IIT-JEE 2010 · Paper 1 · Physics Q59

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PhysicsSingle correct+3 / -1Question 59 of 84

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

\dfrac1{R_{100}}=\dfrac1{R_{40}}+\dfrac1{R_{60}}

R_{100}=R_{40}+R_{60}

R_{100}>R_{60}>R_{40}

\dfrac1{R_{100}}>\dfrac1{R_{60}}>\dfrac1{R_{40}}

Answer and worked solution

Official answer: D

Rated resistances. At the same rated voltage, $R=\dfrac{V^2}P$ , so $R_{100}<R_{60}<R_{40}$ when hot. The filaments are of the same kind, and their resistances scale together on cooling, so the same order holds at room temperature.

So $\dfrac1{R_{100}}>\dfrac1{R_{60}}>\dfrac1{R_{40}}$ . (A) and (B) are not general relations, and (C) has the order reversed.

(D)

Topics:Electrical power and heating

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IIT-JEE 2010 · Paper 1, Physics question 59