Problem: Find the temperature coefficient of copper at 0 degree Celsius given that the resistance of a copper coil increases from 80 ohm at 10 degree Celsius to 98.8 ohm at 62 degree Celsius.

Solution:
To find the temperature coefficient of copper at 0 degree Celsius, we need to use the formula:

α = (1/R) × (ΔR/ΔT)

where,
α = temperature coefficient of copper at 0 degree Celsius
R = resistance of the copper coil at 10 degree Celsius
ΔR = change in resistance of the copper coil (98.8 ohm - 80 ohm = 18.8 ohm)
ΔT = change in temperature (62 degree Celsius - 10 degree Celsius = 52 degree Celsius)

Step 1: Convert the temperature to Kelvin scale
To use the formula, we need to convert the temperature to Kelvin scale by adding 273.15 to each temperature value.

10 degree Celsius = 283.15 Kelvin
62 degree Celsius = 335.15 Kelvin
0 degree Celsius = 273.15 Kelvin

Step 2: Calculate the temperature coefficient
Now, we can substitute the values in the formula and solve for α.

α = (1/80) × (18.8/52) = 0.0004525 per degree Celsius

Therefore, the temperature coefficient of copper at 0 degree Celsius is 0.0004525 per degree Celsius.

Explanation:
The temperature coefficient of a material is a measure of how much its resistance changes with temperature. It is expressed in units of ohms per degree Celsius (or per Kelvin). The formula for calculating the temperature coefficient is α = (1/R) × (ΔR/ΔT), where R is the resistance of the material at a given temperature, ΔR is the change in resistance, and ΔT is the change in temperature.

In this problem, we were given the resistance of a copper coil at two different temperatures and asked to find the temperature coefficient of copper at 0 degree Celsius. We first converted the temperatures to Kelvin scale and then used the formula to calculate the temperature coefficient. The result tells us how much the resistance of copper changes per degree Celsius at 0 degree Celsius.

This calculation is important in many applications where the resistance of a material needs to be controlled or measured accurately over a range of temperatures. Knowing the temperature coefficient helps engineers design circuits and devices that will function properly under different temperature conditions.

Temperature coefficient of resistance is a constant and depends on conductor material.

so

alpha = (98.8-80)/(62-10) = 0.3615 ohm/deg C.

this value does not change at 0 degree Celsius.