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A virtual current of 4A and 50Hz flows i...

A virtual current of `4A` and `50Hz` flows in an `AC` circuit contaning a coil. The power consumed in the coil is `240W`.If the virtual voltage across the coil is 100v then its inductance will be

A

1/3`pi`

B

1/`5pi` H

C

1/`7pi` H

D

1/`9pi` H

Text Solution

Verified by Experts

The correct Answer is:
B
Power consumed in the coil
P = `I_(rms)^(2)` R
`therefore R = P / I_rms^(2) = 240 / 16 = 15 Omega`
Impedance, `Z = V/I = 100/4 = 25Omega`
Now, `X_L = sqrt Z^(2) - R^(2)`
= `sqrt (25)^(2) - (15)^(2)` = 20 `Omega`
`therefore` 2pi nuL = 20`
`L = 20 / 2pi xx 50 = 1 / 5pi` H
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