Current Electricity 5 Question 10
10. 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 (2010)
(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) $\frac{1}{R _{100}}>\frac{1}{R _{60}}>\frac{1}{R _{40}}$
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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).
