A silver wire has resistance of 2.1ohms at 27.8 degree celsius and resistance of 2.8ohms at 98 degree celsius. Determine the temperature coefficient of resistance of silver wire and its resistance at zero deg.

To determine the temperature coefficient of resistance (α) of a material, we can use the formula:

α = (R2 - R1) / (R1 * (T2 - T1))

where:
- R1 and R2 are the resistances of the material at temperatures T1 and T2, respectively.

In this case, we have:
- R1 = 2.1 ohms at 27.8 degrees Celsius
- R2 = 2.8 ohms at 98 degrees Celsius
- T1 = 27.8 degrees Celsius
- T2 = 98 degrees Celsius

Plugging the values into the formula, we get:

α = (2.8 - 2.1) / (2.1 * (98 - 27.8))

Simplifying the equation:

α = 0.7 / (2.1 * 70.2)
= 0.7 / 147.42
≈ 0.004745 ohms/°C

Therefore, the temperature coefficient of resistance (α) for the silver wire is approximately 0.004745 ohms/°C.

To determine the resistance of the silver wire at zero degrees Celsius, we can use the formula:

R0 = R - α * R * T

where:
- R0 is the resistance at zero degrees Celsius
- R is the resistance at the given temperature
- α is the temperature coefficient of resistance
- T is the given temperature

In this case, we want to find R0 when T = 0 degrees Celsius. Therefore, the equation becomes:

R0 = R - α * R * 0

Since the last term in the equation becomes zero, we can simplify it further:

R0 = R

So, the resistance of the silver wire at zero degrees Celsius is equal to its resistance at any given temperature. In this case, R0 = 2.1 ohms.