JEE Main · 2007 · 29 Apr 2007 · Offline · Current Electricity

The resistance of a wire is 5 ohm at

5 0^{\circ} C

and 6 ohm at

10 0^{\circ} C

. The resistance of the wire at

0^{\circ} C

will be

Answer: (C)

Solution

Model the resistance by

R = R_{0} (1 + α t)

. The two readings give

5 = R_{0} (1 + 50 α)

and

6 = R_{0} (1 + 100 α)

; dividing one by the other gives

6 (1 + 50 α) = 5 (1 + 100 α)

, i.e.

6 + 300 α = 5 + 500 α

, so

α = \frac{1}{200}

per degree. Substituting back,

5 = R_{0} (1 + \frac{50}{200}) = 1.25 R_{0}

, so the resistance at

0^{\circ}

C is

R_{0} = 4 Ω

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option