# 9 Examples Of Parallel Circuit

A parallel circuit equips current to travel through different (distinct) or branches of the circuit. The current across paths can be distinct, but the voltage across each parallel path is identical.
A circuit can be a parallel circuit or series circuit, or a combination of parallel and series circuits. There are several different parallel circuit examples.

Some of the examples are listed below:

## Resistors in Parallel

Suppose there is more than one resistor connected between two circuitry nodes, then the resistors are connected in parallel with each other. In other words, when both the terminal of the resistors are connected respectively to each end of the other resistors. The value of resistance can be different or identical in parallel circuit combinations as a requirement. The voltage (or potential difference) over each resistor is identical in parallel combination as there is a variety of paths for current to flow. The value of current will vary with resistance in each path. If the value of resistance of each path is identical, then the current flow through each part will also become identical.

For example, if two resistors of the same resistance are connected in parallel with each other, then the current flowing through them will be the same. With Current Division rules the current into and out of each path of the circuit can be determined.

But when two resistors, R1 and R2, of different resistance, are connected in parallel, the current flowing through them will differ. As V=IR (Ohm’s Law) as V is the same for all parallel circuit components, the value of I depends on the value of R.

The whole parallel circuitry of the resistor can be replaced by a sole resistor of the value equal to the equivalent resistance of the overall parallel combination of the resistors.

The equivalent resistance represents the overall resistance effect of all the resistors connected in parallel.

Equation of equivalent resistance in parallel combination with resistor:

$1\frac{1}{R_e}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}…..+\frac{1}{R_n}$

Where $R_e$ -> Equivalent resistance.

$R_1, R_2, R_3….R_n$ -> Different resistance connected in parallel.

When two resistors (R) in parallel are of the same value, the equivalent resistance of both resistors is half of the one resistor (R).

As $\frac{1}{R_e}=\frac{1}{R}+\frac{1}{R}$=>$\frac{1}{R_e} = \frac{2}{R}$ =>$R_e = \frac {R}{2}.$

The resulting equivalent resistance of the resistor in parallel is always lower than the individual resistor, and as more resistance is added, the equivalent resistance decreases.

## Capacitor in Parallel

Suppose there is more than one capacitor connected between two nodes of a circuit, then the capacitors are in parallel combination with each other. in other words, when both the terminals of the capacitor are connected respectively to each and other capacitors.

When capacitors are linked in parallel, the resulting capacitance (or total capacitance) equals the addition (or sum) of each capacitor’s capacitance in the combination.

$C_t = C_1 + C_2 +C_3 ……. +C_n$

Where $C_t$-> total capacitance of the parallel combination.

$C_1, C_2, C_3 …. C_n$ -> different capacitor connected in parallel.

The voltage across each capacitor in parallel combination is the same, but the charge stored by each capacitor depends upon the value of capacitance of each capacitor, according to Q=CV. So as the capacitance of the capacitor varies, the stored charge will also change as the applied voltage across all the capacitors in parallel combination is identical.

For example, if three capacitors are linked in parallel, the capacitance of every piece capacitor can be distinct or identical. Suppose every capacitor connected in parallel is of exact capacitance. In that case, the charge stored by each capacitor will be the same, but if the capacitance of each capacitor is different, each capacitor will hold a different amount of charge. The total charge (Q) stored by the overall capacitor (in parallel combination) is the sum of individual charges.

$Q= Q_1 + Q_2 + Q_3$

Where $Q_1, Q_2, Q_3$ is the charge stored by the capacitor $C_1, C_2, C_3,$ respectively.

As we know Q= CV

So, $C_t V = C_1 V + C_2 V + C_3 V$

$C_t = C_1 + C_2 + C_3$

## Inductor in Parallel

Suppose there is more than one inductor connected between two nodes of a circuit, then the inductor is connected in parallel combination with each other. In other words, when both ends (or terminals) of the inductor are connected respectively to each and of the other inductor.

The current flow through each inductor is not equal to the overall current but is the summation of each current passing through each inductor connected in parallel. The inductance of a parallel combination of the inductor is lesser than that of the combined inductance.

