Three identical capacitors P , Q and S , each of the capacitance C , are connected to a battery of voltage V , as shown in the figure. If the energy stored in the capacitor P and total energy stored i

Question

Three identical capacitors P , Q and S , each of the capacitance C , are connected to a battery of voltage V , as shown in the figure. If the energy stored in the capacitor P and total energy stored in the system are U P ​ and U T ​ , respectively, then the ratio U T ​ U P ​ ​ is : NEET 2026 (Re-NEET)

TestHub · Accepted Answer

From the given circuit diagram, capacitors $P$ and $Q$ are connected in series, and their combination is connected in parallel with capacitor $S$ .

The equivalent capacitance of the series combination of $P$ and $Q$ is:
$C_{PQ} = \frac{C \times C}{C + C} = \frac{C}{2}$

The total equivalent capacitance of the system is:
$C_{e q} = C_{PQ} + C_{S} = \frac{C}{2} + C = \frac{3 C}{2}$

The total energy stored in the system is:
$U_{T} = \frac{1}{2} C_{e q} V^{2} = \frac{1}{2} (\frac{3 C}{2}) V^{2} = \frac{3}{4} C V^{2}$

Since capacitors $P$ and $Q$ are identical and connected in series across the battery of voltage $V$ , the potential difference across each of them is equal. Thus, the voltage across capacitor $P$ is:
$V_{P} = \frac{V}{2}$

The energy stored in capacitor $P$ is:
$U_{P} = \frac{1}{2} C_{P} V_{P}^{2} = \frac{1}{2} C (\frac{V}{2})^{2} = \frac{1}{8} C V^{2}$

The ratio of the energy stored in capacitor $P$ to the total energy stored in the system is:
$\frac{U _{P}}{U _{T}} = \frac{\frac{1}{8} C V ^{2}}{\frac{3}{4} C V ^{2}} = \frac{1}{8} \times \frac{4}{3} = \frac{1}{6}$

Answer: $1/6$

Physics - Capacitor Question with Solution | TestHub

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