Question

The resistance of a wire at $ 0^\circ \text{C} $ is $ 20\, \Omega $. If the temperature coefficient of resistance is $ 5 \times 10^{-3}\, ^\circ \text{C}^{-1} $, at what temperature will the resistance double?

• A. \( 10^\circ \text{C} \)
• B. \( 200^\circ \text{C} \)
• C. \( 250^\circ \text{C} \)
• D. \( 300^\circ \text{C} \)

Hint:

Use \( R = R_0 (1 + \alpha T) \) to relate resistance change with temperature.

Answer 1

The Correct Option is B

Temperature dependence of resistance: \[ R_T = R_0 (1 + \alpha T) \] We are given: \[ \frac{R_T}{R_0} = 2, \quad \alpha = 5 \times 10^{-3} \] \[ 2 = 1 + \alpha T \Rightarrow \alpha T = 1 \Rightarrow T = \frac{1}{\alpha} = \frac{1}{5 \times 10^{-3}} = 200^\circ \text{C} \]