual inductance of the synchronous motor

In an AC rotating synchronous motor, steady-state speed is proportional to the frequency of the current passing through its armature. Therefore, a magnetic field is produced. The current rotates at the same speed as that of the rotating synchronous speed of the field current on the rotor. Due to this phenomenon, a mutual induction develops between the armature and the field wingdings. It is known as field-armature mutual inductance.

Table of contents : Inductors in Series and Parallel

What are inductors?

Inductors

Inductors are nothing but magnetic energy storage devices. Physically it is a coil of conducting wire, either wrapped around a solid core or without any core. The latter one is called an air-core inductor. 

When current flows through the inductor, it creates a magnetic field. Coiling up a lot of wire increases the strength of the magnetic field. The direction of the magnetic field is determined with the help of the right-hand thumb rule. 

When current first starts to flow through the coil, the magnetic field starts to expand, then after some time, it stabilizes and stores some amount of magnetic energy. When the field gradually collapses, the magnetic energy gets turned back into electrical energy. Inductors produce magnetic flux, proportional to the current flowing through them.

To know more about inductive reactance click here.

What is self inductance?

Self inductance Definition

Self inductance is the characteristic of a coil by which the coil opposes any sudden change of current in it. 

Self inductance of a coil,

Where, N = number of turns in the coil, ? = magnetic flux and i is the current flowing through the coil

Self inductance of a solenoid with n turns, l length and A cross-sectional area,

What is mutual inductance?

Mutual Inductance Definition

In the case of two coils, the change in current in one coil induces EMF in the neighboring coil. This incident is known as mutual induction, and this property of the primary coil is called mutual inductance.

How to calculate inductors in series ?

Adding inductors in series | Two inductors in series

In a inductors in series connection, we can see from the diagram that the current in each inductor is equal. So the total voltage drop across the inductors is the sum of every individual inductor’s voltage drop. Suppose L is the total inductance of the circuit. So total voltage drop V_Total will be

V_Total = V₁ + V₂ 

The V1 and V2 is the voltage drop across the the individual inductor respectively.

By Kirchhoff’s rule we can write,

L=L₁+L₂

( Answer )

The equivalent inductance of inductors in series  | Formula for inductor in series

Similar to the previously found equation for two inductors, if we connect n number of inductors in series with self inductance L₁, L₂, L₃,…..L_n in series, the equivalent inductance for inductors in series circuit will be, 

L_eq = L₁ + L₂ + L₃ + ….. + L_n

( Answer )

How to calculate inductors in Parallel?

Inductors in parallel 

In a parallel connection, we can conclude from the diagram that the total current flowing through the circuit is the summation of the individual coil’s current. The voltage across each inductor is the same.

If the supply voltage is V then,

The equivalent inductance of inductors in parallel  | Inductor in parallel formula

The equivalent inductance of n inductors with self inductance L₁, L₂, L₃,…..L_n connected in parallel is,

Inductors in series with mutual inductance

For the above derivations, we assumed that there is no mutual inductance in between the inductors. Now, if the inductors are connected in such a manner that the magnetic field produced by one affects the inductance of others, the inductors are said to be ‘mutually connected.’

Coupled inductors in series

The magnetic fields of the inductors can be either aiding or opposing each other depending upon the orientation of the coils. Coupling can be classified into two types-

Series Aiding Type of Coupling :

In this type of coupling, the magnetic fields of the inductors are in the same direction. So the currents that flow through the inductors are also in the same direction. For two inductors with self inductances L₁ and L₂ and mutual inductance M, we can write,

Total induced EMF = Self-Induced EMFs in L₁ and L₂ + induced EMF in one coil due to change of current in other for mutual inductance

Therefore,

The equivalent inductance =  L₁+ L₂ +2M

Series opposing type of coupling:

In this type of coupling, the magnetic fields of the inductors are in the opposite direction. So the directions of the currents are opposite to each other. For two inductors with self inductances L1 and L2 and mutual inductance M, we can write,

Total induced EMF = Self-Induced EMFs in L₁ and L₂ + induced EMF in one coil due to change of current in other for mutual inductance

Therefore, equivalent inductance =  L₁+ L₂ -2M

What will be Impedance of capacitor and inductor in series LC circuit ?

Impedance of capacitor and inductor in series LC circuit:

For the above capacitor and inductors in series circuit, we are going to assume that there is no resistance. We place a fully charged capacitor along with an inductor in the circuit. Initially, the switch is open. Suppose the capacitor plates have charge Q₀ and -Q₀. 

At t=0, the switch is closed. The capacitor begins to discharge , and the current starts increasing in the coils of the inductor with inductance L. Now, if we apply Kirchhoff’s law, we get,

(voltage drop across the inductor is E)

A solution to this second order differential equation is,

where Q₀ and ? are constants depending on the initial conditions

If we put the value of Q in (1), we get,

Therefore,

Energy stored in LC series circuit

For the above capacitor and inductors in series circuit

Total energy in LC circuit= energy stored in the electric field + energy stored in the magnetic field

[since ⍵=1/LC ]

Impedance of capacitor and inductor in series | Impedance in LC circuit

For the above capacitor and inductors in series circuit

Total impedance of LC circuit X_LC=X_L-X_C if X_L>X_C

                                                      =X_C-X_L if X_L<X_C

Inductors in series and parallel problems

An inductor and a capacitor are connected with a 120 V, 60 Hz AC source. For the following LC circuit, find total impedance and the current flowing through the circuit.

Given: 

L= 300 mH    C = 50 µF    V = 120 V   f = 50 Hz

We know, X_L= 2πfL and  X_C= 1/2πfC  

Putting the given value of L and C we get,

X_L = 113 ohm

X_C= 53 ohm

Therefore, total impedance, Z = X_L – X_C = 113 – 53= 60 ohm

Current in the circuit, i = V/Z = 120/60 = 2 A

2. An LC circuit consists of an inductor of L = 20mH and a capacitor of C = 50µF. The initial charge on the capacitor plate is 10mC. What is the total energy? Also, find out the resonance frequency.

