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Q.

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), is connected in series with a light bulb B as shown. The mains electrical supply is 220 V at 50 Hz and the light bulb is rated at 220V, 1100 W. What Lmax is required if the rate of energy dissipation in the light bulb is to be varied by a factor of 5 from its upper limit of 1100 W?

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a

0.69 H

b

0.28 H

c

0.38 H

d

0.56 H

answer is B.

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Detailed Solution

For power to be consumed at the rate of11005=220 W, we have P=EvIvcosθ 220=220×220R2+L2ω2×RR2+L2ω2 where R=V2P=22021100=44Ω220=(220)2×44442+(Lω)2⇒442+(Lω)2=220×44(Lω)2=220×44−442=44(220)−44)=44×176=88 ΩL=882π×f=882π×50=882×22×750=0.28 H

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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), is connected in series with a light bulb B as shown. The mains electrical supply is 220 V at 50 Hz and the light bulb is rated at 220V, 1100 W. What Lmax is required if the rate of energy dissipation in the light bulb is to be varied by a factor of 5 from its upper limit of 1100 W?