Question

A $60\,\mu F$ capacitor is connected to a $110\,V (rms)$, $60\,Hz$ ac supply. The rms value of current in the circuit is

• A. $1.49\,A$
• B. $14.9\,A$
• C. $2.49\,A$
• D. $24.9\,A$

Answer 1

Answer: (C)

$2.49\,A$

Answer 2

Capacitor C $=60 \mu F$ Peak voltage $V _{ rms }=110 V$ $AC$ supply freqency $f =60 Hz$ $I _{ rms }=\frac{ V _{ rms }}{ X _{ C }}$ Capacitive Reactance $X _{ C }=\frac{1}{ wC }$ $I _{ rms }=\frac{ V _{ rms }}{\frac{1}{ wC }}$ $\therefore I _{ rms }= V _{ rms } 2 \pi fC$ $\therefore I _{ rms }=110 \times 2 \pi \times 60 \times 60 \times 10^{-6}$ $\therefore I _{ rms }=2.49 \,A$ Thus the rms value of current in the circuit is $2.49 \,A$