Question

The temperature coefficient of resistance of a wire at $0^{o}C$ is $0.00125{{}^{o}C}^{-1}$. At ${25}^{o}C$ its resistance is one ohm. The resistance of the wire will be $1.2ohm$ at

• A. $225K$
• B. ${544}^{o}C$
• C. ${260}^{o}C$
• D. $185K$

Answer 1

The correct option is B ${544}^{o}C$

$R_t=R_6(1-\alpha t)$

$R_t\to$ Resistance at temperature $t$

$R_o\to$ Resistance at $0°C$

$a\to$ Temperature coefficient

$\therefore 1=R_0[1+(0.00125\times 298\left)\right]\to \left(1\right)$

$\therefore 1=R_0[1+(0.00125\times t^{\prime }\left)\right]\to \left(2\right)$

Dividing $\left(1\right)$ and $\left(2\right)$ we get

$t^{\prime }=817.52k\approx 544.37°C$