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

Answer:

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, $\alpha = 5.74\times 10^{- 3}^{\circ}C$

Reference temperature, $T_{o} = 20^{\circ}C$

Resistance, $R_{t} = 2R_{o}$

Now, using the formula:

$R_{t} = R_{o}(1 + \alpha \Delta T)$

$2R_{o} = R_{o}(1 + \alpha \times (T _ T_{o}))$

$2 = 1 + 5.74\times 10^{- 3}\times (T - 20^{\circ})$

$\frac{1}{5.74\times 10^{- 3}} = T - 20^{\circ}$

$T = 174.216 + 20 = 194.216^{\circ}$

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