Question

Two parallel plate capacitors of capacitances 2 $\mu F$ and 3 $\mu F$ are joined in series and the combination is connected to a battery of V volts. The values of potential across the two capacitors $V_1$ and $V_2$ and energy stored in the two capacitors $U_1$and $U_2$ respectively are related as_____
Fill in the blank with the correct answer from the options given below

• A. $\quad \frac{V_2}{V_1} = \frac{U_2}{U_1} = \frac{2}{3}$
• B. $\quad \frac{V_2}{V_1} = \frac{U_2}{U_1} = \frac{3}{2}$
• C. $\quad \frac{V_2}{V_1} = \frac{2}{3} \quad \text{and} \quad \frac{U_2}{U_1} = \frac{3}{2}$
• D. $\frac{V_2}{V_1} = \frac{3}{2} \quad \text{and} \quad \frac{U_2}{U_1} = \frac{2}{3}$

Answer 1

Answer: (D)

$\frac{V_2}{V_1} = \frac{3}{2} \quad \text{and} \quad \frac{U_2}{U_1} = \frac{2}{3}$

Answer 2

In series, the potential across each capacitor is inversely proportional to the capacitance. Since $C_1 = 2 \, \mu F$ and $C_2 = 3 \, \mu F$, the ratio $\frac{V_2}{V_1} = \frac{C_1}{C_2} = \frac{3}{2}$. The energy stored in a capacitor is proportional to $C \times V^2$, so the energy ratio is $\frac{U_2}{U_1} = \frac{2}{3}$.