Question

A silver wire has a resistance of 2.1 Ω at 27.5° C, and a resistance of 2.7 Ω at 100°C. Determine the temperature coefficient of resistivity of silver.

Answer 1

Answer:

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Answer 2

Answer:

The temperature coefficient of resistivity = α  = 0.0039 / °C.

Explanation:

Given:

Resistance at temperature 27.5°C =  $R_{0}$ = 2.1 Ω

ΔT = change in temperature =  100°C - 27.5°C = 72.5°C.

Temperature coefficient of resistivity = α

Resistance at temperature 100°C = $R_{T}$ = 2.7 Ω

The formula to calculate the resistance at particular temperature:

$R_T= R_{0}[1 + \alpha\Delta T]$

$1 + \alpha\Delta T = \dfrac{R_{T}}{R_{0}}$

$\alpha\Delta T = \dfrac{R_{T}}{R_{0}} - 1$

Plugging the values of the above constant, we have:

$\alpha\times 72.5 = \dfrac{2.7}{2.1} - 1$

$\alpha = \dfrac{0.286}{72.5}$

α  = 0.0039 / °C