An electric bulb is designed to consume `55 W` when operated at 110 volts. It is connected to a `220 V, 50 Hz` line through a choke coil in series. What should be the inductance of the coil for which the bulb gets correct voltage?

Explanation

Power `=55 W`, Voltage = `110 V`,
Resistance `=V^2/P`
`=(110 xx 110)/55 = 220 W`
Frequency (f) `=50 Hz`, `omega = 2 pi f`
`=2pi xx 50 xx 100 pi`
Current in the circuit
=`V/Z = (V)/(sqrt(R^2 + (omegaL)^2)`
Voltage drop across the resistor
`=ir=(VR)/(sqrt(R^2 +(omegaL)^2`
implies `110 = (220 xx 200)/(sqrt((220)^2 + (100piL)^2)`
`=(220)^2/(sqrt((220)^2 + (100 pi L)^2)`
implies `220 xx 2 = sqrt ((220)^2 + (100 pi L)^2)` implies `(220)^2 +(100 pi L)^2 = (440)^2`
implies `48400 + 10^4pi^2L^2=193600`
implies `10^4pi^2L^2 = 193600 - 48400`
`=145200`
implies `L^2 = 145200/(pi^2 xx 10^4)`
`=1.4726`
`L=1.2135 ~=1.2 Hz`