Effect of Temperature on Resistance

In this article we are going to discuss the effect of temperature on resistance.

The resistance of a metallic conductor increases linearly with the increase in temperature. The resistance/ temperature graph is a straight line as shown below in Fig.1.

Fig.1

Now, let’s consider a metallic conductor with resistance R₀ at 0°C and  R1 at t₁°C. In the normal temperature range, the increase in resistance is R1 – R₀.

This increase in resistance is :

• directly proportional to the initial resistance i.e., R1 – R₀∝ R₀
• directly proportional to the rise in temperature i.e., R1 – R₀∝ t₁
• depends on the nature of the material

Now, if we combine the first two, we get,

R1 – R₀∝ R₀t₁

Or        R1 – R₀ = α₀ R₀t₁ …………………..(Eq.1)

Where  α₀ is a constant called temperature co-efficient of resistance at 0°C.

Its value varies with the nature of the material and temperature.

Rearranging Eq.1, we get,

R1 = R₀ ( 1 + α₀t₁ )………………….(Eq.2)

Temperature Co-efficient of Resistance

From Eq.1, we get,

α₀ = (R1 – R₀)/ R₀t₁     

Hence temperature co-efficient of resistance of a conductor is defined as the increase in resistance per ohm original resistance per °C rise in temperature.

The temperature  co-efficient α₁ at t₁°C is given by:

α₁ = α₀ /( 1+α₀t₁)

Similarly, temperature  co-efficient α₂ at t₂°C is given by:

α₂ = α₀ /( 1+α₀t₁)

The relation between α₁ and α₂ is given by:

If the resistance of a conductor is R2 at t₂°C and R1 at t₁°C and ( t₂> t₁), then,

R2 = R1 [ 1 + α₁ (t₂– t₁)]

Here α₁ is the temperature co-efficient  at t₁°C .