Given: 

L= 20 mH    C = 50 µF    Q₀ = 10 mC

Total energy E = Q₀²/2C = (10 x .001)2 / 2x 0.00005 = 1 J

Resonance frequency f =1/2√LC= 1/(2 x 3.14 x √(20 x 0.001 x 0.00005)) = 159 Hz ( Answer )

Resistor and inductor in series LR circuit

Circuits containing resistors and inductors are known as LR circuits. When we connect a voltage source, the current starts flowing through the circuit. Now, if we apply Kirchhoff’s law, we get,

  ( V₀ is the voltage of the source)

Integrating both the sides with limit i = 0 to I and t = 0 to t , we get,

Therefore,

Time constant of LR circuit

? = L/R is called the time constant of LR circuit

Impedance of inductor and resistor in series | Impedance of LR circuit

The resistance and the inductance are the components responsible for the total impedance of the LR circuit.

The total impedance,

Numerical problems

A 24 V battery is removed from a circuit consisting of a resistor with 2-ohm resistance and an inductor with 0.03 H inductance. Calculate the initial current at t = 0 second. Find out how long it takes for the current to decrease to 50% of the initial current.

          If the battery is suddenly removed from the circuit, then the current takes some time before dropping to zero. 

           At t = 0, i = V₀/R = 24/2 = 12 A

         Time constant ? = L/R = 0.03/2 = 0.015 second

         i = i₀e^-t/? where I₀ is the initial current before closing the switch

        0.5 = e^-t/0.015

        t/0.015 = -ln(0.5)

        t = 0.01 s ( Answer )

A 2 Ohm resistor and an 8 mH inductor are connected in series with a power supply of 6 volts. How much time will it take for the current to become 99.9% of the final current?

Time constant of the circuit = L/R = 8 x 0.001 / 2 = 4 ms

I = I_final x 99.9/100

I_final (1 – e^-t/?) = I_final x 0.999

1 – e^-t/? = 0.999

e^-t/? = 0.001

t/? = 6.9

t= 6.9 x 4 = 27.6 ms ( Answer )

The impedance of resistor, capacitor, and inductor in series RLC circuit

The above has a resistor, an inductor, and a capacitor connected in series with an AC source. When the circuit is in the closed condition, the electric current starts to oscillate sinusoidally. This phenomenon is analogous to the spring-mass system in simple harmonic motion.

If we apply Kirchhoff’s law in the circuit, we get,

Now, comparing this with the equation of damped harmonic motion, we can get a solution here.

Impedance of a series RLC circuit

A RLC circuit has three elements responsible for total impedance.

1. Resistor impedance R
2. Capacitor impedance or capacitive reactance X_C = 1/⍵C = 1/2πfC
3. Inductor impedance or inductive reactance X_L = ⍵L = 2πfL

Therefore, total impedance,

Numerical Problems

A series RLC circuit consists of a resistor of 30 ohm, an inductor of 80 mH and a capacitor of 40 µF. It is given an AC supply voltage of 120 V and 50 Hz. Find out the current in the circuit.

Solution :

Inductive reactance X_L= 2πfL = 2 x 3.14 x 80 x 0.001 x 50 = 25.13 ohm

Capacitive reactance X_C = 1/2πfC = 79.58 ohm

Total impedance, Z = √{R² +(X_C – X_L)²}= √{(30)² +(79.58-25.13)²} = 62.17 ohm

Therefore, current in the circuit, i = 120/62.17 = 1.93 A

2. Derive the equation for current in the below circuit where V= sin4t

Applying Kirchhoff’s law in the circuit, we can write,

Sin4t – 3i – 2di/dt + Q/0.5 = 0

Sin4t = 3i + 2di/dt + 2Q

Taking differentiation on both the sides,

4cos4t = 3di/dt + 2d²i/dt² +2 i(t)

i(t) + 3/2(di/dt) + d²i/dt² = 2cos4t       This is the required equation for current. ( Answer )

Inductors in series and parallel miscellaneous MCQs

1. An LC circuit stores a total energy of E. Maximum charge on the capacitor is Q . Energy stored in the inductor while the charge on the capacitor is Q/2 is

1. E           
2. E/2               
3. E/4               
4. 3E/4 ( Answer )

Solution:  Total energy = E = Q²/2C

                 Total energy = E_C + E_i 

      When, charge on the capacitor is Q/2, total energy,

          Q²/2C  =  (Q/2)²/2C + Ei

        E_i = Q²/2C x (1-¼) = 3E/4    ( Answer )

2. If the current in one coil becomes steady, what would be the current flowing through the neighboring coil?

1. Double of first coil
2. Half of first coil
3. Zero ( Answer )
4. Infinity

Solution: Current is induced when magnetic flux in coil changes. Hence, if the current is steady in one coil, no flux will be generated and current in the neighboring coil will be zero.

3. A 7 ohm resistor is connected in series with a 32 mH inductor in inductors in series circuit. If the supply voltage is 100 volt, 50 Hz then calculate the voltage drop across the inductor.

1. 67 V
2. 82 V (Answer)
3. 54 V
4. 100 V

Detailed Solution of the problem:

The inductive reactance X_L for the circuit = 2 x 3.14 x 50 x 0.032 = 10 ohm

             Total impedance Z = √(R² + X_L²) = √(7² + 10²) = 12.2 ohm

Therefore, current across the circuit = 100/12.2 = 8.2 A

The voltage drop across the inductor = iX_L = 8.2 x 10 = 82 V  (Answer)

4. Find the equivalent impedance for the infinite ladder circuit shown below-

1. j4 ohm
2. j8 ohm
3. j4(√2 – 1) ohm
4. j4(√2 + 1) ohm (Answer)

Solution:  For the above infinite circuit let us assume that,

              Z₁ = j8 ohm and Z₂ = j4 – j2 = j2 ohm

If the equivalent impedance is Z then, we can write

Z = Z₁ + (Z₂ || Z) = Z₁ + ZZ₂/Z + Z₂

Z( Z + Z₂ ) = Z₁Z₂ + ZZ₁ + ZZ₂

Z² + j2Z = -16 + j8Z + j2Z

Z² – j8Z + 16 = 0

Solving the quadratic equation, we get,

Z = j4(√2 + 1) ohm (Answer)

5. Self inductance of a solenoid is 5 mH. The coil has 10 turns. What will be the inductance of the coil if the number of turns is doubled?

