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JIPMER 2017
Exam
JIPMER
Year
2017
Subject
Physics
Chapter
Capacitance

JIPMER 2017 · Physics · Capacitance

Two condensers, one of capacity C and the other of capacity (C)/(2)...

Two condensers, one of capacity CC and the other of capacity C2\frac{C}{2}, are connected to a VV-volt battery, as shown. Two condensers, one of capacity C and the other of capacity (C)/(2) , are connected to a V -volt battery, as shown. The The work done in charging fully both the condensers is

Options

  1. ACV2C V^2
  2. B14CV2\frac{1}{4} C V^2
  3. C34CV2\frac{3}{4} C V^2
  4. D12CV2\frac{1}{2} C V^2

Correct answer

C. 34CV2\frac{3}{4} C V^2

Step-by-step solution

The two condensers in the circuit are in parallel order, hence C′=C+C2=3C2C^{\prime}=C+\frac{C}{2}=\frac{3 C}{2} The work done in charging the equivalent capacitor is stored in the form of potential energy. Hence, W=U=12C′V2=12(3C2)V2=34CV2W=U=\frac{1}{2} C^{\prime} V^2=\frac{1}{2}\left(\frac{3 C}{2}\right) V^2=\frac{3}{4} C V^2
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