A copper conductor has its specific resistance of 1.6 × 10−6 ohm-cm at 0°C and a resistance temperature coefficient of 1/254.5 per °C at 20°C. Find (i) the specific resistance and (ii) the resistance - temperature coefficient at 60°C.Read more on Sarthaks.com - https://www.sarthaks.com/457433/copper-conductor-specific-resistance-ohm-resistance-temperature-coefficient-254-20c

(i) To find the specific resistance at 60°C, we first need to find the change in temperature. The change in temperature (ΔT) is 60°C - 20°C = 40°C.

The formula to find the new resistance at a different temperature is:

Rt = R0 * (1 + α * ΔT)

Where: Rt is the resistance at the new temperature, R0 is the initial resistance, α is the temperature coefficient of resistance, and ΔT is the change in temperature.

Given: R0 = 1.6 × 10−6 ohm-cm, α = 1/254.5 per °C, and ΔT = 40°C.

Substituting these values into the formula, we get:

Rt = 1.6 × 10−6 * (1 + 1/254.5 * 40) = 1.6 × 10−6 * (1 + 0.157) = 1.6 × 10−6 * 1.157 = 1.85 × 10−6 ohm-cm.

So, the specific resistance at 60°C is 1.85 × 10−6 ohm-cm.

(ii) The resistance temperature coefficient at a given temperature can be calculated using the formula:

αt = α0 / (1 + α0 * ΔT)

Where: αt is the resistance temperature coefficient at the new temperature, α0 is the initial resistance temperature coefficient, and ΔT is the change in temperature.

Given: α0 = 1/254.5 per °C, and ΔT = 40°C.

Substituting these values into the formula, we get:

αt = 1/254.5 / (1 + 1/254.5 * 40) = 1/254.5 / (1 + 0.157) = 1/254.5 / 1.157 = 1/294.3 per °C.

So, the resistance temperature coefficient at 60°C is 1/294.3 per °C.