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, $$100\,W,\,60W$$ 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 :
$$\frac{1}{{{R_{100}}}} > \frac{1}{{{R_{60}}}} > \frac{1}{{{R_{40}}}}$$
Solution :
We know that $$P = \frac{{{V^2}}}{R}$$
For a given potential difference at a particular temperature
$$P \propto \frac{1}{R}$$
It is given that the powers of the bulbs are in the order
$$100W > 60W > 40W$$
$$\therefore \frac{1}{{{R_{100}}}} > \frac{1}{{{R_{60}}}} > \frac{1}{{{R_{40}}}}$$