# Temperature coefficient of resistance – formula

The temperature dependence of resistance of a conductor can be expressed with the formula **R**_{2} = **R**_{1} ( 1 + α t), where α is the temperature coefficient of resistance of the conductor. **R**_{2} and **R**_{1} represent the resistance of the conductor at t_{2}° centigrade and t_{1}° centigrade respectively. In the equation, t = temperature difference = (t_{2} – t_{1})

## Temperature coefficient of resistance formula

The formula to find out the Temperature coefficient of resistance of the conductor α = (**R**_{2} – **R**_{1}) / (**R**_{1} 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 = (t_{2} – t_{1}) = 150 – 0 = 150°C.

R_{2} = 4.8 Ω

R_{1} = 3 Ω

Temperature coefficient of resistance α = (R_{2} – R_{1}) / (R_{1} t) = (4.8-3) /(3x 150) = 0.004 °C^{-1}