A \( 60\,\mu\mathrm{F} \) capacitor is connected to a 110 V, 60 Hz ac supply. What is the rms value of the current in the circuit?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2.49 A
In a purely capacitive ac circuit, the capacitive reactance \( X_C=1/\omega C \) limits the current. The rms current is \( I=V/X_C \), where \( V \) is the rms voltage of the supply.
\( \begin{aligned} \omega &= 2\pi\nu \\ &= 2\pi\times60\,\mathrm{Hz} \\ &= 377\,\mathrm{rad\,s^{-1}} \end{aligned} \)
\( C=60\,\mu\mathrm{F}=60\times10^{-6}\,\mathrm{F} \)
\( \begin{aligned} X_C &= \frac{1}{\omega C} \\ &= \frac{1}{377\,\mathrm{rad\,s^{-1}}\times60\times10^{-6}\,\mathrm{F}} \\ &\approx 44.2\,\Omega \end{aligned} \)
\( \begin{aligned} I &= \frac{V}{X_C} \\ &= \frac{110\,\mathrm{V}}{44.2\,\Omega} \\ &\approx 2.49\,\mathrm{A} \end{aligned} \)