Temperature coefficient of resistance – formula

The temperature dependence of resistance of a conductor can be expressed with the formula R₂ = R₁ ( 1 + α t), where α is the temperature coefficient of resistance of the conductor. R₂ and R₁ represent the resistance of the conductor at t₂° centigrade and t₁° centigrade respectively. In the equation, t = temperature difference = (t₂ – t₁)

Temperature coefficient of resistance formula

The formula to find out the Temperature coefficient of resistance of the conductor α = (R₂ – R₁) / (R₁ t)

For metals, the value of the Temperature coefficient of resistance α is positive and lies between 10^-2 to 10^-4 °C^-1.

Temperature coefficient of resistance – Numerical problem solved

1 ) A metallic wire has a resistance of 3 Ω at 0°C and 4.8 Ω at 150°C. Find the Temperature coefficient of resistance.

Solution:

t = temperature difference = (t₂ – t₁) = 150 – 0 = 150°C.

R₂ = 4.8 Ω

R₁ = 3 Ω

Temperature coefficient of resistance α = (R₂ – R₁) / (R₁ t) = (4.8-3) /(3x 150) = 0.004 °C^-1