The temperature coefficient of resistivity of iron is 5.0 x 10-3 / oC; that of carbon is - 0.50 x 10-3 / oC. When an iron wire and a carbon rod, each having the same 10 resistance at 20 oC, are cooled from that temperature to - 80 oC, the new ratio of the resistance of the carbon rod to the resistance of the iron wire at the lower temperature is

1. - 0.10.

2.+; 2.1.

3. - 10.

4. +; 1.9.

5.+; 10.

2. + 2.1

Explanation:

Formula for resistance is as follows

R_t = R₀ (1 + α t)

R_t is resistance at changed temperature, Ro is resistance at initial temperature, α is temperature coefficient of resistivity. t is temperature change.

For iron, R₀ = 10, α = 5 x 10⁻³, t = - 100 degree

R_t = 10 (1 + 5 x 10⁻³ x - 100)

= 10 (1 - 5 x 10⁻³ x 100)

10 x (1 -.5)

10 x. 5

For carbon

, R₀ = 10, α = - 0.5 x 10⁻³, t = - 100 degree

R_t = 10 (1 - 0. 5 x 10⁻³ x - 100)

= 10 (1 +.5 x 10⁻³ x 100)

10 x (1 +.05)

10 x 1.05

Required ratio

= 10 x 1.05 / 10 x. 5

= 105 / 50

= 21 / 10

= 2.1