how hot would a copper wire need to be for its resistance to be 2% larger than its value at room temperature (20 Centigrade)?

To determine the temperature at which the resistance of a copper wire is 2% larger than its value at room temperature (20 degrees Celsius), we can use the temperature coefficient of resistance (TCR) for copper. The TCR for copper is approximately 0.00393 ohms/ohm/degree Celsius.

First, we need to calculate the resistance of the copper wire at room temperature. The resistance of copper increases linearly with temperature according to the formula:

Rt = Ro * (1 + TCR * (T - To))

Where:
Rt = Resistance at temperature T
Ro = Resistance at reference temperature To
TCR = Temperature coefficient of resistance
T = Temperature
To = Reference temperature

In this case, we want to find the temperature (T) at which the resistance is 2% larger than the resistance at room temperature (Rt = 1.02 * Ro):

1.02 * Ro = Ro * (1 + TCR * (T - To))

We can simplify it:

1.02 = 1 + TCR * (T - To)

Now we can plug in the values:

1.02 = 1 + 0.00393 * (T - 20)

Solving for T:

0.02 = 0.00393 * (T - 20)
0.02 / 0.00393 = T - 20
5.09167 = T - 20
T = 5.09167 + 20
T ≈ 25.09 degrees Celsius

Therefore, the copper wire needs to be approximately 25.09 degrees Celsius (or 25.09°C) for its resistance to be 2% larger than its value at room temperature (20°C).

The equation and temperature coefficient of resistivity that you need to answer this can be found at:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html