In the series LCR circuit, the voltmeters reading are $V_{1} = 100 V$ and $V_{2} = 120 V$ as shown in the figure. The voltage of AC source is 130 V. The power factor of the circuit is $\frac{x}{13}$ . Calculate the value of x?

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answer is 5.

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Detailed Solution

$\begin{array}{l} \cos ϕ = \frac{V_{R}}{V} = \frac{50}{130} = \frac{5}{13} \\ V_{R}^{2} + V_{L}^{2} = {(100)}^{2} \\ 130 = \sqrt{V_{R}^{2} + {(V_{L} - V_{C})}^{2}} \\ 16900 = V_{R}^{2} + 1400 \\ V_{R} = \sqrt{2500} = 50 V \end{array}$

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