Question

A $60\mu F$ capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.

Answer 1

Given: The capacitance of the capacitor is $60\mu F$.

The RMS value of the voltage supplied is $110V$.

The frequency of the AC supply is $60Hz$.

To find: The RMS value of the current.

We know that the impedance of the capacitor is determined by:

$X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}\Rightarrow \frac{1}{2\times 3.14\times 60\times 60\times {10}^{-6}}$

$\Rightarrow 44.2\Omega$

The RMS value of the current is obtained as

$I_{rms}=\frac{E}{X_C}\Rightarrow \frac{110}{44.2}⟹2.49A$