KVPY SX SB Exam 2015 Question Paper

Question : 32 of 120

Marks: +1, -0

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 generates a pure ac)

$√ 481 V$
31V
61 V
$√3361 V$

Validate

Solution:

Voltmeter between

A\ &\ B V_L = 36 V

...(1)
between

A\ &\ C √{ V_L^2 + V^2_ R}= 39

...(2)
between

B\ &\ D √{ V_L^2 + V^2_ R} = 25

...(3)
from equation (1) & (2)

V_R^2 = 39^2-36^2

V_R = 15 V

...(4)
From Eq. (3) & (4)

V_C^2 = 25^2– 15^2

V_C = 20 V

...(5)
When connected through AD

V_\rms=√{(V_L-V_C)^2+V_R^2}

⇒

√{16^2+15^2}

⇒

√481 \V

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