Capacitors in Parallel

Define Capacitors in Parallel

A capacitor is a device that stores charge. The equivalent capacitance of capacitors in parallel is the individual sum of all the capacitance connected in parallel. Hence, the net capacitance increases. Multiple capacitors in parallel can be replaced by an equivalent single capacitor.

The capacitance of an equivalent single capacitor is the individual sum of all capacitors in parallel. Hence, the equivalent capacitance increases, and therefore by connecting the capacitors in parallel, the circuit can store more energy.

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Equivalent Capacitance of Capacitors in Parallel

In order to obtain the equivalent capacitance C_eq of N capacitors in parallel, consider the circuit shown below:

The capacitors have the same voltage v across them. On applying KCL,

Where Ceq is the net equivalent capacitance of capacitors in parallel as shown in the circuit below and is given by,

Voltage and Current in Capacitors in Parallel

The voltage v across capacitors in parallel is the same and equal to the supply voltage. However, the current has multiple paths to flow so the current divides across the capacitors. Consider two capacitors C₁ and C₂ connected in parallel as shown below:

The net charge Qnet is given by,

The current across capacitors can be written as,

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Capacitors in Parallel Formula

The overall equivalent capacitance of capacitors in parallel is the individual sum of all the capacitance of capacitors. Mathematically it can be written as:

C_eq= C₁+ C₂+ C₃+ . . . . . C_N for N parallel connected Capacitors

The voltage across all the capacitors will be the same as they are in parallel, but the current divides across the capacitors.

For two capacitors C₁ and C₂ connected in parallel, the current across them i₁ and i₂, respectively, is given by:

If all the capacitors in parallel have the same value of capacitance, then, the current divides equally among all the capacitors. If N capacitors of equal capacitance are connected in parallel, the current across each capacitor is given by,

i_n=i/N

where,

• i= total supply current,
• i_n= current across the nth capacitor