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Q.

In the figure shows $R = 100 Ω, L = \frac{2}{π} H$ and $C = \frac{8}{π} μ F$ are connected in series with an a.c. source of $200 v o l t$ and frequency $f . V_{1}$ and $V_{2}$ are two hot-wire voltmeters. If the readings of $V_{1}$ and $V_{2}$ are same then:

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a

$f = 125 H z$

b

Current through R is 2A.

c

$f = 250 π H z$

d

$V_{1} = V_{2} = 1000 v o l t$

answer is A, C, D.

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Detailed Solution

$V_{1} = V_{2} \Rightarrow X_{L} = X_{C}$
$\Rightarrow f = \frac{1}{2 π \sqrt{L C}} = 125 H z$
$I_{0} = \frac{v_{o}}{R} = \frac{200}{100}$ $(∵ x = 0 ∴ Z = R)$
= 2A
$V_{1} = V_{2} = I X_{L} = I . (ω L) = I . L . \frac{1}{\sqrt{L C}}$
= $1 \sqrt{\frac{L}{C}} = 2 \sqrt{\frac{(2 / π)}{(8 x 10^{- 6} /_{π})}}$
= 1000 volt

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