Question

When the temperature of a wire is increased from 303 K to 356 K, the resistance of the wire increases by 10\%. The temperature coefficient of resistance of the material of the wire is:

• A. 2 × 10⁻³ ◦C ^{1.1 × 10−3 ◦C−1}
• B. 2 × 10⁻⁴ ◦C⁻¹
• C. 1.1 × 10⁻³ ◦C⁻¹
• D. 1.1 × 10⁻⁴ ◦C⁻¹

Hint:

The temperature coefficient of resistance is calculated from the fractional change in resistance per unit temperature change.

Answer 1

The Correct Option is A

The resistance-temperature relation is given by: \[ R_T = R_0 (1 + \alpha \Delta T) \] where: - \( R_T = 1.1 R_0 \) (given increase by 10\%), - \( \Delta T = 356 - 303 = 53 K \), - \( \alpha \) is the temperature coefficient. \[ 1.1 R_0 = R_0 (1 + \alpha \times 53) \] \[ 1.1 = 1 + 53\alpha \] \[ \alpha = \frac{0.1}{53} = 1.88 \times 10^{-3} \approx 2 \times 10^{-3} \]