Question

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

Answer 1

Correct Answer: 22

Given:
\[C = 2 \, \mu\text{F}, \quad E = 110\sqrt{2} \sin(100t).\]
The capacitive reactance is:
\[X_C = \frac{1}{\omega C},\]
where $\omega = 100 \, \text{rad/s}$ and $C = 2 \times 10^{-6} \, \text{F}$.
Substitute:
\[X_C = \frac{1}{100 \cdot 2 \times 10^{-6}} = \frac{1}{2 \times 10^{-4}} = 5000 \, \Omega.\]
The peak current is:
\[i_0 = \frac{E_0}{X_C},\]
where $E_0 = 110\sqrt{2} \, \text{V}$.
Substitute:
\[i_0 = \frac{110\sqrt{2}}{5000}.\]
The RMS value of current is:\[i_{\text{rms}} = \frac{i_0}{\sqrt{2}}.\]
Substitute:\[i_{\text{rms}} = \frac{110\sqrt{2}}{5000\sqrt{2}} = \frac{110}{5000}.\]
Simplify:\[i_{\text{rms}} = \frac{110}{5000} \, \text{A} = 22 \, \text{mA}.\]
Thus, the RMS value of current in the circuit is:\[i_{\text{rms}} = 22 \, \text{mA}.\]