Electro Magnetic Induction And Alternating Currents Question 419

Question: A typical light dimmer used to dim the stage lights in a theatre consists of a variable induction for L (where inductance is adjustable between zero and Lmax connected in series with a light bulb B as shown. The mains electrical supply is 220 V a 50 Hz, the light bulb is rated at 220 V, 1100 W. What Lmax is required if the rate of energy dissipation in to mains the light bulb is to be varied by a factor of 5 from its upper limit of 1100W?

Options:

A) 0.69 H

B) 0.28 H

C) 0.38 H

D) 0.56 H

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Answer:

Correct Answer: B

Solution:

  • For power to be consumed at the rate of

    11005=220W,

    we have P=EvIvcosθ 220=220×220R2+L2ω2×RR2+L2ω2

    Where R=V2P=22021100=44Ω

    220=(220)2×44442+(Lω)2;442+(Lω)2=220

    (Lω)2=220×44442

    =44(22044)=44×176=88Ω

    L=882π×f=882π×50=882×22×750=0.28H



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