Question

A wire has a resistance of \( 10 \, \Omega \) at \( 20^\circ \text{C} \). If the temperature coefficient of resistance of the material is \( 0.004 \, \text{per}^\circ \text{C} \), what is the resistance of the wire at \( 50^\circ \text{C} \)?

• A. \( 12 \, \Omega \)
• B. \( 10.6 \, \Omega \)
• C. \( 15 \, \Omega \)
• D. \( 20 \, \Omega \)

Hint:

Use the formula \( R_t = R_0 (1 + \alpha (t - t_0)) \) to find the resistance at a new temperature. The temperature coefficient of resistance shows how much resistance changes per degree Celsius.

Answer 1

The Correct Option is A

Step 1: Use the formula for resistance at a new temperature \[ R_t = R_0 (1 + \alpha (t - t_0)) \] Where: - \( R_t \) is the resistance at the new temperature - \( R_0 \) is the resistance at the reference temperature - \( \alpha \) is the temperature coefficient of resistance - \( t \) is the new temperature - \( t_0 \) is the reference temperature Given: - \( R_0 = 10 \, \Omega \) - \( \alpha = 0.004 \, \text{per}^\circ \text{C} \) - \( t_0 = 20^\circ \text{C} \) - \( t = 50^\circ \text{C} \) Substitute the values into the formula: \[ R_t = 10 \times (1 + 0.004 \times (50 - 20)) = 10 \times (1 + 0.004 \times 30) = 10 \times (1 + 0.12) = 10 \times 1.12 = 12 \, \Omega \] Answer: Therefore, the resistance of the wire at \( 50^\circ \text{C} \) is \( 12 \, \Omega \). So, the correct answer is option (1).