Capacitors in Parallel

Capacitors connected in parallel, the total capacitance is the sum of the individual capacitors’ capacitances. If two or more are connected in parallel, the effect is that of a single equivalent capacitor having the sum total of the plate areas of the individual capacitors.

Now lets consider the parallel connection of N capacitors, as shown

i = i_{1} + i_{2} + … + i_{N}

We have

i = C_{1}\frac{dv}{dt}+C_{2}\frac{dv}{dt}+ … + C_{N}\frac{dv}{dt} = (C_{1}+C_{2}+ … + C_{N})\frac{dv}{dt}=(\sum_{n=1}^{N}C_{n})\frac{dv}{dt}

In the circuit the current is

i = C_{p}\frac{dv}{dt}

If we require that this circuit be an equivalent circuit as shown in the image, the equivalent capacitance of N parallel capacitors is simply the sum of the individual capacitances. An initial voltage would be equal to that which is present across the parallel combination. It’s very interesting to notice that the equivalent capacitance of series and parallel capacitors is analogous to the equivalent conductance of series and parallel conductances.