An alternating emf E = 110 √ 2 sin 100t volt is applied to a capacitor of 2μF, the rms value of current in the circuit is .............. mA.

Question

An alternating emf \(\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}\) volt is applied to a capacitor of \(2 \mu \mathrm{F}\), the rms value of current in the circuit is ............ \(\mathrm{mA}\).

Answer 1

Correct answer is :  22

\(C=2 \mu f ; \quad E=110 \sqrt{2}\ \sin (100\ t)\)

\(\mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{c}}=\frac{1}{100 \times 2 \times 10^{6}}\)

\(=\frac{10000}{2}=5000 \Omega\)

\(\mathrm{i}_{\mathrm{o}}=\frac{110 \sqrt{2}}{5000}\)

\(\mathrm{i}_{\mathrm{rms}}=\frac{110 \sqrt{2}}{5000 \sqrt{2}}\)

\(=\frac{110}{5} \mathrm{~mA}\)

\(=22 \mathrm{~mA}\)