1. 10 mH
2. 5 mH
3. 20 mH (Answer)
4. 30 mH

Solution: Self inductance of the solenoid with N turns and A cross-sectional area is = μ₀N²A / l

          Here μ₀ x 100 x A / l = 5

                  μ₀A / l = 1/20

If the number of turns is doubled then new self inductance = μ₀A / l x N’² = 1/20 x (20)2 = 20 mH (Answer)

Frequently Asked Questions | Short Note

How to add inductors in series and parallel? | Inductors in series vs parallel:

Answer :

In series, the sum of the self inductance of all the inductors is the total inductance of the circuit. For parallel connection, the sum of the inverse of all the self inductances is the inverse of the total inductance.

How does adding inductors in series to a circuit affect the current?

Answer :

Inductors added in the series share the same current. Thus the total voltage of the circuit is higher than the voltages of individual inductors.

What are differentially coupled series inductors?

Answer :

It is another name for the series opposing inductors where the magnetic fluxes produced by the inductors are opposite in direction. The total inductance is in this type of inductor is the sum of self inductance of the inductors – 2 x the mutual inductance.

What is the mutual inductance of two coils in series?

Answer :

Mutual inductance of two iron-core coils with turns N₁ and N₂, cross-sectional area A, length L and permeability μ_r is,

What is series inductor filter?

Answer :

Series inductor filter is an inductor connected in series in between the load and the rectifier. It is called a filter as it blocks AC and allows DC.

An inductor of 1 henry is in series with a capacitor of 1 microfarad. Find the impedance when the frequency is 50 Hz and 1000 Hz.

Answer :

Impedance, Z = X_L – X_C 

X_C when frequency is 50 Hz = 1/2πf₁C = 3183 ohm

X_C when frequency is 1000 Hz = 1/2πf₂C = 159 ohm

X_L when frequency is 50 Hz = 2πf₁L = 314 ohm

X_L when frequency is 1000 Hz = 2πf₁L = 6283 ohm

Therefore, impedance Z₁ when frequency is 50 Hz = 6283 – 159 = 6124 ohm

impedance Z₂ when frequency is 1000 Hz = | 314 – 3183 | = 2869 ohm.

Inductor:

An inductor is a passive component of an electrical circuit that opposes current. It is a coil of wire wrapped around a magnetic material. Applied voltage induces current across the inductor. When current flows through the inductor, it generates a magnetic field. Magnetic fields don’t change. Therefore, the inductor tries to prevent the current flowing through it from changing.

Reactance:

Reactance is defined as an opposition to current flow in an electrical circuit. It is denoted by ?. 

Inductive Reactance X_L:

Inductive reactance is the reactance offered by an inductor: the greater the reactance, the smaller the current. 

In a dc circuit inductive reactance would be zero (short-circuit), at high frequencies an inductor has infinite reactance (open-circuit).

Inductive Reactance Units | SI unit of inductive reactance

Inductive reactance acts as an opposition to the current flow in the circuit. So the SI unit of inductive reactance is the same as that of resistance, i.e. Ohms. 

Symbol for Inductive reactance

Inductive reactance is denoted by ?_L or X_L. 

Derivation of Inductive Reactance 

Suppose we have the following electric circuit with inductance L connected to an AC voltage source. This source creates an alternating current that flows inside the inductor if the switch is closed. So, the electric current in the circuit at any moment is given by,

I=I_OCosωt

Where I₀= peak value of the current

           ω= angular frequency

Now, if we apply Kirchhoff’s second law or Kirchhoff’s loop law in this circuit, we get,

So, the voltage across the inductor V is equal to the inductance multiplied by the derivative of electric current I with respect to time. 

If  cos(ωt+90°)= 1, then V=V₀=LI₀ω (peak voltage)

We know by Ohm’s law, 

Inside a resistor, 

V₀=I₀R 

where R= resistance

V₀=I₀\\X_L   

As the inductive reactance is similar to resistance, we can get an analogous equation-

where ?_L=inductive reactance

By comparing V₀ found in the previous equation, it can be concluded that,

X_L = ωL = 2πfL

where f=frequency

Inductive Reactance formula

The inductive reactance of a coil is,

?_L=ωL or ?_L=2?fL

Where ω is the angular frequency, f is the frequency of the applied voltage, and L is the inductance of the coil.

Derivation of Inductive Reactance

Inductive reactance in series

In the above circuit, three inductances L₁, L₂ and L₃ are connected in series. Therefore, if we apply Kirchhoff’s law,

Taking the peak value, we can say that,

V_o = I_oω(L₁ + L₂+ L₃)

So, total inductance L=L₁+L₂+L₃

Therefore, inductive reactance in series connection, ?_L=ω(L₁+L₂+L₃+…..L_n)

Inductive reactance in parallel

In the above circuit, three inductances, L₁, L₂ and L₃, are connected in parallel. If the total inductance is L, by Kirchhoff’s law, we can say,

So,

Therefore, inductive reactance in parallel connection,

Inductance and inductive reactance

Magnetism and electricity co-exist in electrical circuits. If a conductor is placed in a continuously changing magnetic field, a force is generated in the conductor. It is called the electromotive force or EMF. The ability to create voltage for the change in current flow is called inductance. 

EMF helps the current flow in the circuit. While current passes through the inductor coil, it tries to oppose the current. This reaction is known as inductive reactance.

What is the difference between inductance and inductive reactance ?

Inductance

• Inductance:

• Unit of inductance is Henry or H.
• Dimension of inductance is [ML₂T_-2A_-2]
• It does not depend upon frequency.
• The greater the inductance, the more the induced EMF and current will be.

Inductive reactance

• Inductive reactance XL=ωL.
• Unit of inductive reactance is ohm or Ω.
• Dimension of inductive reactance is [ML₂T_-3I_-2].
• It is dependent upon frequency.
• The greater the inductive reactance, the lesser the current will be.

Inductive Reactance in DC circuit

In a DC circuit, power frequency is equal to zero. Hence ?_L is also zero. The inductor would behave like a short circuit in the steady-state.

