# Capacitors and Capacitance – Notes

Notes » Capacitors and Capacitance

### Capacitor

A capacitor essentially consists of two conducting surfaces separated by a layer of an insulating medium called dielectric. The conducting surfaces may be in the form of either circular (or rectangular) plates or be of spherical or cylindrical shape.

The purpose of a capacitor is to store electrical energy by electrostatic stress in the dielectric.

### Capacitance

The property of a capacitor to ‘store electricity’ may be called its capacitance.

The capacitance of a capacitor is defined as the amount of charge required to create a unit potential difference between its plates.

Suppose we give Q coulomb of charge to one of the two plate of capacitor and if a potential difference of V volts is established between the two, then its capacitance is :

C = Q/V = charge / potential differnce

Hence, capacitance is the charge required per unit potential difference.

By definition, the unit of capacitance is coulomb/volt which is also called farad.

One farad is defined as the capacitance of a capacitor which requires a charge of one coulomb to establish a potential difference of one volt between its plates.

One farad is actually too large for practical purposes. Hence, much smaller units like microfarad (μF), nanofarad (nF) and picofarad (pF) are generally employed.

1 μF = 10-6 F
1 nF = 10-7 F

1pF = 10-12 F

### Capacitors in Series

C1, C2, C3 = Capacitances of three capacitors
V1, V2, V3 = p.ds. across three capacitors.
V = applied voltage across combination
C = combined or equivalent or joining capacitance.
In series combination, charge on all capacitors is the same but p.d. across each is different.

1/= 1/1/1/3

= + C­+ C­3

### Energy Stored in a Capacitor

On charging the capacitor, the electrostatic field set up in the dielectric medium store energy. On discharging the capacitor, the field collapses and the stored energy is released.

1/2 (CV2) joules  = 1/2 (QV) joules = Q2/2joules

V =  voltage in volts.

### Current-Voltage Relationships in a Capacitor

The charge on a capacitor is given by the expression Q = CV. By differentiating this relation, we get :

i = dQ/dt = d (CV)/dt = C dv/dt

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