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Q.
If a capacitor of $8\,\mu F$ is connected to a $220\,V$, $100\,Hz$ ac source and the current passing through it is $65\,mA$, then the rms voltage across it is
Alternating Current
Solution:
Here, $V_{rms} = 220\,V$,
$I_{rms} = 65\,mA = 0.065\,A$
$C=8\,\mu F=8\times10^{-6}\,F$,
$\upsilon=100\,Hz$
Capacitive reactance,
$X_{C}=\frac{1}{2\pi\upsilon C}$
$=\frac{1}{2\times3.14\times100\times8\times10^{-6}}$
$=199\,\Omega$
Then rms voltage across the capacitor is
$V_{Crms}=I_{rms}\,X_{C}=0.065\times199$
$=12.94\,V$