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 $L_{\max })$, is connected in series with a light bulb $B$ as shown. The mains electrical supply is $220V$ at $50Hz$ and the light bulb is rated at $220V,1100W$. What $L_{\max }$ 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 $1100W$ ?

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

Answer 1

Answer: (B)

For power to be consumed at the rate of
$\frac{1100}{5}=220W$,
we have $P=E_v{I}_v\cos \theta$
$220=\frac{220\times 220}{\sqrt{R^2+L^2{\omega }^2}}\times \frac{R}{\sqrt{R^2+L^2{\omega }^2}}$
where $R=\frac{V^2}{P}=\frac{220^2}{1100}=44\Omega$
$220=\frac{(220{)}^2\times 44}{44^2+(L\omega {)}^2}$
$\Rightarrow 44^2+(L\omega {)}^2=220\times 44$
$(L\omega {)}^2=\sqrt{220\times 44-44^2}$
$=\sqrt{44(220)-44)}$
$=\sqrt{44\times 176}=88\Omega$
$L=\frac{88}{2\pi \times f}=\frac{88}{2\pi \times 50}$
$=\frac{88}{2\times 22}\times \frac{7}{50}=0.28H$