JEE Main · 2006 · 30 Apr 2006 · Offline · Current Electricity

The resistance of a bulb filament is

100Ω

at a temperature of

10 0^{\circ} C

. If its temperature coefficient of resistance be 0.005 per

^{\circ} C

, its resistance will become

200Ω

at a temperature of

Answer: (B)

Solution

The resistance varies with temperature as

R_{T} = R_{0} [1 + α (T - T_{0})]

, taking the reference at

10 0^{\circ} C

where

R = 100 Ω

. Requiring

R = 200 Ω

gives

200 = 100 [1 + 0.005 (T - 100)]

, so

1 = 0.005 (T - 100)

and

T - 100 = 200

. The filament reaches

200 Ω

at a temperature of

30 0^{\circ} C

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option