Question

A $30V,90W$ lamp is to be operated on a $120VDC$ line. For proper glow, a resistor of ..... should be connected in series with the lamp.

• A. $10$
• B. $20$
• C. $30$
• D. $40$

Answer 1

Answer: (C)

$30$

Resistance of the lamp $R=\frac{V^2}{P}$

$\therefore$ $R=\frac{{30}^2}{90}$

$⟹$ $R=10\Omega$

Current flowing through the lamp $I=\frac{P}{V}$

$\therefore$ $I=\frac{90}{30}=3A$

DC line voltage $V_d=120$ V

Resistance of the line must be $R^{\prime }=\frac{V_d}{I}$

We get $R^{\prime }=\frac{120}{3}=40\Omega$

Let $R_1$ be the external resistance to be connected in series with the lamp for proper glow.

$\therefore$ $R+R_1=R^{\prime }$

OR $10+R_1=40$

$⟹$ $R_1=30\Omega$