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

Resistance of bulb , `R = (110)^(2)/(55) =220Omega`
Voltage across bulb `V_(R) = 110 V = iR =I xx 220 implies I = (1)/(2)A`
`V_(R)^(2) + V_(L)^(2) =V^(2)`
`(110)^(2) + V_(L)^(2) = (220)^(2) implies V_(L)^(2) = (220)^(2) - (110)^(2)`
`= (330) (110) = (110)^(2) xx 3`
`V_(L) = 110sqrt3V`
`V_(L) = iX_(L) implies 110sqrt3 = (1)/(2) X_(L)`
`X_(L) = 220 sqrt3 Omega`
`X_(L) = omegaL =2pi fL = 2pi xx 50L = 220 sqrt3`
`L = ((2.2)sqrt3)/(pi) =1.2H`
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