# In the circuit given below, the position of switch S is shifted from 1 to 2 . choose the correct statement

(A)Heat generated in the circuit is $\large\frac{1}{2}$$CE_1E_2 (B)Heat generated in the circuit is \large\frac{1}{2}$$CE_2^2$

(C)A charge of amount $CE_2$ will be supplied by battery $E_1$

(D)A charge of amount $CE_2$ will be supplied by battery $E_2$

When switch is at position 1, C is connected in series with $E_1\; and\; E_2$
By KVL
$Q_i= C( E_2 -E_1)$
When switch is moved to position 2, $Q_f= -E_1C$
$\Delta Q= Q_f -Q_i =-C E_2$
Net +ve charge pulled by battery $(E_1)= CE_2$
Work done in process of charge transfer $=CE_1E_2=\Delta w$
Change in energy of the capacitance
$\Delta W_c=\large\frac{q_f^2}{2C} -\frac{Q_i ^2}{2C}$
$\qquad= \large\frac{1}{2}$$E_1^2 C -\large\frac{1}{2}$$ (E^2-E_1)^2 C$
$\qquad= \large\frac{1}{2}$$(2 E_1 E_2-E_2^2)C$
Remaining part is lost as heat
$H= \Delta W- \Delta W_c$
$\quad= \large\frac{1}{2} {E_2}^2 C$
Hence B is the correct answer.

edited Aug 1, 2014