Question

In the circuit shown in the following figure, the potential difference cross 3µF capacitor is

• A. 4 V
• B. 6 V
• C. 10 V
• D. 16 V

Answer 1

Answer: (C)

10 V

Answer 2

1. For series capacitors, the same charge Q develops on both. The voltage across the 3 µF capacitor is

   $$V_{3} = \frac{Q}{3},$$

   and across the 5 µF capacitor is

   $$V_{5} = \frac{Q}{5}.$$

2. Applying Kirchhoff’s Voltage Law (KVL) around the loop:

   $$20\,V - V_{3} - V_{5} - 4\,V = 0 \quad \Rightarrow \quad V_{3} + V_{5} = 16\,V.$$

3. Substitute the capacitor voltage expressions:

   $$\frac{Q}{3} + \frac{Q}{5} = 16 \quad \Rightarrow \quad Q\left(\frac{5+3}{15}\right) = 16 \quad \Rightarrow \quad Q\left(\frac{8}{15}\right)= 16.$$

4. Solving for Q:

   $$Q = 16 \times \frac{15}{8} = 30\,\mu C.$$

5. Now, voltage across the 3 µF capacitor:

   $$V_{3} = \frac{30\,\mu C}{3\,\mu F} = 10\,V.$$