Question

If R₁ is the resistance of a conductor at T₁ and R₀ at T₀ and the coefficient of resistance at T₀ is α₀, the relation between these quantities is:
1. R­₁ = R₀ + α₀ (T₁ + T₀)R₀
2. R­₀ = R₁ + α₀ (T₁ - T₀)R₁
3. R­₁ = R₀ + α₀ (T₁ - T₀)
4. R­₁ = R₀ + α₀ (T₁ - T₀)R₀

Answer 1

Correct Answer - Option 4 : R­₁ = R₀ + α₀ (T₁ - T₀)R₀

Concept:

The resistance of conductor changes when the temperature of that conductor changes.

New resistance is given by:

\({{R}_{t}}={{R}_{0}}\left( 1+\alpha \text{ }\!\!\Delta\!\!\text{ }T \right)\)

Where Rt = Final resistance or the resistance of the conductor after temperature changes

R0 = Initial resistance or the resistance of the conductor before temperature changes

α = temperature coefficient 

ΔT = final temperature – initial temperature 

Calculation:

R₁ is the resistance of a conductor at T₁ and R₀ T₀ an coefficient of resistance at T₀ is α₀

The required relation is,

R­₁ = R₀ + α₀ (ΔT)R₀

= R₀ + α₀ (T₁ - T₀)R₀