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Byju's Answer

Standard XII

Physics

Impedance

An ac voltmet...

Question

An ac voltmeter connected between points A and B in the circuit below reads 36V. If it is connected between A and C, the reading is 39 V. The reading when it is connected between B and D is 25V. 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.)

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31 V

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61 V

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Solution

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