Question

The resistance of a conductor is $5\text{ohm}$ at ${50}^{\circ }\text{C}$ and $6\text{ohm}$ at ${100}^{\circ }\text{C}$. Its resistance at $0^{\circ }\text{C}$ is

• A. $3\text{ohm}$
• B. $4\text{ohm}$
• C. $1\text{ohm}$
• D. $2\text{ohm}$

Answer 1

The correct option is B $4\text{ohm}$

We know that $R_T=R_o(1+\alpha T)$ where $R_T=$ resistance at temp $T$,
$R_o=$ resistance at $0^{\circ }\text{C}$
$\alpha =$ temperature coefficient of resistance.
$5=R_o[1+50\alpha ].....\left(1\right)$
and
$6=R_o[1+100\alpha ].....\left(2\right)$
Dividing $\left(1\right)$ by $\left(2\right)$,
$\frac{5}{6}=\frac{1+50\alpha }{1+100\alpha }$
$\Rightarrow 6+300\alpha =5+500\alpha$
or $1=200\alpha$
or $\alpha =\frac{1}{200}$
From Eq. $\left(1\right)$,
$5=R_o[1+50\times \frac{1}{200}]$
or $5=R_o[1+\frac{1}{4}]$
or $R_o=\frac{5\times 4}{5}\Omega =4\text{Ohm}$