The self-inductance of a choke coil is `10mH`. When it is connected with a `10 V DC` source, then the loss of power is `20 "watt"`. When it is connected with `10 "volt" AC` source loss of power is `10"watt"`. The frequency of `AC` source will be

Options

A. 50 Hz
B. 60 Hz
C. 80 Hz
D. 100 Hz

Explanation

`P = (v ^(2))/(R)`
`R = (10 xx 10 )/(20) = 5 Omega `
For AC source
`P = 10 ` watt
`QP = v _(rms) . ( v _(rms))/( Z )xx (R)/(Z)`
`10 = 10 xx (10 . R)/( Z ^(2))`
`Z ^(2) = 10 R`
`R ^(2) + X ^(2) = 10 xx R`
`25 + X ^(2) = 10 xx 5`
`X _(L) ^(2) = 25`
`X _(L) = sqrt2 = 5`
` omega xx L = 5`
`f = ( 5 xx 10 ^(2))/(2pi) = (250)/(3.14) = 80 Hz`