Relation between inductance and reactance

Reactance ? consists of two components-

• Inductive reactance or ?_L
• Capacitive reactance or ?_C

Therefore

Total inductive reactance formula

Difference between inductance and reactance

Inductance:

• Unit of inductance is Henry or H.
• Dimension of inductance is [ML²T^-2A^-2]
• It does not depend upon frequency.
• Inductance is directly proportional to current.

Inductive reactance

• Reactance

• Unit of reactance is ohm or Ω
• Dimension of inductive reactance is [ML²T^-3I^-2]
• It is dependent on frequency. 
• Reactance is inversely proportional to current.

The inverse of inductive reactance is susceptance

The quantity reciprocal to inductive reactance is known as inductive susceptance. It is denoted by B_L. 

Inductive susceptance is similar to conductance G, which is the inverse of resistance.

So the unit of B_L is also siemen or S.

Physically inductive susceptance represents the capability of a purely inductive electrical circuit to allow the flow of current through it.

Reactance and susceptance 

Reactance measures a circuit’s reaction against the change in current with time, while susceptance measures how susceptible the circuit is in conducting the varying current.

Resistance, reactance, capacitance, inductance impedance-comparison 

Parameters	Resistance	Reactance	Capacitance	Inductance	Impedance
Definition	The measure of obstruction caused by the conductortowards the current is known as resistance.	The characteristic of the inductor and the capacitor to oppose any change in current is called reactance.	The capacity of a conductor to store electric charge is known as capacitance.	The property of a conductor to generate an EMF due to the change in current is known as inductance.	Impedance is the entire opposition in an electrical circuit caused by the inductor, the capacitor and the resistor.
Symbol	Resistance is represented by R	Reactance is represented by ?	Capacitance is represented by C	Inductance is represented by L	Impedance is represented by Z
Unit	Ohm	Ohm	Farad	Henry	Ohm
General Expression	Resistance in a circuit with voltage v and current i is, R = V/I	Reactance in a circuit with voltage source’s angular frequency ω is, X= ωL + 1/ωC	The capacitance of a parallel plate capacitor with medium permittivity ϵ, A plate area and d separation between plates is, C=ϵA/d	The inductance of a coil with induced voltage V is, L=V/ dI/dT	The total impedance of a circuit can be written as Z=ZR+ZC+ZL

Capacitive reactance

Just like the inductive reactance, capacitive reactance is the impedance caused by the capacitor. It is denoted by Xc. When DC voltage is applied in an RC circuit, the capacitor starts charging. Subsequently, current flows, and the capacitor’s internal impedance obstructs it. 

Capacitive reactance

What is the difference between inductive reactance and capacitive reactance ?

Capacitive Reactance vs Inductive Reactance

Capacitive reactance	Inductive reactance
The reactance of the capacitor	The reactance of the inductor
It is denoted by XC	It is denoted by XL
XC =1/ωC	XL =ωL
When a sinusoidal AC voltage is applied to a capacitor, the current leads the voltage by a phase angle of 90°	When a sinusoidal AC voltage is applied to an inductor, the current lags the voltage by a phase angle of 90°
It is inversely proportional to the frequency.	It is directly proportional to the frequency
In DC supply, the capacitor behaves like an open circuit.	In DC supply, the inductor behaves like a short circuit.
At high frequency, the capacitor acts as a short circuit.	At high frequency, the inductor acts as an open circuit.

AC circuit in LR series combination

There are two components in the above circuit- resistor R and inductor L. Let the voltage across the resistor is Vr, and the voltage across the inductor is VL.

The phasor diagram shows that total voltage V, resistor voltage V_r and inductor voltage V_L forms a right-angled triangle.

By applying Pythagoras theorem, we get,

V²=V_r²+V_L²

where φ=phase angle

How to find inductive reactance ? | Important formulas

X_L = 2πfL

Power P=V_rmsI_rmsCosφ

Calculate the inductive reactance | Inductive reactance calculation example

Find the AC voltage required for 20 mA current to flow through a 100 mH inductor. Supply frequency is 500 Hz.

Given: i= 20 mA   f=400 Hz    L=100mH

As the series is purely inductive, the impedance in the circuit, Z=X_L

We know, X_L=ωL=2?fL=2 x 3.14 x 400 x 0.1=251.2 ohm

Therefore, supply voltage V=iX_L= .02 x 251.2= 5.024 volts

Calculate X_L of a 5 mH inductor when 50 Hz Ac voltage is applied. Also find I_rms at each frequency when V_rms is 125 volts.

X_L=2?fL=2 x 3.14 x 50 x 5 x .001 = 1.57 ohm

Calculate inductive reactance using voltage and current

A resistance of 20 ohm, inductance of 200 mH and capacitance of 100 µF are connected in series across 220 V, 50 Hz mains. Determine X_L, X_C and current flowing through the circuit.

We know, V=220 volt  R=20 ohm  L=0.2 H   f=50 Hz

X_L=2?fL=2 x 3.14 x 50 x 0.2=62.8 ohm

=1/(2 x 3.14 x 50 x 0.0001)=31.8 ohm

Therefore total impedance,

= (20)2+(62.8-31.8)2=36.8 ohm

So, current

Resistance-Reactance-Impedance: Comparative study

Resistance	Reactance	Impedance
Opposes electron flow	Opposes change in current	Combination of reactance and resistance
R=V/I	X=XL + XC	Z=(R2 + XL2)1/2
Measured in ohm	Measured in ohm	Measured in ohm
Does not depend upon frequency	Depends upon frequency	Depends upon frequency

Leakage reactance in induction motor

Leakage reactance is the impedance caused by the leakage inductor in an induction motor. A rotating magnetic field develops in the induction motor due to the applied 3-phase power. Most of the magnetic flux lines generated by the stator winding travel across the rotor. Though a very few flux lines close in the air gap and fail to contribute to magnetic field strength.This is the leakage flux.

Due to this leakage flux, a self-inductance is induced in the winding. This is known as leakage reactance.

Sub-transient reactance of induction motor

In a short circuit, the magnetic flux generated in the damper winding reduces steady-state reactance. It is known as sub-transient reactance. The term ‘sub-transient’ suggests that the quantity operates even faster than the ‘transient’. 

FAQs

To what is inductive reactance proportional? 

Inductive reactance is directly proportional to the frequency.

What is inductive reactance and how does it affect an AC circuit ?

Unlike DC, in the AC circuit, the current varies with respect to time. 

