Question:
A 60 μF capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.
Solution:
Capacitance of capacitor, C = 60 μF = 60 × 10−6 F
Supply voltage, V = 110 V
Frequency, ν = 60 Hz
Angular frequency, $\omega=2 \pi v$
Capacitive reactance $X_{\mathrm{c}}=\frac{1}{\omega C}$
$=\frac{1}{2 \pi v C}$
$=\frac{1}{2 \times 3.14 \times 60 \times 60 \times 10^{-6}} \Omega^{-1}$
Rms value of current is given as:
$I=\frac{v}{X_{\mathrm{c}}}$
$=110 \times 2 \times 3.14 \times 60 \times 10^{-6} \times 60=2.49 \mathrm{~A}$
Hence, the rms value of current is 2.49 A.