Capacitors in Parallel

By Mohit Uniyal|Updated : August 26th, 2022

Capacitors in parallel provide a higher value of equivalent capacitance. Series and parallel combination of capacitors is a powerful tool for reducing circuits. A capacitor stores electrostatic energy in the form of an electric field. The voltage connected across the capacitors in parallel is the same and equal to the supply voltage.

For AC supply, the higher the capacitance, the more amount of time taken by the capacitor for charging and discharging. Capacitors in parallel provide higher equivalent capacitance. The article elaborates on capacitors in parallel, the formula to find the equivalent capacitance of capacitors in parallel, and current and voltages in 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.

Equivalent Capacitance of Capacitors in Parallel

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

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

Capacitors in parallel 1

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

Capacitors in Parallel 2

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,

capacitors in parallel 3

The current across capacitors can be written as,

capacitors in parallel 4

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:

Ceq= C1+ C2+ C3+ . . . . . CN 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 Cconnected in parallel, the current across them i1 and i2, respectively, is given by:

capacitors in parallel

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,

in=i/N

where,

  • i= total supply current,
  • in= current across the nth capacitor
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FAQs on Capacitors in Parallel

  • When several capacitors are connected in parallel, the equivalent capacitance of the circuit increases, hence being able to store more energy. The overall equivalent capacitance is calculated by adding the individual capacitance of all the capacitors in parallel.

  • When N number of capacitors are connected in parallel, the overall equivalent capacitance can be calculated as

    C_eq=C_1+C_2+C_3+ . . . . . C_N

  • A capacitor can store energy in an electrostatic field. Capacitors in parallel increase the overall equivalent capacitance and hence, more energy can be stored.

  • The voltage across each capacitor in parallel has the same voltage but the charge adds up. The total voltage rating will not change in a parallel combination. Capacitors in parallel are used to increase the total storage of electric charge.

  • Capacitors in parallel have the same voltage. The total equivalent charge is the sum of charges stored by individual capacitors in parallel. The charge can be the same only when the capacitance of all the capacitors is equal.

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