Question

The temperature coefficient of a certain conducting material is 5.74 × 10-3 (°C)-1. (a) At what temperature would the resistance be 2 times the resistance at 20.0°C? (Use 20.0°C as the reference point in .) (b) Does this temperature hold for all copper conductors, regardless of shape or size?

Answer 1

Temperature at which the resistance is twice the resistance at
`20^(\circ)C` is
`194.216^(\circ)C`

Solution:

As per the question:

Temperature coefficient,
`\alpha = 5.74* 10^(- 3)^(\circ)C`

Reference temperature,
`T_(o) = 20^(\circ)C`

Resistance,
`R_(t) = 2R_(o)`

Now, using the formula:

`R_(t) = R_(o)(1 + \alpha \Delta T)`

`2R_(o) = R_(o)(1 + \alpha * (T _ T_(o)))`

`2 = 1 + 5.74* 10^(- 3)* (T - 20^(\circ))`

`(1)/(5.74* 10^(- 3)) = T - 20^(\circ)`

`T = 174.216 + 20 = 194.216^(\circ)`

• Yes, this temperature holds for all all the conductors of copper, irrespective of the size and shape of the conductor.