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

The correct option is D $\frac{1}{R_{100}}>\frac{1}{R_{60}}>\frac{1}{R_{40}}$

We know that power is given by-

$P=\frac{V^2}{R}$

Now, in circuit with same voltage the wattage of bulbs are written.

$⟹P\propto \frac{1}{R}$

Now, $100W>60W>40W$

$⟹P_{100}>P_{60}>P_{40}$

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

Answer-(D)