Question 15: Electrostatics & Capacitance

Question

Two capacitors $$C$$ and $$\frac{C}{2}$$ are connected to a battery of $$V$$ volts, as shown below
The work done in charging both the capacitors fully is

Accepted Answer

The two capacitors are in parallel.
The equivalent capacitance $$C^{\prime}=C+\frac{C}{2}=\frac{3 C}{2}$$
Work done in charging the equivalent capacitor is stored in the form of potential energy.
$$\begin{aligned}
W & =U=\frac{1}{2} C^{\prime} V^2 \
& =\frac{1}{2} 	imes \frac{3 C}{2} 	imes V^2 \
& =\frac{3}{4} C V^2
\end{aligned}$$

Answer

$$2 C V^2$$

Answer

$$\frac{3}{4} C V^2$$

Answer

$$\frac{1}{2} C V^2$$

Answer

$$\frac{1}{4} C V^2$$

Electrostatics & Capacitance

Two capacitors $C and \frac{C}{2} are connected to a battery of V$ volts, as shown below The work done in charging both the capacitors fully is

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