# Series and Parallel combination of Capacitor

Capacitor is a passive element, in which the energy is stored in the form of electrostatic field. This property of capacitor is called as capacitance. The unit of capacitance is Farad(F), which was named after the British Scientist Michael Faraday.

If V is the voltage applied to the capacitor and q is the charge stored, then the value of capacitance is given by,

## Capacitor in series

Consider three capacitors C1, C2 and C3 that are connected in series. Let V be the voltage supply that is connected to the series capacitors and I be the current flowing from the supply. Here, each capacitor carries an equal amount of charge q.

The voltage drops across each capacitor be V1, V2 and V3. So the total voltage V is given by V = V1 +V2 + V3.

Across each capacitor, the potential difference is given by,

Thus the resultant voltage is

If C_{s} is the effective capacitance of the series combination, then the voltage V is given by,

From (1) and (2),

If there are ‘n’ number of capacitors connected in series, then the equivalent capacitance value is given by

## Capacitors is parallel

Let us consider three capacitors C1, C2 and C3 connected in parallel. Let V be the supply voltage and I be the current flowing from the supply.

For parallel capacitors, the voltage across each capacitor is the same. Thus the charge on the three capacitors is given by

The total charge in all the capacitor is

The effective capacitance of the circuit is given by,

From equations (3) and(4),

If there are ‘n’ number of capacitors connected in parallel, then the effective capacitance is given by

Hence the effective capacitance of the capacitors connected in parallel is the sum of the capacitances of the individual capacitors.

**For example**, if a capacitor of 0.6 μF is connected in series with the parallel combination of three capacitors with capacitances 0.2 μF, 0.4 μF and 0.7 μF, then how to determine the effective capacitance of the circuit.

In the given problem, C_{1} =0.6μF is in series with the parallel combination of C_{2} = 0.2 μF, C_{3} = 0.4 μF, C_{4} = 0.7 μF.

C_{p} = C_{2} + C_{3} + C_{4} = 0.2 + 0.4 + 0.7 = 1.3 μF.

*C _{eff} = 0.411 μF*

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