What happens when the capacitive reactance is greater than the inductive reactance?

If X_C is more than X_L, then the overall reactance is capacitive. 

What is induction?

The change in magnetic field causes voltage and current in the circuit. This phenomenon is known as induction. 

What does inductance do in a circuit?

Inductance opposes the change in current flowing through the circuit.

What is inductance of a coil?

The inductance of a coil originates from the magnetic field due to varying current.

Why is L used for inductance?

According to the initials, I should have been used for representing inductance. But as I is already being used for current, L is used for inductance to honour scientist Heinrich Lenz for his extraordinary contribution in the field of electromagnetism. 

Can self inductance be negative?

Self-inductance is purely a geometric quantity, and it depends upon the external circuitry. Therefore it cannot be negative. The minus sign in Lenz law indicates the opposing nature of EMF towards the magnetic field.

Do Motors have inductance?

Back EMF is a crucial factor in motors. Both AC and DC motors make use of a low AC voltage source to measure inductance.

What is unit of inductance?

SI unit of inductance is volt -second per ampere or Henry.

Why does inductor block AC and allows DC?

The inductor creates an EMF when current flows through it. In AC, the EMF is very high as the frequency is increased. Therefore the opposition is also significant. But in DC supply, there’s no EMF, and consequently no opposition takes place. So it is said that the inductor blocks AC and allows DC.

Does inductor allow DC current?

Inductor allows DC current as there’s no opposite force acting in the circuit.

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Avalanche Photodiode Definition

Avalanche photodiodes or APDs are highly sensitive semiconductor devices that transform optical signals into electrical signals. These are operated under high reverse bias. The term ‘avalanche’ comes from the avalanche breakdown phenomenon.

Avalanche Photodiode Symbol

The symbol of avalanche photodiode is the same as that of Zener diode.

Avalanche Photodiode structure

The structure of the ordinary Avalanche photodiode is similar to the PIN photodiode. It consists of two heavily doped (p+ and n+ region) and two lightly doped (I or intrinsic region and P region) regions. The width of the depletion layer in the intrinsic region is relatively thinner in APD than the PIN photodiode. The p+ region acts like the anode, and n+ acts like the cathode. Reverse bias is mostly applied across the pn+ region.

Avalanche photodiode Circuit Diagram

For applying reverse bias conditions, the p+ region is connected to the negative terminal, and the n+ region is connected to the battery’s positive terminal.

Avalanche photodiode working principle

• Avalanche breakdown takes place when the diode is subjected to high reverse voltage.
• The reverse bias voltage increases the electric field across the depletion layer.
• Incident light enters the p+ region and further gets absorbed in the highly resistive p region. Here electron-hole pairs are produced.
• A comparatively weaker electric field causes separation between these pairs. Electrons and holes drift with their saturation velocity towards the pn+ region where a high electric field exists.
• As the velocity is maximum, the carriers collide with other atoms and generate new electron-hole pairs. A large number of e-h pairs results in high photocurrent.

Avalanche photodiode Characteristics

• The intrinsic region in APD is slightly p-type doped. It is also called ?-region.
• The n+ region is thinnest, and it is illuminated through a window.
• The electric field is maximum at the pn+ junction, and then it starts decreasing through the p region. Its intensity lessens in ?-region and gradually vanishes at the end of the p+ layer.
• Even a single photon absorbed leads to the generation of a vast number of electron-hole pairs. This is called the internal gain process.
• Excess electron-hole pair generation due to the collision of charge carriers is called avalanche multiplication. Multiplication factor or gain,

M=I_ph/I_pho

Where i_ph= multiplied APD photocurrent

            i_pho=photocurrent before multiplication

M value strongly depends upon reverse bias and temperature also.

Avalanche Photodiode Operation

APDs are operated in completely depleted mode. Besides the linear avalanche mode, APDs can also work in the Geiger mode. In this mode of operation, the photodiode is operated at a voltage above breakdown voltage. Recently another mode has been introduced, which is called Sub-Geiger mode. Here along with single-photon sensitivity, the internal gain is also very high, just below the breakdown.

Impact ionization in Avalanche Photodiodes 

After the photons are absorbed in ?-layer, a sufficient number of electron-hole pairs are formed. The electric field separates the pairs, and the independent charge carriers run towards the n+ and p+ regions. In the p region, the electrons experience a massive electric field. In the effect of this field, electrons drift with their saturation velocity and collide. This collision helps in charge multiplication. This overall phenomenon is called impact ionization.

Ionization rate, k=α/β

Where ⍺= rate of electrons

            ꞵ= rate of holes  

Avalanche Photodiode Diagram

Avalanche Photodiode Datasheet

Photodetector	Wavelength	Responsivity	Dark Current
InGaAs APD	1310-1550 nm	0.8 A/W	30 nA
Germanium APD	1000-1500 nm	0.7 A/W	1000 nA

Avalanche Photodiode Module

APDs are part of modules that contain additional electronic elements apart from the photodiode. There can be a trans-impedance op-amp in some packages that improve the performance and increases bandwidth and responsivity. Some packages are optimized to be used in optical fiber. Some incorporate thermosensors to provide better stability.

Avalanche Photodiode Array

Avalanche photodiode arrays are small in size and also yield lease gain. These are designed especially for use in LIDAR, laser rangefinders, etc. Although APD arrays are not mainstream products yet, some manufacturers are making these due to their unique features.

Avalanche Photodiode Noise

The primary components of noise in APD are 

• Quantum or shot noise (i_Q): The avalanche process is the primary reason behind this. 
• Dark current noise: Dark current noise is generated from the absence of light in a photodiode. It can further be classified into bulk current noise(i_DB) and surface current noise(i_DS).
• Thermal noise: It is the noise of the amplifier connected to the photodiode.

Due to carrier multiplication, significant noise is added to the existing noises. It is known as excess noise factor or ENF.

