Q129 / 150 · MHT CET 2024 (09 May Shift 2) · Physics
The potential difference that must be applied across the series and parallel combination of 4 identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is
- A$1: 2$
- B$1: 4$
- Correct answerC$4: 1$
- D$2: 1$
Solution
The equivalent capacitance for series combination,
$C_1=\frac{C}{4}...(i)$
$\therefore \quad$ Potential energy, $\mathrm{U}_1=\frac{1}{2} \mathrm{C}_1 \mathrm{~V}_1^2$...(ii)
The equivalent capacitance for parallel combination,
$C_2=4 C...(iii)$
$\therefore \quad$ Potential energy, $U_2=\frac{1}{2} C_2 V_2^2$...(iv)
Given that, $\mathrm{U}_1=\mathrm{U}_2$
$\begin{array}{ll}
\therefore & \mathrm{C}_1 \mathrm{~V}_1^2=\mathrm{C}_2 \mathrm{~V}_2^2 \\
\therefore & \frac{\mathrm{~V}_1}{\mathrm{~V}_2}=\sqrt{\frac{\mathrm{C}_2}{\mathrm{C}_1}} \\
\therefore & \frac{\mathrm{~V}_1}{\mathrm{~V}_2}=\sqrt{\frac{4 \mathrm{C}}{\frac{\mathrm{C}}{4}}}=\sqrt{\frac{16}{1}} \\
\therefore & \frac{\mathrm{~V}_1}{\mathrm{~V}_2}=\frac{4}{1}
\end{array}$
...(From(ii) and (iv))
...(From (i) and (iii))
Hence, the correct answer is option: 'C'.