A parallel plate capacitor made of circular plates, each of radius R = 6 cm, has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with an angular frequency of \( 300\,\mathrm{rad\,s^{-1}} \). The rms value of the conduction current will be
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 6.9\,\mu\mathrm{A} \)
In an ac circuit with a capacitor, the capacitive reactance \( X_C=1/\omega C \) limits the current. So the rms current is \( I=V/X_C \), where \( V \) is the rms supply voltage. The radius of the plates is not needed, since the capacitance is given.
\( C=100\,\mathrm{pF}=100\times10^{-12}\,\mathrm{F} \)
\( \begin{aligned} I &= \frac{V}{X_C} \\ &= \omega CV \\ &= 300\,\mathrm{rad\,s^{-1}}\times100\times10^{-12}\,\mathrm{F}\times230\,\mathrm{V} \\ &= 6.9\times10^{-6}\,\mathrm{A} \\ &= 6.9\,\mu\mathrm{A} \end{aligned} \)