Electronics Engineering (ELEX) Board Practice Exam

A copper wire has a resistance of 200 Ω at 20°C. What is the resistance of the wire at 90°C?

1. 220 Ω

2. 232 Ω

3. 252 Ω

4. 260 Ω

The correct answer is: 252 Ω

To determine the resistance of a copper wire at a different temperature, you can use the temperature coefficient of resistance formula. For copper, the temperature coefficient is approximately 0.00393 per degree Celsius. The resistance of a conductor at a temperature can be calculated with the equation: \[ R_t = R_0 (1 + \alpha (T_t - T_0)) \] Where: - \( R_t \) is the resistance at temperature \( T_t \). - \( R_0 \) is the resistance at the initial temperature \( T_0 \). - \( \alpha \) is the temperature coefficient of resistance. - \( T_t \) is the final temperature. - \( T_0 \) is the initial temperature. Given: - \( R_0 = 200 \, \Omega \) - \( T_0 = 20°C \) - \( T_t = 90°C \) Now, substituting the values into the equation: 1. Calculate the temperature difference: \[ T_t - T_0 = 90°C - 20°C = 70°C \] 2. Using the temperature coefficient for copper: \[ \alpha = 0.00393 /