Question

Two condensers one of capacity $\frac{C}{2}$ and other capacity $C$ are connected to a battery of voltage $V$ as shown. The work done in charging fully both the condensers is

• A. \frac{1}{2} CV^2
• B. \frac{3}{4} CV^2
• C. \frac{3}{2} CV^2
• D. 2 CV^2

Hint:

For parallel circuits, the voltage remains constant across all components. Simply find the total capacitance and use $1/2 CV^2$.

Answer 1

The Correct Option is A

Step 1: From the diagram, the two capacitors are connected in parallel to the battery of voltage $V$.
Step 2: The equivalent capacitance $C_{eq}$ for capacitors in parallel is the sum of individual capacitances: \[ C_{eq} = C + \frac{C}{2} = \frac{3C}{2} \]
Step 3: The energy stored in the capacitors (which equals the work done in charging them) is given by the formula: \[ W = \frac{1}{2} C_{eq} V^2 \]
Step 4: Substitute the value of $C_{eq}$: \[ W = \frac{1}{2} \left( \frac{3C}{2} \right) V^2 = \frac{3}{4} CV^2 \]