Five ideal AC voltmeters are connected as shown in the figure. Given $R = 200 Ω, L = 0.4 H a n d C = 6 μ F$ . The AC source generates 30 V of peak value at $\frac{500}{π} H z$

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The value of impedance Z of the circuit is nearly $307 Ω$

$V_{1} reads nearly 13.8 V$

$\begin{array}{l} V_{4} reads nearly 16.1 V \end{array}$

$V_{5} reads nearly 21.2 V$

answer is A, B, C, D.

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Detailed Solution

$V_{r m s} = \frac{V}{\sqrt{2}} = \frac{30.0 V}{\sqrt{2}} = 21.2 V$
$ω = 1000 r a d / s s o X_{L} = ω L = (5) (80.0 Ω) = 400 Ω a n d X_{C} = \frac{1}{ω C} = \frac{833 Ω}{5} = 167 Ω$
$Z = \sqrt{{(200 Ω)}^{2} + {(400 Ω - 167 Ω)}^{2}} = 307 Ω . I_{r m s} = \frac{V_{r m s}}{Z} = \frac{21.2 V}{307 Ω} = 0.0691 A . V_{1} r e a d s V_{R, r m s} = 13.8 V$
$V_{2} r e a d s V_{L, r m s} = 27.6 V . V_{3} r e a d s V_{C, r m s} = 11.5 V$
$V_{4} r e a d s | V_{L, r m s} - V_{C, r m s} | = | 276. V - 11.5 V | = 16.1 V . V_{5} r e a d s V_{R, r m s} = 21.2 V$
EVALUATE: The resonance frequency for this circuit is $ω_{0} = \frac{1}{\sqrt{L C}} = 645 r a d / s$ is