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)

Options

A. `sqrt(481 )V`
B. 31V
C. 61V
D. `sqrt(3361)V `

Answer

A

Explanation

`V_(L) = 36 V " "`. . . (i)
Voltmeter between A and C
`sqrt(V_(L)^(2) + V_(R)^(2)) = 39 " "` . . . (ii)
Voltmeter between B and D
`sqrt(V_(C)^(2)+V_(R)^(2)) = 25 " "` . . . (iii)
From eq. (i) and (ii)
`V_(R)^(2) = 39^(2) - 36^(2) rArr V_(R) = 15 V " "` . . . (iv)
From eq. (iii) and (iv)
`V_(C)^(2) = 25^(2) - 15^(2) rArr V_(C) = 20 V `
`V_(rms) = sqrt((V_(L) - V_(C))^(2) + V_(R)^(2)) = sqrt(16^(2) + 15^(2)) = sqrt(481 )V`