# 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 R_{0} at 0°C and R1 at t_{1}°C. In the normal temperature range, the increase in resistance is R1 – R_{0}.

This increase in resistance is :

- directly proportional to the initial resistance i.e., R1 – R
_{0}∝ R_{0} - directly proportional to the rise in temperature i.e., R1 – R
_{0}∝ t_{1} - depends on the nature of the material

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

R1 – R_{0}∝ R_{0}t_{1}

Or R1 – R_{0 }= α_{0 }R_{0}t_{1 }…………………..(Eq.1)

Where α_{0 }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 = R_{0 }( 1 + α_{0}t_{1 })………………….(Eq.2)

#### Temperature Co-efficient of Resistance

From Eq.1, we get,

α_{0} = (R1 – R_{0})/ R_{0}t_{1 }

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 α_{1} at t_{1}°C is given by:

α_{1} = α_{0 }/( 1+α_{0}t_{1})

Similarly, temperature co-efficient α_{2} at t_{2}°C is given by:

α_{2} = α_{0 }/( 1+α_{0}t_{1})

The relation between α_{1 }and α_{2 }is given by:

If the resistance of a conductor is R2 at t_{2}°C and R1 at t_{1}°C and ( t_{2}> t_{1}), then,

R2 = R1 [ 1 + α_{1} (t_{2}– t_{1})]

Here α_{1} is the temperature co-efficient at t_{1}°C .