Question

A $15.0\mu$F 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, when happens to the capacitive reactance and the current?

Answer 1

Given : $C=15\times {10}^{-6}F$
Rms value of voltage $V_{rms}=220V$
Frequency of source $f=50Hz$
Capacitive reactance $X_C=\frac{1}{2\pi fC}=\frac{1}{2\pi \times 50\times 15\times {10}^{-6}}=212.3\Omega$
Rms value of current $I_{rms}=\frac{V_{rms}}{X_C}=\frac{220}{212.3}=1.04A$
Peak value of current $I_o=\sqrt{2}{I}_{rms}=\sqrt{2}\times 1.04=1.465A$
Since $X_C\propto \frac{1}{f}$
So capacitive reactance gets halved if the frequency is doubled.
Also, $I_{rms}\propto \frac{1}{X_C}\propto f$
Socurrent becomes doubled if the frequency is doubled.