Question

In the figure shown, the voltage across \( C_3 \) will be:

• A. \( \frac{C_1 V}{C_1 + C_2 + C_3} \)
• B. \( \frac{C_3 V}{C_1 + C_2 + C_3} \)
• C. \( \frac{C_2 V}{C_1 + C_2 + C_3} \)
• D. \( \frac{(C_1 + C_2) V}{C_1 + C_2 + C_3} \)

Hint:

For capacitors in series and parallel, use the respective formulas for equivalent capacitance and apply the voltage division rule to find the voltage across each capacitor.

Answer 1

The Correct Option is D

Step 1: Understanding the Capacitor Circuit.
In this circuit, capacitors \( C_1 \) and \( C_2 \) are in series and their equivalent capacitance \( C_s \) is: \[ C_s = \frac{C_1 C_2}{C_1 + C_2} \] This series combination is in parallel with \( C_3 \). The total equivalent capacitance \( C_{\text{eq}} \) of the circuit is: \[ C_{\text{eq}} = C_s + C_3 = \frac{C_1 C_2}{C_1 + C_2} + C_3 \] Step 2: Voltage Across \( C_3 \).
The voltage across \( C_3 \) is given by the voltage division rule: \[ V_{C_3} = \frac{C_s}{C_{\text{eq}}} \times V = \frac{(C_1 + C_2)}{C_1 + C_2 + C_3} \times V \] Step 3: Final Answer.
Thus, the voltage across \( C_3 \) is \( \frac{(C_1 + C_2) V}{C_1 + C_2 + C_3} \).