Question

Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel.

(a) What is the total capacitance of the combination?

(b) Determine the charge on each capacitor if the combination is connected to a 100 V supply.

Answer 1

(a) Capacitances of the given capacitors are

C₁ = 2 pF

C₂ = 3 pF

C₃ = 4 pF

For the parallel combination of the capacitors, equivalent capacitorC'is given by the algebraic sum,

C' = 2 + 3 + 4 = 9 pF

Therefore, the total capacitance of the combination is 9 pF.

(b) Supply voltage, V = 100 V

The voltage through all the three capacitors is same = V = 100 V

Charge on a capacitor of capacitance C and potential difference V is given by the relation,

q = VC …....(i)

For C = 2 pF,

Charge = VC = 100 × 2 = 200 pC = 2 × 10⁻¹⁰ C

For C = 3 pF,

Charge = VC = 100 × 3 = 300 pC = 3 × 10⁻¹⁰ C

For C = 4 pF,

Charge = VC = 100 × 4 = 400 pC = 4 × 10⁻¹⁰ C