Question

The temperature coefficient of resistance of a wire is 0.00125 per degree celsius. At 300K its resistance is 1 ohm. The resistance of the wire will be 2 ohm at following temperature:
A. 1154K.
B. 400K.
C. 600K.
D. 1400K.

Answer 1

Hint: To solve this question, we have to remember that the resistance of a metallic conductor increases with increase in temperature. The dependence of resistance with temperature is given by, $R_t=R_0\left(1+\alpha t\right)$ where $R_0$ is resistance at $0^{0}C$ and $R_t$ is the resistance at $t^{0}C$ and $\alpha$ is the temperature coefficient of resistance.

Complete answer:
Given that,
Temperature coefficient, $\alpha$ = 0.00125.
When t = 300 K, resistance, $R_1$ = 1 ohm.
We can write this as:
$R_1=1=R_0\left(1+0.00125\times 300\right)$ ……. (i)
Similarly,
When resistance, $R_2$ = 2 ohm, temperature = t K.
We can write this as:
$R_2=2=R_0\left(1+0.00125\times t\right)$ ……… (ii)
Dividing equation (ii) by (i), we will get
$\Rightarrow {\displaystyle \frac{R_2}{R_1}}={\displaystyle \frac{2}{1}}={\displaystyle \frac{R_0\left(1+0.00125\times t\right)}{R_0\left(1+0.00125\times 300\right)}}$
Solving this,
$\Rightarrow 2\left(1+0.00125\times 300\right)=\left(1+0.00125\times t\right)$
$\Rightarrow 2.75=\left(1+0.00125\times t\right)$
$\Rightarrow {\displaystyle \frac{2.75-1}{0.00125}}=t$
$\Rightarrow 1400K=t$
Hence, the temperature of the wire will be 1400 K when resistance is 2 ohm.

So, the correct answer is “Option D”.

Note:
This type of questions can also get solved by using the formula, $\alpha ={\displaystyle \frac{R_2-R_1}{R_1\left(t_2-t_1\right)}}$ per ${}^{0}C$ or per K. We can also solve in terms of resistivity, ${\alpha }_r={\displaystyle \frac{{\rho }_2-{\rho }_1}{{\rho }_1\left(t_2-t_1\right)}}$ per ${}^{0}C$ or per K.