Question

The resistance of a conductor at ${20}^o$C is $3.15$ ohm and at $100$ ${}^{o}C$ is $3.75$ohm. Determine the temperature co-efficient of resistance of the conductor. What will be the resistance of the conductor at $0$ ${}^{o}C$?

Answer 1

Given: The resistance of a conductor at ${20}^{\circ }C$ is $3.15\Omega$ and at ${100}^{\circ }C$ is $3.75\Omega$.

To find the temperature co-efficient of resistance of the conductor.

Solution:

Here $R_{20}=3.15,R_{100}=3.75$

We know that $R_t=R_0(1+\alpha t)$

where $R_0=$ resistance at $0^{\circ }C$

and $R_t=$ resistance at $t^{\circ }C$

$\alpha =$ temperature coefficient of resistance

Now,

$R_{20}=3.15=R_0(1+20\alpha )....\left(i\right)$

$R_{100}=3.75=R_0(1+100\alpha )....\left(ii\right)$

Dividing (i) and (ii), we get

$\frac{R_0(1+20\alpha )}{R_0(1+100\alpha )}=\frac{3.15}{3.75}⟹3.75(1+20\alpha )=3.15(1+100\alpha )⟹3.75+75\alpha =3.15+315\alpha ⟹240\alpha =0.6⟹\alpha ={0.0025}^{\circ }{C}^{-1}$

From equation(i) ,

$R_0=\frac{3.15}{1+20\alpha }⟹R_0=\frac{3.15}{1+20\left(0.0025\right)}⟹R_0=\frac{3.15}{1+0.05}⟹R_0=3\Omega$

is the temperature co-efficient of resistance of the conductor.