ENF or F(M)= kM + (2-1/M)(1-k)

Where M = multiplication factor

            k = impact ionization coefficient

Therefore the mean square value of total noise i_N in APD is,

Where 

q= charge of an electron

I_p= photocurrent

B= bandwidth

M= multiplication factor

I_D= bulk dark current

I_L= surface leakage current

Thermal noise in trans-impedance amplifier is,

Where k_B= Boltzmann constant

           T= absolute temperature

           R_L= load resistance

Difference Between PIN and Avalanche Photodiode | Avalanche Photodiode vs. PIN Photodiode

Avalanche Photodiode Amplifier

Like PIN photodiodes, APDs also use the four-channel trans-impedance amplifier for reduced noise, high impedance, and low power consumption. Some amplifiers offer temperature flexibility and high reliability also. All these characteristics make the photodiode suitable for use in LIDAR receivers.

Avalanche Photodiode detector

APDs are preferred over PIN photodiodes in light detection for their increased sensitivity. As a relatively high voltage is given, the number of charge carriers overgrows, and they are accelerated in the effect of strong electric fields. The internal collision occurs, and charge multiplication takes place. As a result, the photocurrent value rises, which improves the overall photo-detection process.

Avalanche Photodiode in optical fiber communication

In optical fiber communication systems, APDs are usually needed for the detection of weak signals. Circuitry must be optimized enough to detect the weak signals maintaining a high SNR(Signal to noise ratio). Here,

SNR=(power from the photocurrent/power of photodetector) + power of amplifier noise

For achieving a good SNR, quantum efficiency must be high. As this value is nearly close to the maximum value, most of the signals are detected.

Comparison between APD and PMT | Avalanche Photodiode vs Photomultiplier tube

Avalanche Photodiode	Photomultiplier Tube
It consists of four layers with different doping concentrations.	It consists of a photocathode, dynodes, and a vacuum glass tube.
It uses the avalanche multiplication phenomenon to produce charge carriers.	It uses the photon absorption technique for the emission of excess electrons.
It converts photons into electrons.	It amplifies the number of electrons.
APDs are highly sensitive.	The sensitivity of PMT is limited.
The cost of APDs is lower than that of PMTs.	PMTs are the costliest devices.

APDs and quenching circuits 

1. Passive quenching circuit: This type of circuit uses a load resistor, a passive element, to quench the breakdown pulse. Photoelectrons trigger the avalanche. A large current is passed through the circuit to avoid the shortage of electrons or holes in the avalanche region, and the diode remains in conducting state.

2. Active quenching circuit: While the diodes are recharged, the probability of another photoelectron striking it is very low. To minimize the dead-time, ‘active quenching’ is done. The bias voltage is temporarily dropped, and this delay allows the collection of all electrons and holes. When again the voltage is increased, no electron remains at the depletion region.

InGaAs Avalanche Photodiode

InGaAs or Indium Gallium Arsenide is vividly used in semiconductor devices. InGaAs avalanche photodiodes are used for achieving long-reach optical fiber communications. These can perform photo-detection in the range of 1100-1700 nm. InGaAs avalanche photodiodes are better than ordinary germanium avalanche photo diodes in terms of SNR and sensitivity.

Large area avalanche photodiode

Large area APDs or LAAPDs are lightweight photodiodes that possess a large activation area. Its features include fast response time, improved SNR, insensitivity to magnetic fields, etc.

Ultraviolet–UV Avalanche photodiode

Ultraviolet avalanche photo diodes offer outstanding sensitivity if operated in Geiger mode. The silicon carbide UV APD shows a high signal gain and extreme sensitivity. UV APDs are ideal for ultraviolet flame detection.

Silicon Avalanche Photodiode

High silicon APDs are great for low light detection. Internal multiplication features great photosensitivity that makes it capable of detecting low light signals. It also has improved linearity, low terminal capacitance, and low-temperature coefficient. Some applications of Si avalanche photo diodes are optical rangefinders, laser radars, FSO, etc. 

Silicon Avalanche Photodiode array

In multi-element silicon APDs, the depletion region is fabricated just below the photosensitive area. Due to this, the APD array multiplies the incident light. The charge carriers struck in the depletion region. This implies that Si avalanche photo diode arrays have low crosstalk because of the gain.

Geiger mode avalanche photodiode

Geiger mode avalanche photo diodes are developed to provide an alternative to the photomultiplier tubes. GAPDs use the single-photon counting principle at a voltage little more than the threshold breakdown voltage. At this voltage, even a single electron-hole pair is capable of triggering a strong avalanche. In this situation, the quenching circuits reduce the voltage by a fraction of a second. This stops the avalanche for the time being, and photo-detection is possible.

Photon counting techniques with silicon avalanche photodiodes

Over the years, two types of photon counting techniques are being used in avalanche photo diodes. 

• ‌Geiger mode
• ‌Sub-geiger mode

Studies suggest that the Geiger mode improves the performance excellently for using quenching circuits.

Single photon avalanche photodiode | Single Photon counting Avalanche Photodiode

These are also called SAPD. SAPDs are highly photosensitive and optimized for high quantum frequency. Some of its applications include an image sensor, 3D imaging, quantum cryptography, etc.

Advantages and Disadvantages of Avalanche Photodiode

Advantages of Avalanche Photodiode

• ‌It can detect light of low intensity.
• ‌Sensitivity is high.
• ‌Response time is faster.
• ‌A single photon can generate a large number of electron-hole pairs.

Disadvantages of Avalanche Photodiode

• ‌High operating voltage is required.
• ‌Excess noise due to carrier multiplication.
• ‌Output is not linear.

Application of Avalanche Photodiode

• LASER scanner.
• ‌Barcode reader.
• ‌laser Rangefinders.
• ‌Speed gun.
• ‌Laser microscopy.
• ‌PET scanner.
• ‌Antenna Analyzer bridge.

FAQs

What is the response time of avalanche photodiode?

The average response time of different avalanche photo diodes can range from 30 ps to 2 ms.

What happens when you send too much light to an avalanche photodiode (APD)?

Too much exposure to light overheats the diode and may damage the device.

How does an avalanche photodiode work?

Avalanche photodiode utilizes the avalanche breakdown voltage to multiply charge carriers and increase current.

What is the difference between PIN photodiode and avalanche photodiode?

Avalanche photodiodes have four layers, and PIN photodiodes have three layers. Also, unlike PIN photo diodes, APDs have heavy internal gain and photosensitivity due to charge multiplication.

What are the drawbacks of avalanche photo diode?

