Capacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. A common form of energy storage device is a parallel-plate capacitor. Capacitance is typified by a parallel plate arrangement and is defined in terms of charge storage. When a capacitor is fully charged there is a potential difference, between its plates, and the larger the area of the plates and/or the smaller the distance between them, the greater will be the charge that the capacitor can hold and the greater will be its Capacitance.

Where,

Q is the the charge on the conductor,

V is the potential applied across the conductor and

C is proportionality constant called as capacitance.

If capacitors are connected in series, the capacitance formula is given by

If capacitors are connected in parallel, the capacitance formula is given by

Where C

Capacitance formula is used in finding the capacitance of any number of capacitors in the given circuit.

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Problems based on capacitance are mentioned below:

### Solved Examples

**Question 1: **Find the capacitance of the capacitor if 5 coulomb of charge is flowing and potential applied is 2 V.

** Solution: **

Given: Charge Q = 5 C,

Voltage applied V = 2 V

The Capacitance is given by C = $\frac{Q}{V}$

= $\frac{5 C}{2 V}$

= 2.5 F.

**Question 2: **Find capacitance if capacitors 6 F and 5 F are connected

(i) In series

(ii) In parallel.

** Solution: **

The capacitance in series is given by Cs = $\frac{1}{C_{1}}$ + $\frac{1}{C_{2}}$

= $\frac{C_{1} + C_{2}}{C_{1} C_{2}}$

= $\frac{6 + 5}{30}$

= 0.367 F.

The capacitance in parallel is given by C_{p} = C_{1} + C_{2}

= 6 + 5

= 11 F.

Given: Charge Q = 5 C,

Voltage applied V = 2 V

The Capacitance is given by C = $\frac{Q}{V}$

= $\frac{5 C}{2 V}$

= 2.5 F.

(i) In series

(ii) In parallel.

The capacitance in series is given by Cs = $\frac{1}{C_{1}}$ + $\frac{1}{C_{2}}$

= $\frac{C_{1} + C_{2}}{C_{1} C_{2}}$

= $\frac{6 + 5}{30}$

= 0.367 F.

The capacitance in parallel is given by C

= 6 + 5

= 11 F.

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