Question

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. $\frac{1}{R_{100}} > \frac{1}{R_{60}} > \frac{1}{R_{40}}$

Answer 1

Answer: (D)

$R = \frac{V^2}{P} \, or \, R\propto \frac{1}{P}$
$\therefore \, \, \, \, \, \, \, \frac{1}{R_{100}} > \frac{1}{R_{60}} > \frac{1}{R_{40}}$