# A silver wire has a resistance of 2.1 Ω at 27.5 °C,

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.

Solution:

Temperature, T1 = 27.5°C

Resistance of the silver wire at T1R1 = 2.1 Ω

Temperature, T2 = 100°C

Resistance of the silver wire at T2R2 = 2.7 Ω

Temperature coefficient of silver = α

It is related with temperature and resistance as

$\alpha=\frac{R_{2}-R_{1}}{R_{1}\left(T_{2}-T_{1}\right)}$

$=\frac{2.7-2.1}{2.1(100-27.5)}=0.0039^{\circ} \mathrm{C}^{-1}$

Therefore, the temperature coefficient of silver is $0.0039^{\circ} \mathrm{C}^{-1}$.