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

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 /