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

The Correct Option is D

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 \(\frac{U_2}{U_1} = \frac{2}{3}\).