APDs are susceptible to high noise due to impact ionization, and the output is non-linear. Other limitations has been discussed in “disadvantages of Avalanche Photo-diodes” section.

What is the primary advantage of an avalanche photodiode?

The primary advantage of the avalanche photo-diode is its sensitivity and ability to detect low-light signals.

What is the temperature effect on avalanche gain?

Gain varies linearly with temperature as reverse breakdown voltage has a linear relationship with temperature.

Why does avalanche breakdown increase with temperature?

A rise in temperature increases the vibration of atoms and decreases the mean free path. Since the path becomes smaller, charge carriers need more energy to travel. Therefore, the breakdown voltage needs to be increased.

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Topic of Discussion : PIN Photodiode

What is PIN Photodiode ?

A Photodiode is a PN junction diode that operates in reverse bias. As the name suggests, PIN photodiode is a particular type of photodiode in which an intrinsic layer is placed in between a heavily doped p-type and a heavily doped n-type layer. As resistivity decreases with an increase in impurity and vice-versa, p and n layers have very low resistivity , while resistivity in the I layer is very high. PIN-Photodiode has a large depletion region which is used in the reception of light.

PIN Photodiode Symbol

Symbolic representation of the PIN-photodiode is the same as that of the standard p-n junction diode except for the downward arrows over the diode , which indicate light.

PIN Photodiode Structure

PIN-Photodiode comprises three layers- p-layer, I or intrinsic layer , and n-layer. P-layer is doped with a trivalent impurity , and N-layer is doped with a pentavalent impurity. The I-layer is undoped or very lightly doped. P terminal acts like anode , and N terminal acts like cathode. Unlike the general PN junction diode, the width of the intrinsic layer in the PIN-Photodiode is larger.

It can be constructed in two ways:

• Planar Structure: In this type of structure, a thin epitaxial film is fabricated on p-layer.
• Mesa Structure: In this type of structure, already doped semiconductor layers are grown on the intrinsic layer.

PIN Photodiode Circuit Diagram

The PIN-photodiode works as a photodetector only when it is functioning in reverse bias. The Anode is connected with the negative terminal of the battery. The positive side of the battery is connected to the cathode through a resistor.

Operation of pin photodiode | Working principle of PIN Photodiode

• When reverse bias is applied to the device, the depletion region starts expanding in the intrinsic layer. The width goes on increasing until it reaches the thickness of the I layer.
• As a result, the depletion region becomes free of any mobile charge carriers. So no current flows. At this point, no electron-hole recombination takes place in the depletion region.
• When the light of sufficient energy ( h? ≥ bandgap energy of the semiconductor) enters the I region, each photon absorbed generates one electron-hole pair. These pairs experience a strong force due to the barrier electric field present in the depletion region. This force separates the pairs , and charge carriers move in opposite directions , and current is generated. Thus optical energy gets converted into electrical energy.
• As the current is generated from the light energy, it is called photocurrent and written as I_p.

PIN Photodiode Characteristics

• Resistivity: It offers low resistivity in P , and N layers ( less than 1kΩ/cm) and high resistivity in I layer ( up to 100 kΩ/cm)

• Capacitance: As capacitance is inversely proportional with the gap between P and N layers, capacitance in this photodiode is lower than the standard diode.    

Where ?₀= dielectric value of free space

             ?_r= dielectric constant of the semiconductor

             A= area of the intrinsic layer

             d= width of depletion region

• Breakdown Voltage: The intrinsic layer widens the depletion region , due to which breakdown voltage is very high.

• The flow of current: The current flow is directly proportional to the amount of light incident on the detector.

• Forward bias condition: If it is operated in forward bias mode, the width of depletion layer reduces and current flows. In this case, the diode behaves like a variable resistor.

• Quantum efficiency(?): It is referred to the number of electron-hole pairs generated per photon having energy h?

• Responsivity: It measures the output gain per input (photon).

Modes of operation in PIN Photodiode

It has primarily two modes of operation-

• Unbiased Photovoltaic Mode 
• Reverse Biased Photoconductive Mode 

PIN Photodiode IV curves

Photodiode pin diagram

Photodiode pin configuration

Name of the pin	Identification
Cathode	Shorter in length
Anode	Longer in length

3 pin photodiode

Three-pin photodiodes are high-speed Silicon PIN-photodiodes especially designed to detect nearby infrared light. At low bias, these devices provide the facility of wideband characteristics,  which makes them usable for optical communication and other photometry.

Noise in PIN Photodiode

Noise refers to any undesirable occurrence or an error in the received information signal. It is the amalgamation of disturbing energies coming from different sources.

Following are the noises that attribute to the total noise of a photodiode:

• Quantum or shot noise
• Dark current noise
• Thermal noise

While the first two types of noises are generated from the statistical nature of photon to electron conversion procedure, thermal noise is associated with the amplifier circuitry.

Quantum or shot noise: 

It happens due to the proton to the electron conversion process. The Poisson process is followed here.  Mean square value of Shot noise i_q on photocurrent i_p is,

Where, q= charge of an electron

             B= bandwidth

Dark current noise:

Dark current is the current that flows through the circuit when no light is incident on the photodetector. It has two major components- bulk dark current noise and surface leakage current noise. Bulk dark current is the result of thermally generated holes and electrons in the PN junction.

Mean square value of bulk dark current noise i_db on dark current i_d is,

Mean square value of surface leakage current noise i_ds on surface leakage current i_L is,

Thermal Noise:

It is also called Johnson noise. The thermal noise of the load resistor is much higher than the thermal noise of the amplifier as load resistance has a smaller value than amplifier resistance.

Therefore, mean square value of thermal noise i_r due to the load resistance R_L

 Where K_B= Boltzmann constant

             T= absolute temperature

             B= bandwidth

InGaAs PIN Photodiode

InGaAs( indium gallium arsenide) is an alloy of indium arsenide and gallium arsenide. Gallium arsenide can efficiently convert electricity into coherent light.

InGaAs PIN-Photodiode or photodetectors are optoelectronic devices capable of providing very high quantum efficiency that can range from 800 to 1700 nm. They exhibit low capacitance in extended bandwidth, high linearity, high sensitivity due to increased resistance, low dark current, and uniformity across the detector’s active area. All of these characteristics help to increase flexibility and offer a wide range of applications.

