Question

In the circuit three ideal cells of e.m.f. V, V and 2V are connected to a resistor of resistance R, a capacitor of capacitance C and another resistor of resistance 2R as shown in figure. In the steady state find: 

1. the potential difference between P and Q and
2. potential difference across capacitor C.

Answer 1

i. Steady-State Condition:

The capacitor C is fully charged, so no current flows through it (acts as an open circuit).

Potential at Q:

Assume P = 0 V

By using Kirchhoff’s Voltage Law (KVL) in the top branch:

V − IR = V_(PQ)

Using KVL in the bottom branch:

2V − I(2R) = V_(PQ)

Solving for I using the outer loop:

V − IR = 2V − 2IR

I = `V/R`

V(PQ) = 0 V − 0 V

= 0 V

ii. Voltage across capacitor C:

Since both P and Q are at the same potential, V_C = 0 V.