Question

An $8\mu F$ capacitor is connected across $220V,50Hz$ 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

Answer: (A)

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