Question

Two capacitors of capacity \(C\) and \(C/3\) are connected to a battery of voltage \(V\) as shown. The work done in charging both the capacitors fully is

• A. \(CV^{2}/3\)
• B. \(4CV^{2}/3\)
• C. \(2CV^{2}/3\)
• D. \(3CV^{2}\)

Hint:

Both capacitors sit directly across the battery, so they are in parallel. The battery work is the total charge times V.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Both capacitors are connected directly across the battery, so they are in parallel and the equivalent capacity is \(C+\dfrac{C}{3}=\dfrac{4C}{3}\).

Step 2: Charge from the battery
\(Q=C_{eq}V=\dfrac{4CV}{3}\)

Step 3: Work done
The battery moves this charge through a potential difference \(V\), so \(W=QV=\dfrac{4CV^{2}}{3}\). (Half of this is stored in the capacitors; the rest is lost as heat in the wires.)

Final Answer:
The work done in charging both capacitors is 4CV²/3. \[ \boxed{\text{(B) }\dfrac{4CV^{2}}{3}} \]