Question

The temperature coefficient of resistance of a conductor is 0.0025 per degree Celsius l. At 200K its resistance is 4ohms. The resistance of the conductor will be 8ohms at temperature about ?
(1) 400K
(2) 300K
(3) 600K
(4) 800K

Answer 1

Given :

Resistance of conductor is 4 Ω

Temperature coefficient of resistance is 0.0025

Temperature is 200k

To Find :

Temperature at which resistance will change to 8 Ω

Solution :

let the temperature required is T K

•∆R is change in resistance of conductor due to change in temperature from 200 K to T K

∆R = 8-4 = 4Ω

•Also , ∆R is directly proportional to Intital resistance R1

•∆R is directly proportional to change in temperature ∆T

=> ∆R is directly proportional to

R1∆T

hence , ∆R = aR1∆T

•where a is temperature coefficient of resistance

a = 0.0025 = 25 × 10^-⁴

R1 = 4 Ω

∆R = 4

(25 × 10^-⁴)×4×∆T = 4

∆T = 10⁴/25

∆T = 400

T -200 = 400

T = 600 K

•Hence , at T = 600 K resistance of conductor will change to 8 Ω

so , option (3) is correct