The total current flowing through the overall parallel combination is the sum total of individual currents flowing through each conductor so

$I= I_1 + I_2 + I_3 ….. + I_n.$

Where I is the overall current, and $I_1, I_2, I_3, ….. I_n$ is the current through the [/latex]L_1, L_2, L_3, … L_n[/latex].

The relationship of current, voltage, and inductance of an inductor can be defined as V= L (di/dt)

As $V=L_t\frac{\partial (I_1 + I_2 + I_3…..+I_n) }{\partial t}$

=> $L_t(\frac{\partial I_1}{\partial t}+\frac{\partial I_2}{\partial t}+\frac{\partial I_3}{\partial t}…..+ \frac{\partial I_n}{\partial t})$

=> $L_t(\frac{V}{L_1}+\frac{V}{L_2}+\frac{V}{L_3}…..\frac{V}{L_n})$

$\frac{1}{L_t}=\frac{1}{L_1}+\frac{1}{L_2}+\frac{1}{L_3}……..+\frac{1}{L_n}$

Where $L_t$ => overall inductance of the parallel combination of inductors.

$L_1, L_2, L_3, … L_n$ are the individual inductors in the parallel combination.

The above equation holds when there is no natural inductance or magnetic coupling between any inductors.

## Resistor and Capacitor in Parallel

If there is at least one resistance and one capacitor connected between two circuit nodes, then the resistor and capacitor are connected in a parallel combination.

When resistor and capacitor are in parallel combination, the overall impedance will be at a phase angle between 0 degrees to – 90 degrees, and current will have a phase angle between 0 degrees to 90 degrees.

In a parallel combination of resistor and capacitor, the parallel circuit components share the same voltage. The phase angle depends on the value of the current that passes (or flow) through the capacitor and the resistor. If the current through the capacitor is higher, the phase angle will be close to 90 degrees. If the current through the resistor is greater than the phase angle, it will be close to 0 degrees.

Overall impedance $Z= \frac{R X_C}{\sqrt{R^2 +X_C^2}}$

Where $X_c$ -> impedance of capacitor.

R -> resistance of the resistor.

Phase angle = $tan^{-1}\frac{I_C}{I_R}$

$I_C$ -> current through capacitor.

$I_R$ -> current through the resistor.

If the RC parallel circuit consists of only one capacitor and one resistor, then the circuit is of first-order type.

## Resistor and Inductor in Parallel

If at least one inductor and resistor are connected between two circuit nodes, then the inductor and the resistor are in a parallel combination. The overall phase angle of this combination is always lying between 0 degrees to -90 degrees. The value of the phase angle depends upon the value of the current into and out of the inductor and the resistor. If the current through the inductor is more than that of the resistor, then the angle will be close to -90 degrees, and if the current through the resistor is more than the phase angle will be close to zero degrees.

The overall impedance (Z) is $\frac{1}{Z}=\frac{1}{R}+\frac{1}{jL}$

Phase angle = $tan ^-tan^{-1}\frac{I_L}{I_R}$

Where R and L are the resistance and inductance of resistor and inductor, respectively.

$I_L$ and $I_R$ are the currents through the inductor and resistor, respectively.

If the LR circuit is composed of only one inductor and one resistor, then the circuit is the first-order LR circuit.

## Parallel combination of Resistor, Inductor and Capacitor

If the resistor-capacitor and inductor are connected between two nodes of a circuit, then this is the parallel combination of resistor-capacitor and inductor

The voltage across each element is the same, but the total current flowing through this combination gets divided across each component depending upon the importance of each element

This RLC in parallel combination circuit is a resonating circuit.. When the overall current through the circuit is in phase with the applied voltage, it resonates at a particular frequency called resonating frequency.

By using phasor diagram: $I_S^2=I_R^2+(I_L^2-I_C^2)$

Where $I_L$ -> current through the inductor.

$I_C$ -> current through the capacitor.

$I_R$ -> current through the resistor.

$I_S$ -> current through the overall circuit.

## Inductor and capacitor in parallel

If at least one inductor and a capacitor are connected between two circuit nodes, then the inductor and capacitor are in a parallel combination. The LC parallel circuit is in resonance when the capacitor’s impedance is equal to the inductor’s impedance. At that time, they cancel out each other to provide a minimum current in the circuit, whereas the overall impedance of the circuit is maximum.

