In the given circuit as shown in figure, in the steady state, obtain the expression for (i) potential drop (ii) the charge and (iii) the energy stored in the capacitor C.

Explanation

In the steady state, the capacitor C is the fully charged. So no current flows through the arm BE of the circuit.
`:.` Effective emf of the circuit `= 2V- V=V`
Effective resistance of the circuit `= 2 R +R = 3R`
Current in the circuit, `I= (V)/(3R)`
Potential difference between across B and E
`= 2 V - I xx 2R= 2V - (V)/(3R) xx 2R = 4/3 V`
(i) potential difference across C
`=4/3 V - V= V/3`
(ii) Charege on capacitor
`Q= CV = C xx V/3 = (CV)/(3)`
(iii) Energy stored in the capacitor
`=1/2 C(V/3)^(2)= (CV^(2))/(18)`