Question

An $8\, \mu F$ capacitor is connected across $220\,V, 50 \,Hz $ line. What is the peak value of the charge through capacitor?

• A. $2.5 \times 10^{-3}\,C$
• B. $2.5 \times 10^{-4}\,C$
• C. $5 \times 10^{-5}\,C$
• D. $7.5 \times 10^{-2}\,C$

Answer 1

The Correct Option is A

Capacitive reactance
$X_{c}=\frac{1}{\omega C}=\frac{1}{2 \pi \times 50 \times 8 \times 10^{-6}} $
$=398\, \Omega $
$C_{\text{rms}}=220 V, V_{\text{peak}}=\sqrt{2} \times 220 $
$=311 \,V$
$q_{\text{rms}}=V_{\text{rms}} C=1.76 \times 10^{-3}\, C $
$q_{\text{rms}}=V_{\text{rms}} C=1.76 \times 10^{-3} \,C$
Peak vaiue of charge
$q_{\text{peak}}=\sqrt{2} q_{\text{rms}}=1.76 \times 10^{-3} \times \sqrt{2} $
$=2.5 \times 10^{-3} \,C$