Question

A silver wire has a resistance of 4.2ohm at 27 degree celcius and 5.4 ohm at 100 degree celcius find the Temperature coefficient .

Answer 1

Answer:

Hey mate plzz refer to the attachment

Answer 2

Answer:

Temperature coefficient = $3.91\times 10^{-3}\ ^\circ C^{-1}$.

Explanation:

Given,

The silver wire has a resistance of $\rm 4.2\ \Omega$ at $\rm 27^\circ C$ and $\rm 5.4\ \Omega$ at $\rm 100^\circ C$.

such that,

$\rm R_1 = 4.2\ \Omega\\T_1= 27^\circ C\\R_2 = 5.4\ \Omega\\T_2= 100^\circ C$

The resistance of a material is related with the temperature according to the following relation:

$\rm R= R_o[1+\alpha(T-T_o)]$

where,

R = resistance of the wire at temperature T.

$\rm R_o$ = resistance of the wire at temperature $\rm T_o$.

$\alpha$ = temperature coefficient of the wire.

Putting,

$\rm R=R_1\ \text{and } R_o = R_2\\T=T_1\ \text{and } T_o = T_2$

$\rm R_2= R_1[1+\alpha(T_2-T_1)]\\1+\alpha(T_2-T_1)=\dfrac{R_2}{R_1}\\\alpha(T_2-T_1)=\dfrac{R_2}{R_1}-1\\\alpha =\dfrac{1}{(T_2-T_1)} \left(\dfrac{R_2}{R_1}-1 \right)=\dfrac{1}{(100-27)} \left(\dfrac{5.4}{4.2}-1 \right)=3.91\times 10^{-3}\ ^\circ C^{-1}$