Capacitors in Parallel

Capacitors in Parallel

AU : May-04

Key Point : When capacitors are in parallel, the same voltage exists across them, but charges are different.

Q₁ = C₁ V, Q₂ = C₂ V, Q₃ = C₃ V

• The total charge stored by the parallel bank of capacitors Q is given by,

Q = Q₁ + Q₂ + Q₃

C₁ V + C₂ V + C₃ V

= (C_l + C₂ + C₃) V          ...(5.12.1)

• An equivalent capacitor which stores the same charge Q at the same voltage V, will have

Q = C_eqV     ...(5.12.2)

• Comparing equation (5.12.1) and (5.12.2),

As     C_eq = C_l + C₂ + C₃

Q = C₁ V + C₂ V + C₃ V

It is easy to find Q₁, Q₂ and Q₃ if V is known.

• parallel capacitors are shown in the Fig. 5.12.1

Ex. 5.12.1 If Cj = 100 mF and C₂ = 50 mF, calculate the joint capacitance and total energy stored with a steady applied potential difference of 1000 V in each case.

AU : May-04, Marks 8

Sol. : The four cases are shown in the Fig. 5.12.2.

Review Question

1. Deduce an expression for a joint capacitance of two capacitors C₁ and C₂ in parallel.