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An electric bulb rated 100W 40 V has to be operated at 50V 50Hz AC supply. What is the value of inductance of inductor in the bulb? Asked by joshimohit1050 | 22 Jul, 2021, 07:12: PM Expert Answer
Power rating of bulb, P = 100 W

Voltage rating of bulb , V = 40 V

Current I drawn by bulb , I = 100 / 40 = 2.5 A

Resistance of bulb , R = V / I = 40 / 2.5 = 16 Ω

To get 2.5 A current in 50V , 50Hz ac power supply , required impedence Z is given as

Z = Vm / Im = 50 / 2.5 = 20 Ω

When an inductance L is in series with bulb of resistance R , impedence Z is given as ............................. (1)
where ω is angular frequency that is given as ω = 2π f , where f = 50 Hz is frequency of alternating voltage

if we substitute R = 16 Ω in above eqn.(1) , then we get Lω = 12 Ω

Hence , inductance L = 12 / ω = 12 / ( 2π f )  = 12 /[( 2π (50) ] =  ( 0.12 / π )  H

Answered by Thiyagarajan K | 22 Jul, 2021, 07:58: PM
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