Question

The temperature coefficient of resistance of a wire is 0.00125 per⁰C. At 300K its resistance is 1Ω*.* The resistance of wire will be 2Ω at

• A. 1154K
• B. 1100K
• C. 1400K
• D. 1127K

Answer 1

Answer: (D)

1127K

Answer 2

Resistance of wire varies with temperature as R =$R_{0}(1 + \alpha T_{c})$ where α is temperature coefficient of resistance

⇒ $\frac{R_{27}}{R_{T_{c}}} = \frac{R_{0}(1 + 27\alpha)}{R_{0}(1 + \alpha T_{c})} = \frac{1}{2}$

⇒ $T_{c}$= $\frac{1 + 54\alpha}{\alpha}$= $\frac{1 + 54 \times 0.00125}{0.00125}$= 854°C

$\therefore$ $T_{K}$ = $(854 + 273) = 1127K$ = 1127 K.