Question

Capacitors are charged and connected as shown in figure. If switch is closed at $t=0$, find work done by battery.

• A. $220\text{nJ}$
• B. $110\text{nJ}$
• C. $55\text{nJ}$
• D. $200\text{nJ}$

Answer 1

Answer: (A)

$220\text{nJ}$

(Let $X$ charge be shifted by the cell in the circuit)
Using KVL across entire circuit,
$10-\left(\frac{12+X}{6}\right)+\left(\frac{9-X}{3}\right)=0$
$10-2-\frac{X}{6}+3-\frac{X}{3}=0$
$\frac{-X}{6}-\frac{X}{3}+11=0$
$\frac{X}{6}+\frac{X}{3}=11$
$\frac{3X}{6}=11$
$X=22nC$
$W=q.\in =22\times 10$
$=220\text{nJ}$