A typical light dimmer used to dim the stage lights in a theater consists of a variable induction for L (where inductance is adjustable between zero and `L_(max)`) connected in series with a light bulb B as shown in fig. the mains electrical supply is 220 V at 50 Hz, the light bulb is rated at 220 V, 1100 W. What `(L_(max))` is required if the rate of energy dissipated in the light blub is to be varied by a factor of 5 from its upper limits of 1100 W?

Options

A. 0.69H
B. 0.28 H
C. 0.38 H
D. 0.56 H

Answer

B

Explanation

Resistance of bulb: `R=(V_(0)^(2))/(P_0) = ((220)^(2))/(1100)=44 Omega`
when L is amximum, power consumed will be minimum which is `P=(1100)/(5) = 220 W`
Now `P = I_(v)^(2) R implies 220 = I_(v)^(2) xx 44 implies (I_V) = sqrt(5)A`
`(I_V) = (E_V)/(Z) implies sqrt(5) = (220)/(sqrt(44^(2)+X_(L)^(2))) implies X_(L) = 88 Omega`
`implies 2 pi f L_(max) = 88 implies 2 xx 22/7 xx50 L_(max) = 88`
`L_(max) = 0.28 H`.