Example

Question:

A 15.0 μF capacitor is connected to a 220 V, 50 Hz source. Find the capacitive reactance and the current (rms and peak) in the circuit. If the frequency is doubled, what happens to the capacitive reactance and the current?

Solution:

The capacitive reactance is \[ X_C = \frac{1}{2\pi \nu C} = \frac{1}{2\pi (50~\text{Hz})(15.0 \times 10^{-6}~\text{F})} = 212~\Omega \] The rms current is \[ I = \frac{V}{X_C} = \frac{220~\text{V}}{212~\Omega} = 1.04~\text{A} \] The peak current is \[ i_m = \sqrt{2} I = 1.41 \times 1.04~\text{A} = 1.47~\text{A} \] If the frequency is doubled, the capacitive reactance is halved and the current is doubled.