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Question

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?

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Solution

Power consumed by the electric bulb, P = 55 W
Voltage at which the bulb is operated, V= 110 V
Voltage of the line, V = 220 V
Frequency of the source, v = 50 Hz
P =V2R,
where R = resistance of electric bulb
R=V2P
=110×11055=220 Ω
If L is the inductance of the coil, then total reactance of the circuit (Z) is given by,
Z = R2+ωL2
=2202+100πL2 ω=2πf
Here, ω = angular frequency of the circuit
Now, current through the bulb, I=VZ
Voltage drop across the bulb, V = VZ×R
As per question,
110=220×2202202+100πL2110=22022202+100πL2220×2=2202+100πL22202+100πL2=440248400+104π2L2=193600104π2L2=193600-48400L2=145200π2×104 =1.4726L=1.21351.2 H

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