Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the…

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, $100 \mathrm{~W}, 60 \mathrm{~W}$ and $40 \mathrm{~W}$ bulbs have filament resistances $R_{100}, R_{60}$ and $R_{40}$, respectively, the relation between these resistances is
  1. $\frac{1}{R_{100}}=\frac{1}{R_{40}}+\frac{1}{R_{60}}$
  2. $R_{100}=R_{40}+R_{60}$
  3. $R_{100}>R_{60}>R_{40}$
  4. $\frac{1}{R_{100}}>\frac{1}{R_{60}}>\frac{1}{R_{40}}$

Solution

$R=\frac{V^2}{P}$ or $R \propto \frac{1}{P}$ $\therefore \quad \frac{1}{R_{100}}>\frac{1}{R_{60}}>\frac{1}{R_{40}}$ Hence, the correct option is (d).

Asked in: JEE Advanced 2010 (Paper 1)

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