Question

At 0°C a specimen of copper has a resistance of
4m2 and its temperature coefficient of
resistance is 1/234.5 per 'C. Find the value of
its temperature coefficient at 70°C.
​

Answer 1

Answer:

. 5.19 mΩ

Explanation:

The resistance of conductor changes when the temperature of that conductor changes.

New resistance is given by

\({{R}_{t}}={{R}_{0}}\left( 1+\alpha \text{ }\!\!\Delta\!\!\text{ }T \right)\)

Where Rt = the resistance of conductor after temperature changes

R0 = the resistance of conductor before temperature changes

α = temperature coefficient

ΔT = final temperature – initial temperature

Calculation:

Given, R0 = 4 mΩ

\(\alpha =\frac{1}{234.5}/{}^\circ ~C\)

ΔT = 70 - 0 = 70° C

Resistance at 70° C

\({{R}_{t}}={{R}_{0}}\left( 1+\frac{1}{234.5}\times 70 \right)=5.19~m\text{ }\!\!\Omega\!\!\text{ }\)

Answer 2

Answer:

The value of temperature coefficient is not constant, it depends on the initial temperature on which the increment of resistance is based

When the increment is based on initial temperature of 0°C, the value of this coefficient is α0; Which is nothing but the reciprocal of the respective inferred zero resistance temperature of the substance

But at any other temperature, temperature coefficient of electrical resistance is not same as this α0

Actually, for any material, the value of this coefficient is maximum at 0°C temperature

Say the value of this coefficient of any material at any t0 C is αt, then its value can be determined by the following equation,