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 , and respectively, the relation between th

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 [2010]

Smart Achievers · Accepted Answer

(4)

We know that power $P = \frac{V^{2}}{R}$

$∴$ For a constant V at a particular temperature, $P \propto \frac{1}{R}$

It is given that the power of the bulbs are in the order $100 W > 60 W > 40 W$

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

Solution

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

Ans.
(4)

We know that power $P = \frac{V^{2}}{R}$

$∴$ For a constant V at a particular temperature, $P \propto \frac{1}{R}$

It is given that the power of the bulbs are in the order $100 W > 60 W > 40 W$

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

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Solution

Q. 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 R100, R60 and R40 respectively, the relation between these resistances is [2010]

1 1R100=1R40+1R60

2 R100=R40+R60

3 R100>R60>R40

4 1R100>1R60>1R40