Concepts Of Physics MCQ Edition [Volume 2]PhysicsCapacitors
Consider the circuit shown in the figure. The switch S is open for a long time and subsequently closed. Calculate the work done by the battery.
Options
- AC E ^2 4
- B2C E ^2
- CC E ^2
- DC E ^2 2
Correct answer
D. C E ^2 2
Step-by-step solution
When the switch S is open, the two capacitors are in series. The equivalent capacitance is C_ eq1 = C C C + C = C 2 . The initial charge supplied by the battery is Q_i = C_ eq1 E = C E 2 . When the switch S is closed, the right capacitor is short-circuited and the left capacitor is directly connected across the battery. The new equivalent capacitance is C_ eq2 = C . The final charge supplied by the battery is Q_f = C_ eq2 E = C E . The extra charge that flows through the battery is Q = Q_f - Q_i = C E - C E 2 = C E