Resonating frequency$f_o=\frac{\omega }{2\pi }=\frac{1}{2\pi \sqrt{LC}}$

Overall impedance $Z_{LC}=\frac{Z_L Z_C}{Z_L+Z_C}$

Where L and C are the inductance and capacitance of inductor and capacitor, respectively.

$X_L and X_C$ are the impedance of the inductor and capacitor, respectively.

When $X_L > X_C,$ then the overall circuit is inductive.

$X_C> X_L,$ then the overall circuit is capacitive.

$X_C= X_L,$ then the circuit has maximum impedance and minimum current, and this circuit is called the rejector circuit.

## Diodes in parallel

If more than one diode is connected between two nodes of a circuit, then the diodes are in parallel combination with each other.

The diode having a low forward voltage drop across it will carry a more significant amount of current than other my connected diode invalid the overall current capacity of the circuit will increase.

The forward voltage drop over (or across) the diode can vary with diode types. It is not necessary to connect all the diode in forward or reverse biased combination in parallel diode combination only. It can be a combination of both forward and reverse biased diode as for the requirement. The current sharing by each diode depends on its electrical capacity.

For example, in a parallel combination of the diode, if one diode is connected in forward biased and another is in reverse biased, then the current will flow through the forward biased diode as a reverse biased diode will block the current.

## Transistor in parallel

When the identical pinout of two or more transistors is linked together in circuitry, this is the parallel combination of transistors.

The parallel combination of the transistor increases the current holding capacity overall. As several transistors increase, the current holding capacity of the overall circuit also increases. Generally, one transistor is sufficient for producing a moderate output current, but when a higher output current is required, adding more transistors in parallel becomes necessary.

## Current source in parallel

The current source cannot be combined in a series but can be combined in parallel as the series combination of current sources violates Kirchhoff’s current law. If there is more than one current source connected between two circuit nodes, then the current source is in parallel combination.

For example, two current sources are connected in parallel combination, when the current source’s positive terminal is linked together and negative terminals of the current source is connected, then The current overall combination will get added. In contrast, when the positive terminal of the current source is connected to the negative terminal of another current source, then the overall current through the combination will get subtracted from each other. This is based on the sign convention of the current source or the direction of the flowing current in the circuitry.

## What is a parallel circuit?

There can be different types of circuits, where the parallel circuit is one type of circuit.

In a circuit where the current has more than one path or branch (between two circuit nodes) to travel through, different circuit elements are connected in different branches of the circuit.

## What is the main disadvantage of parallel circuits?

There are a variety of advantages and disadvantages of a parallel circuit combination depending upon the application and uses.

In a Parallel circuit, the need of wire in parallel combination is more than that of a series circuit; it is the most significant disadvantage of a parallel circuit.

## Why do we connect household appliances in parallel?

The House wiring is in parallel combination, and all the appliances are linked in parallel.

When the appliance is connected in parallel, all the appliances get the same voltage for operation. In parallel combination, the resistance is low. If one appliance is at fault, then the other appliance’s operation will not get affected in parallel combination.

## Can you have two voltage sources in parallel?

Any voltage source (with distinct or similar value) can be linked in series with each other.

Two Voltage sources having different potential differences cannot be connected directly in parallel as it can violate Kirchhoff’s Voltage Law. Only voltage sources of the same potential difference can be connected in parallel with each other.

## What is XL and XC in RLC circuit?

RLC circuit is a circuit in which resistance, capacitor, and inductor can be connected in parallel, series, or other combinations.

XL and XC are the impedance of the inductor and capacitor of the RLC circuit, respectively.

Sneha Panda

I have graduated in Applied Electronics and Instrumentation Engineering. I'm a curious-minded person. I have an interest and expertise in subjects like Transducer, Industrial Instrumentation, Electronics, etc. I love to learn about scientific researches and inventions, and I believe that my knowledge in this field will contribute to my future endeavors. LinkedIn ID- https://www.linkedin.com/in/sneha-panda-aa2403209/