The voltage across a capacitor of capacitance \( 10\,\mu\mathrm{F} \) is \( V=10\cos\omega t \) (in volts). The maximum charge on the capacitor is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 100\,\mu\mathrm{C} \)
The charge on a capacitor at any instant is \( q=CV \), so the maximum charge is reached when the voltage is at its peak value. From \( V=10\cos\omega t \), the peak voltage is \( V_0=10\,\mathrm{V} \).
\( C=10\,\mu\mathrm{F}=10\times10^{-6}\,\mathrm{F} \)
\( \begin{aligned} q_0 &= CV_0 \\ &= 10\times10^{-6}\,\mathrm{F}\times10\,\mathrm{V} \\ &= 10^{-4}\,\mathrm{C} \\ &= 100\,\mu\mathrm{C} \end{aligned} \)