Question

The resistance of a field cold measures 50Ω at 20°C and 53Ω at 70°C. The temperature coefficient of resistance is:

• A. \( 0.0086 \, \text{°C}^{-1} \)
• B. \( 0.0087 \, \text{°C}^{-1} \)
• C. \( 0.0067 \, \text{°C}^{-1} \)
• D. \( 0.0099 \, \text{°C}^{-1} \)

Hint:

The temperature coefficient of resistance \( \alpha \) gives the change in resistance per degree change in temperature. It is calculated using the formula \( \alpha = \frac{R_2 - R_1}{R_1 \cdot (T_2 - T_1)} \).

Answer 1

The Correct Option is B

Step 1: Use the formula for temperature coefficient of resistance: \[ \alpha = \frac{R_2 - R_1}{R_1 \cdot (T_2 - T_1)} \] Where: - \( R_1 = 50 \, \Omega \), - \( R_2 = 53 \, \Omega \), - \( T_1 = 20 \, \text{°C} \), - \( T_2 = 70 \, \text{°C} \).
Step 2: Substitute the values into the formula: \[ \alpha = \frac{53 - 50}{50 \cdot (70 - 20)} = \frac{3}{50 \cdot 50} = 0.0087 \, \text{°C}^{-1} \]