A certain length of wire has its resistance measured as 20 Ω at 20°C and 40 Ω at 60°C. Calculate the temperature coefficient.

Concept of Temperature Coefficient of Resistance:

The temperature coefficient of resistance (α) quantifies how the resistance of a material changes with temperature. The formula to calculate α is:

R_t = R₀ (1 + α (T - T₀))

Where,

• R_t = Resistance at temperature T
• R₀ = Resistance at reference temperature T₀
• α = Temperature coefficient of resistance
• T = Final temperature
• T₀ = Initial temperature

Given Data:

• R₀ = 20 Ω at T₀ = 20°C
• R_t = 40 Ω at T = 60°C

Calculation:

Rearranging the formula to solve for α:

R_t = R₀ (1 + α (T - T₀))

40 = 20 (1 + α (60 - 20))

40 = 20 (1 + 40α)

Dividing both sides by 20, we get:

2 = 1 + 40α

Subtracting 1 from both sides, we get:

1 = 40α

Dividing both sides by 40, we get:

α = 1 / 40

⇒ α = 0.025 per °C

Conclusion:

Hence, the temperature coefficient of resistance is 0.025 per °C.