>Capacitor – Definitions and Overview
>Theory of operation
>A capacitor in a DC Circuit
>A capacitor in an AC Circuit
>Capacitor in Series
>Capacitors in parallel
>Frequently Asked Questions (FAQs) on Capacitors
Capacitor – Definitions & Overview
Capacitor is one of the most important passive equipment which is able to store electrical energies. It is a two-terminal device. Capacitance is known as the effect of the capacitor.
Ancient forms of capacitor was innovated in the year 1704s. A European experiment back then discovered that electric charge could be reserved in a water-filled glass. Later in 1745, Ewald Georg from Germany found that series-connected high-voltage electrostatic generators can store the amount. Previously capacitors were known as condensers or condensator. Alessandro Volta coined the term in 1782. The term capacitor came into existence in 1926.
There are lots of types of capacitors. The capacitors have at least two conductors in the form of a metallic flat surface separated by a dielectric materials. The conductor may be an electrolyte, foil, thin film, etc. the non-conductor is the dielectric substance, increasing the capacitor’s charge capacity. Materials like – air, plastic film, paper, mica, ceramics are used as a dielectric for the capacitor.
When an external voltage is applied at the terminals of a capacitor, an electric field is produced across the dielectric material. Thus, a positive charge is collected on one plate, and a negative amount is collected on another scale. Capacitors are used in almost every electrical and electronic circuit. The difference between a resistor and a capacitor is that a resistor dissipates energy, whereas an ideal capacitor does not.
Theory of Operation
As mentioned earlier, a capacitor has two conductors separated by a dielectric medium. A capacitor works on the principle of Coulomb’s Law. Coulomb’s law states that –
Thus, a charge on one conductor will generate the force on the other conductor’s carrier, which further attracts opposite polarity charges and ripples the same type of charges. That is how an opposite polarity charge is induced on the other conductor’s surface.
Both the conductors hold an equal amount of charges, and the dielectric material develops the electric field.
Capacitance and Units of capacitance:
The capacitance of a standard capacitor is defined as the charge’s ratio to the conductor to the conductors’ voltage.
C = Q / V
C is the capacitance, Q is the charge on each conductor’s surface, and V is the voltage between two conductors.
The S.I unit of capacitance is given by – Farad(F).
One Farad capacitance is defined as the amount of capacitance a capacitor can generate if one coulomb of charge is applied to each conductor having one volt of voltage.
In practical devices, Capacitance is given by –
C = dQ / dV
* Most of the capacitors available in the market have capacitance rang in micro-farad.
A capacitor may behave differently at different times if it is placed in an active electrical circuit. Its behavior can be characterized by a long time limit and a short time limit.
Long time equivalence of a capacitor acts like an open circuit configuration (no current passes).
The short time equivalent of capacitors act like a short-circuit configuration.
V (t) = Q (t) / C = (1/C) * [ ∫t0t I (τ) dτ ] + V (t0)
Taking the derivatives, we get –
I (t) = dQ (t) / dt = C * [ dV(t) / dt ]
Symbol of Capacitor
There are different kinds of capacitor available. Different types of symbols are also there to represent them. Some of them are represented below using the diagrams. They are very useful to describe the circuit.
A capacitor in a DC Circuit
Let us discuss a DC circuit where a capacitor and a resistor are kept in series with a constant voltage source – V0.
Let’s assume the capacitor was previously uncharged, and the opened switch is closed at time t0.
From Kirchhoff’s Voltage Law, we can write –
Vo = VR (t) + VC (t)
VR (t) is the voltage across resistor ‘R’ at time instant ‘t,’ and VC (t) is the measured voltage across the circuit’s capacitor at time instant t.
Vo = i (t) * R + (1/C) * [ ∫t0 t I(τ) dτ ]
Taking derivative on both sides, we get –
RC * [ di (t) / dt] + i(t) = 0
At time t, let say tis zero. The voltage of the resistor is Vo and of the capacitor is zero.
