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Question: The temperature coefficient of resistance for a wire is \(0.00125/{^\circ}C\). At 300K its resistanc...

The temperature coefficient of resistance for a wire is 0.00125/∘C0.00125/{^\circ}C. At 300K its resistance is 1 ohm. The temperature at which the resistance becomes 2 ohm is

A

1154 K

B

1100 K

C

1400 K

D

1127 K

Answer

1127 K

Explanation

Solution

ρ1ρ2=(1+αt1)(1+αt2)⇒12=(1+0.00125×27)(1+0.00125×t)\frac{\rho_{1}}{\rho_{2}} = \frac{(1 + \alpha t_{1})}{(1 + \alpha t_{2})} \Rightarrow \frac{1}{2} = \frac{(1 + 0.00125 \times 27)}{(1 + 0.00125 \times t)}

⇒t=854∘C⇒T=1127K\Rightarrow t = 854{^\circ}C \Rightarrow T = 1127K