Question

Three identical capacitors C₁, C₂ and C₃ of capacitance 6 μF each are connected to a 12 V battery as shown.

Find

(i) charge on each capacitor

(ii) equivalent capacitance of the network

(iii) energy stored in the network of capacitors

Answer 1

The 12 V battery is in parallel with C₁, C₂, and C₃. C₁ and C₂are in series with each other while C₃ is in parallel with the combination formed by C₁and C₂.

Total voltage drop across C₃ = 12 V

q₃ = CV

Where, q = Charge on the capacitor

C₁, C₂, C₃ = 6 μF (Given in the question)

q₃ = 6 × 12 = 72 μC

Voltage drop across C₁ and C₂ combined will be 12 V.

Let the voltage drop at C₁ = V₁

Let the voltage drop at C₂ = V₂

Then,

V = V₁ + V₂

`V_1 = q_1/C`

`V_2 = q_2/C`

`q_1/6+q_2/6 = 12`

As both the capacitors are in series,

`q_1 =q_2 =q`

Then,

`q{1/6 +1/6} =12`

`q xx 1/3 =12`

Or,

q = 36 micro coulombs

Thus, charge on each of C₁ and C₂ is 36 coulombs.