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 at 50 Hz, the light bulb is rated at 220 V, 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 ?

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 at 50 Hz, the light bulb is rated at 220 V, 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 ? (A) 0.69 H (B) 0.28 H (C) 0.38 H (D) 0.56 H

Tardigrade Admin · Accepted Answer

For power to be consumed at the rate of

\frac{1100}{5} = 220 W

, We have

P = E_{v} I_{v} cos θ

220 = \frac{220 \times 220}{R ^{2} + L ^{2} ω ^{2}} \times \frac{R}{R ^{2} + L ^{2} ω ^{2}}

where

R = \frac{V ^{2}}{P} = \frac{22 0 ^{2}}{1100} = 44 Ω

220 = \frac{( 200 ) ^{2} \times 44}{4 4 ^{2} + ( L ω ) ^{2}}; 4 4^{2} + (L ω)^{2} = 220

(L ω)^{2} = 220 \times 44 - 4 4^{2}

= 44 (220 - 44) = 44 \times 176 = 88 Ω

L = \frac{88}{2 π \times f} = \frac{88}{2 π \times 50}

= \frac{88}{2 \times 22} \times \frac{7}{50} = 0.28 H

$0.69 H$

$0.28 H$

$0.38 H$

$0.56 H$

0.69H

0.28H

0.38H

0.56H

$0.69 H$

$0.28 H$

$0.38 H$

$0.56 H$