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7.Alternating Current
hard
An $a.c.$ source of voltage $V$ and of frequency $50\,Hz$ is connected to an inductor of $2H$ and negligible resistance. $A$ current of $r.m.s.$ value $I$ flows in the coil. When the frequency of the voltage is changed to $400\,Hz$ keeping the magnitude of $V$ the same, the current is now
A
$8I$ in phase with $V$
B
$4I$ and leading by $90^o$ from $V$
C
$I/4$ and lagging by $90^o$ from $V$
D
$I/8$ and lagging by $90^o$ from $ V$
Solution
${x}_L =\omega L$
$=2 \pi \times 50 \times 2$
$=200 \pi$
$I= \frac{V}{x_L}=\frac{V}{200 \pi}$
when frequen is yoons
$x_L =\omega L$
$=2 \pi \times 400 \times 2$
$=1600 \pi$
$i=\frac{v}{x_c}=\frac{V}{1600 \pi}=\frac{I}{8}$
Since arcuit is inductive so if will lay $90^{\circ}$ from $V$
Standard 12
Physics
