Question

An electric bulb is designed to consume 55 W when operated at 110 volts. It is connected to a 220 V, 50 Hz line through a choke coil in series. What should be the inductance of the coil for which the bulb gets correct voltage ?

Answer 1

Power = 55 W, Voltage = 110 V,

Resistance = $\frac{V^2}{P}$

= $\frac{110\times 110}{55}$ = 220 W

Frequency(f) = 50 Hz, $\omega =2\pi f$

= $2\pi \times 50=100\pi$

Current in the circuit

= $\frac{V}{Z}=fracV\sqrt{R^2+(\omega L{)}^2}$

Voltage drop across the resistor

= ir= $\frac{VR}{\sqrt{R^2+(\omega L{)}^2}}$

$\Rightarrow 110=\frac{220\times 200}{\sqrt{(220{)}^2+(100\pi L{)}^2}}$

= $\frac{(220{)}^2}{\sqrt{(220{)}^2+(100\pi L{)}^2}}$

$\Rightarrow 220\times 2=\sqrt{(220{)}^2+(100\pi L{)}^2}$

$\Rightarrow (220{)}^2+(100\pi L{)}^2=(440{)}^2$

$\Rightarrow 48400+{10}^4{\pi }^2{L}^2$ = 193600

$\Rightarrow {10}^4{\pi }^2{L}^2=193600-48400$

= 145200

$\Rightarrow L^2=\frac{145200}{{\pi }^2\times {10}^4}$

= 1.4726

L = 1.2135 $\cong$ 1.2 Hz