Question

The temperature coefficient of resistance for a wire is $0.00125^{\circ} C ^{-1}$. At $300\,K$ its resistance is $1\, \Omega$. The temperature at which the resistance becomes $1.5\, \Omega$ is?

• A. 450 K
• B. 727 K
• C. 454 K
• D. 900 K

Answer 1

Answer: (B)

$R_{t_{2}}=R_{0}\left(1+\alpha t_{2}\right)$ and $R_{t_{1}}=R_{0}\left(1+\alpha t_{1}\right)$
$\therefore \frac{R_{t_{2}}}{R_{t_{1}}}=\frac{1+\alpha t_{2}}{1+\alpha t_{1}}$
or $\frac{1.5}{1}=\frac{1+0.00125 \times t_{2}}{1+0.00125 \times 27}$
On solving we get
$t_{2}=454^{\circ} C =454+273=727 \,K$