Question

If the resistance of a wire is 5 $ \Omega $ and 6 $ \Omega $ at 30°C and 40°C respectively, find the temperature coefficient of resistance.

• A. \( 0.0015 \, \text{per °C} \)
• B. \( 0.0030 \, \text{per °C} \)
• C. \( 0.0020 \, \text{per °C} \)
• D. \( 0.0005 \, \text{per °C} \)

Hint:

To find the temperature coefficient of resistance, use the change in resistance with respect to temperature and divide by the product of initial resistance and temperature change.

Answer 1

The Correct Option is C

We use the formula for temperature coefficient of resistance \( \alpha \): \[ \alpha = \frac{R_2 - R_1}{R_1 (T_2 - T_1)} \] where: - \( R_1 = 5 \, \Omega \) (resistance at \( T_1 = 30^\circ \text{C} \)) - \( R_2 = 6 \, \Omega \) (resistance at \( T_2 = 40^\circ \text{C} \)) Substituting the values into the formula: \[ \alpha = \frac{6 - 5}{5 \times (40 - 30)} = \frac{1}{5 \times 10} = \frac{1}{50} = 0.002 \, \text{per °C} \]
Thus, the temperature coefficient of resistance is \( 0.0020 \, \text{per °C} \).