Electrical Engineering ⇒ Topic : Capacitors in Parallel

Capacitors in Parallel

Consider three capacitors, having capacitances C₁, C₂ and C₃ farad respectively, connected in parallel across a p.d. of r volts [See Figure (a) (i)]. In parallel connection, p.d. across each capacitor is the same but charge on each is different

                                                 figure (a)

But Q/V is the total capacitance C_T of the parallel combination [See Fig (a). (ii)]                     

                                   C_T = C₁ + C₂ + C₃

_{Thus capacitors in parallel are treated in the same manner as are resistors in series.}

CAPACITORS IN PARALLEL

In this case, the charge on each capacitor is different but voltage is same as shown in Figure (a).

The total charge Q is given by

                                  Figure (a) Capacitors connected in parall

When n capacitors C₁, C₂, , and C_n are in parallel, it can be expressed as:

                                                                                 ............ (1)

Capacitors in Parallel:-

Figure  shows the arrangement of capacitors in parallel. C₁, C₂ and C₃ are the three capacitors connected in parallel. The voltage across each capacitor is the same, i.e. V volts. Let .q₁, q₂ and q₃ be the corresponding charges on C₁, C₂and C₃. We know that

                               q₁= C₂ V       q₂= C₂V       q₃= C₃V  

                    Arrangement of capacitors in parallel

The total charge on the system of capacitors is given as

Therefore, the equivalent capacitance C is given as

The above equation suggests that the system of parallel capacitors can be represented by a single equivalent capacitor whose capacitance is the sum of the three individual capacitors.

Similarly, if the parallel combination contains n capacitors, then

Thus, in the parallel system of arrangement of capacitors, the equivalent capacitance (C) is always greater than any individual capacitance and is equal to the sum of all the capacitances connected in parallel.