Parallel Combination of Capacitors

A capacitor is the system of two conductors separated by an insulator.

The capacitors are used to store the electrical energy in the form of electric charge.

The capacitors are connected in series or parallel in a circuit according to the requirement.

For the series combination of the capacitors, the total capacitance is less than any one of the series capacitors' individual capacitances.

When the capacitors are connected in parallel, the effective capacitance is equal to the sum of the individual capacitances.

Lets' find the effective capacitance of the capacitors connected in parallel.

Consider three capacitors connected in parallel in a circuit with a voltage source of voltage .

Suppose the capacitance of the capacitors is , and respectively.

Let the charge supplied by the source is , at the junction to which all the capacitors are connected, gets divided into three parts; , and .

Let the charge goes into the first capacitor, in the second capacitor and the in the third capacitor.

The plate of the capacitor connected with the positive terminal of the battery gets accumulated with the positive charge.

The plate of the capacitor connected with the negative terminal of the battery gets accumulated with the negative charge.

When the capacitors are connected in parallel the voltage drop across the capacitors is the same for all the capacitors.

Thus, the charge stored in the first capacitor is as given above.

Similarly, the charge in the second and third capacitors are as given above,

Thus, the total charge in the circuit will be the sum of the individual charges in the capacitors.

Let the equivalent capacitance or effective capacitance of the circuit be , which is equivalent to the all the capacitances of capacitors connected in the circuit.

Thus, the will be as given above,

Putting the value of , , and in the equation of total charge in the circuit we have got,

Therefore, the effective capacitance of the capacitors connected in parallel in a circuit is as given above,

If capacitors are connected in parallel the effective capacitance will be as above,

Revision

The equivalent capacitance or effective capacitance of the circuit is equivalent to the all the capacitances of capacitors connected in the circuit.

Therefore, the effective capacitance of the capacitors connected in parallel in a circuit is as given above,

If capacitors are connected in parallel the effective capacitance will be as above,

The End