At that time, current would be – Io = Vo / R. Now solving the differential equations –
I (t) = (Vo /R) * e (-t / τ0)
V (t) = Vo (1 – e (-t / τ0))
τ0 = RC.
It refers to as the “Time constant” of the circuitry.
A capacitor in an AC Circuit
In an AC circuit, the capacitor produces impedance, which is the vector sum of resistance and reactance. Capacitor’s impedances and reactance is given by the following expressions.
Reactance = X = – 1 / ωC = – 1 / 2πfC
Impedance = Z = 1/ jωC = – j / ωC = –j / 2πfC
Here ω is the angular frequency; j is the imaginary unit.
The impedance depends inversely on capacitance. Increasing the capacitance and frequency causes a decrease in impedance and vice-versa.
Q Factor or Quality Factor of a capacitor is defined as the ratio of reactance to its resistance. The q factor is a measure of efficiency. The formula can be written as –
Q = Xc / R = 1 / ωCR
ω is the angular frequency, C is the capacitance of the capacitor, Xc is the reactance, and R is the equivalent resistance.
Capacitor in Series
The diagram represents the capacitors in the series connection. It shows that the separation distance is added up instead of the plate area. The series of the capacitance acts as a capacitor less than any of its components.
The equivalent capacitance of the given connection, is –
1/Ceq = ∑ 1 / Ci = 1 / C1 + 1 / C2 + … + 1 / Cn
Capacitors in Parallel
The diagram represents the capacitors in parallel connection. An equal amount of voltage is applied to every capacitor. Here the capacitances of the capacitors are added up. The connection of the capacitance acts as an adder.
The equivalent capacitance is –
Ceq = ∑ Ci = C1 + C2 + … + Cn
There is an enormous number of capacitor types, available in the market based on numerous classification parameters. Type of the dielectric material, the device packaging, and the plates’ structure are some of the determining factors to classify capacitor types.
Almost every capacitor types have a dielectric substance. Dielectric substances are placed in between two conductors, the charge capacity can be increased. It is best to have a high permittivity material or high breakdown voltage as a dielectric substance.
There are various dielectric materials available like – paper, plastic, mica, ceramic, glass, air, etc.
Based on dielectric materials, some capacitor types are –
There are also other types, some capacitor types are –
- Voltage-dependent Capacitor
- Frequency-dependent Capacitor
- Parallel Plate Capacitor
- Decoupling Capacitor
Applications of Capacitors
Capacitors are one of the essential devices which are required for almost every electrical circuit. It has numerous applications in various fields. Some of the most important are –
A capacitor has the property of charging and discharging. It can store energy when it is disconnected from the charging source. Using this property, capacitors can be used as a battery or rechargeable battery.
Super-capacitors can accept and deliver charges faster than typical batteries and tolerate a more significant number of charging and discharging cycles than a standard rechargeable battery. But it is more extensive.
The quantity of charge stored in the dielectric layer is equal to or greater than the charge stockpiled in a plate of capacitor.
Capacitors are used in pulsed power applications. Mainly groups of large, primarily constructed, high voltage, and low inductance capacitors are used here.
Banks of capacitors are also used in power supplies to produce smooth outputs in half-wave or full-wave rectifier. Reservoir capacitors can be used for charging up pump circuits.
This helps to shunt away and hide fluctuations of current from the primary source to ensure a clean power supply for the control circuits. Audio circuits also use several capacitors.
Signal Coupling and Decoupling
Capacitors pass the AC signal but block the DC signals. That’s why capacitors are used in separating AC circuits. The process is recognized as – AC coupling or ‘capacitive coupling.’
A decoupling capacitor safeguards one area of the circuitry from other. They are used in power supply grounds. These are also known as a Bypass capacitor. Decoupling capacitors has applications in the biasing of transistors.
Dynamic digital memories for binary computers can be made using capacitors.
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