An ac voltmeter connected between points $A$ and $B$ in the circuit below reads $36 V$ . If it is connected between $A$ and $C$ , the reading is $39 V$ . The reading when it is connected between $B$ and $D$ is $25 V$ . What will the voltmeter read when it is connected between $A$ and $D$ ?) Assume that the voltmeter reads true rms voltage values and that the source generated a pure ac.)

\sqrt{481} V

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31 V

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61 V

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\sqrt{3361} V

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Solution

The correct option is A $\sqrt{481} V$
$V_{L} = 36 . . . . . (1)$
$V_{L}^{2} + V_{R}^{2} = (39)^{2} . . . . (2)$
$V_{R}^{2} + V_{C}^{2} = (25)^{2} . . . . . (3)$
by $(1)$ and $(2)$
$V_{R} = 15 . . . . (4)$
By $(3)$ and $(4)$
$V_{C} = 20$
By $(1), (4)$ and $(5)$
$V_{A D} = \sqrt{V_{R}^{2} + (V_{L} - V_{C})^{2}}$
$= \sqrt{481} V$ .

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The correct option is A √481VVL=36.....(1)V2L+V2R=(39)2....(2)V2R+V2C=(25)2.....(3)by (1) and (2)VR=15....(4)By (3) and (4)VC=20By (1),(4) and (5)VAD=√V2R+(VL−VC)2=√481V.