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Power in an AC Circuit

In series L...

Question

In series $L - C - R$ circuit, the voltages across $R, L$ and $C$ are $V_{R}, V_{L}$ and $V_{C}$ respectively. Then the voltage of applied a.c. source must be

A

V_{R} + V_{L} + V_{C}

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B

\sqrt{{[(V_{R})}^{2} + {(V_{L} - V_{C})}^{2}]}

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C

V_{R} + V_{C} - V_{L}

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D

{[{(V_{R} - V_{L})}^{2} + {(V_{C})}^{2}]}^{1 / 2}

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Solution

The correct option is B $\sqrt{{[(V_{R})}^{2} + {(V_{L} - V_{C})}^{2}]}$
$V = V_{R} + (V_{L} - V_{C}) j$
So value of apply voltage $V = \sqrt{{V_{R}}^{2} + {(V_{L} - V_{C})}^{2}}$

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