GaAs PIN Photodiode

GaAs( Gallium arsenide) is a semiconductor that has high electron mobility and high electron velocity than silicon. It can function at very high frequencies.

GaAs PIN photodiodes are used in detecting optical signals at 850 nm. It has a large activation area that ensures a stable and sensitive response. This can also be used in optical telecommunications as optical receivers, in testing machines, etc. GaAs photodiodes provide fast response, low dark current, and high reliability.

PIN Photodiode detector

The photodetector is used to convert light signal to electrical signal, their amplification, and further processing. In optical fiber systems, the photodetector is an essential element. Semiconductor photodiodes are amongst the most widely used detectors as they offer excellent performance, are small in size, and low in cost.

Example:  Gallium arsenide photodiode, Indium gallium arsenide photodiode, etc

PIN Photodiode in optical communication

 Photodetectors are vividly used in the automobile sector, medical purpose, Safety equipment, cameras, industry, astronomy, and most importantly, in communications. There are two distinct photoelectric mechanisms available for photodetection:

1. External effect: PMT or photomultiplier tubes
2. Internal effect: PN junction photodiodes, PIN-photodiodes, avalanche photodiodes         

Photodetection principle:       

• Electron-hole pair photogeneration occurs
• The PIN junction is reverse biased
• The depletion region sees carrier drift
• Electron-hole pair moves in the opposite direction and causes photocurrent

PIN Photodiode radiation detector | PIN photodiode gamma detector

PIN photodiodes are able to detect individual photons in gamma radiation. A PIN photodiode, a comparator, and four low noise operational amplifiers are together used in this process.  

 In reverse bias condition, when photons strike the depletion region, they produce a small charge directly proportional to the energy of photons. The resultant signal gets amplified and filtered by the op-amps. Comparator distinguishes the signal and the noise. The final output of the comparator shows a high pulse every time a gamma photon with minimum required energy strikes the PIN photodiode.

PIN Photodiode receiver

Optical receivers are responsible for the optical to electrical energy conversion. The most crucial element of the optical receiver is the photodiode.

The receiver must detect distorted, weak signals first and then, based on the amplified version of that signal, decide which type of data was sent. Errors coming from various sources can be found associated with the signal. So signals should be controlled , and processed with utmost precision as noise consideration is a significant factor in the design of the receiver.

Silicon PIN Photodiode

Silicon or Si PIN-photodiodes can accommodate different applications. Due to the PIN structure, it produces fast response and high quantum frequency to detect photons. They are capable of light detection in the range of 250 nm to 1.1 μm. It detects high-energy radiation in high frequencies. The width of the depletion region varies from 0.5 to 0.7 mm.

Si PIN photodiode detector

In PIN photodiodes, the depletion region almost coincides with the intrinsic layer. Charge carrier generation happens due to the incident radiation.

 Along with the light radiation, Gamma radiation, X radiation, particles too can generate charge carriers.

When photons meet with the metal contact of the diode, it produces electron-hole pairs in large numbers. Electrodes collect these , and the signal is generated. Electron-hole pairs that are more mobile helps in receiving easily detectable signals. Those are subsequently processed through a low noise amplifier , and the analyzer detects the amount of radiation from the pulses.

PIN photodiode array

Photodiode arrays are generally used in X-ray machines by scanning the object in the image line by line. X-rays are transformed into light through the scintillator crystal. Then the photodiode measures light intensity.

High-speed PIN Photodiode

High-speed PIN-Photodiodes are preferred for their precise triggering against signal strength, enhanced sensitivity, low operating voltage, and high bandwidth.

PIN Photodiode Amplifier

Operational amplifiers are used with a feedback resistor to convert photocurrent to measurable voltage. It is also called a trans-impedance amplifier.

Application of pin photodiode

PIN-photodiodes are one of the most popular photodiodes that have varied characteristics , making them suitable for different applications. Besides photo-detection, it is used in DVD players, CD drives, switches, medical treatment, and many more.

• ‌High voltage rectifier: The intrinsic layer provides a greater separation between the P and N region, allowing higher reverse voltages to be tolerated.

• ‌RF and DC-controlled microwave switches: The intrinsic layer increases the distance between the P and N layers. It also decreases the capacitance , thereby increasing the isolation in reverse biased condition.

• ‌Photodetector and photovoltaic cells: Light to current conversation occurs in the depletion region. As the width of the intrinsic layer is more, it improves the performance of capturing light.

• ‌RF and variable attenuators
• ‌RF modulator circuit
• ‌MRI machine

PIN Photodiode Advantages and Disadvantages

PIN photodiode Advantages

• ‌It has high light sensitivity.
• ‌The response speed is high.
• ‌Its bandwidth is wide.
• ‌Implementation cost is low.
• ‌It generates low noise.
• ‌Temperature sensitivity is low.
• ‌It is small in size.
• ‌Longevity better than standard diodes.

PIN photodiode Disadvantages

• ‌It can only be operated in the reverse biased condition.
• ‌The voltage applied must be low.
• ‌It is sensitive to every kind of light.
• ‌Temperature specifications have to be maintained.

FAQs

What is the use of polar capacitance in PIN photodetector?

Polar capacitance means the capacitor plates are electrodes having a positive and a negative polarity. In a PIN photodetector, the P and N layers act as electrodes, and as the width of the depletion layer is vast; the capacitance value is low. Due to low capacitance, the speed improves.

What is the advantage of PIN photodiode?

It has high sensitivity, low noise, wide bandwidth, low implementation cost. the detailed explanation is in top section .

What does I in PIN Photodiode stands for?

I in PIN photodiode stands for Intrinsic layer.

What is the difference between a regular photodiode and a PIN photodiode?

The increased intrinsic layer makes PIN photodiodes capable of carrying more current and also improves frequency response. The detailed explanation is in top section .

What are the drawbacks of PIN photodiode?

It is highly light-sensitive , and it can perform well only in reverse bias.

What is photodiode and its symbol?

A photodiode is a semiconductor that converts light energy in electrical energy.

What is a photodiode array?

It is a sensor used in photodetection, spectrophotometry , etc.

What is photodiode most commonly used?

The PIN-photodiode is the most commonly used photodiode.

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