A charged capacitor holds a charge of \(60\ \mu\mathrm{C}\), and the energy stored in it is \(1.8\times10^{-4}\ \mathrm{J}\). The capacitance of the capacitor is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(10\ \mu\mathrm{F}\)
The energy stored in a capacitor can be written in terms of its charge as \( U=Q^{2}/2C \). Both \( Q \) and \( U \) are given, so this form gives \( C \) in one step.
\( \begin{aligned} C &= \frac{Q^{2}}{2U} \\ &= \frac{(60\times10^{-6})^{2}}{2\times1.8\times10^{-4}} \\ &= \frac{3.6\times10^{-9}}{3.6\times10^{-4}} \\ &= 1\times10^{-5}\ \mathrm{F} \\ &= 10\ \mu\mathrm{F} \end{aligned} \)
NCERT (2026-27):
Energy Stored in a Capacitor – “We can write the final result, in different ways”
\( W=\frac{Q^{2}}{2C}=\frac{1}{2}CV^{2}=\frac{1}{2}QV \)\( \qquad (2.69) \)