Question

The temperature coefficient of resistance of a
conductor is 0.0021°C. At 250°C, resistance of
conductor is 4 12, its resistance will be 6 12 at
temperature about
(1) 625°C
(3) 625 K
(2) 425 K
(4) 550 K​

Answer 1

The resistance of the conductor will be 6.12Ω at 625°C (1) temperature.

Given,

resistance at 250°C,$R_{250}$ = 4.12Ω

temperature coefficient of the resistance,α = 0.0021°$C^{-1}$

resistance at t°C,$R_{t}$ = 6.12°C

NOW,

α = $\frac{R_{t}-R_{0} }{R_{0}t }$

∴$R_{250} = R_{0}(1+\alpha t)$

⇒$R_{0} = \frac{R_{250}}{1+\alpha t}$

⇒$R_{0}=\frac{4.12}{1+0.0021*250}$

⇒$R_{0}=2.702$Ω.

∴$t= \frac{R_{t}-R_{0}}{R_{0}\alpha}$

⇒$t=\frac{6.12-2.702}{0.0021*2.702}$

⇒$t=602.37$°C.

The required answer is 602.37°C which is nearly equal to 625°C.