Q. Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances $R_{100},\ R_{60}\ and\ R_{40},$ respectively, the relation between these resistances is
A) $\frac{1}{R_{100}} = \frac{1}{R_{40}} + \frac{1}{R_{60}}\ $
B) $R_{100} = \ R_{40} + \ R_{60}$
C) $R_{100} > \ R_{60} > \ R_{40}$
D) $\frac{1}{R_{100}} > \frac{1}{R_{60}} > \frac{1}{R_{40}}$
Explanation
(b) $\ \ \ \ \ \ \ \ \ R = \frac{V^{2}}{P}$
or $\ \ \ \ R \propto \frac{1}{P}$
$\therefore\frac{1}{R_{100}} > \frac{1}{R_{60}} > \frac{1}{R_{70}}$
Hence, the correct option is (d)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.