Effect of Temperature on Resistance

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

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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 .