Question

When a potential difference of 10 V is applied to a coil of copper wire of mean temperature 20°C, a current of 1.0 A flows in the coil. After some time the current falls to 0.95 A yet the supply voltage remains unaltered. Determine the mean temperature of the coil given that the temperature coefficient of resistance of copper is 4.28×10⁻³/°C referred to 0°C

Answer 1

To determine the mean temperature of the coil, calculate the change in resistance using Ohm's Law and then use the formula ΔR = αRΔT. The mean temperature of the coil is 31.68°C.

Step-by-step explanation:

To determine the mean temperature of the coil, we can use the formula ΔR = αRΔT, where ΔR is the change in resistance, α is the temperature coefficient of resistance, R is the initial resistance, and ΔT is the change in temperature. We can rearrange this formula to solve for ΔT as follows:

ΔT = ΔR / (αR)

Given that the initial current is 1.0 A and the final current is 0.95 A, the change in current is 0.05 A. We can calculate the change in resistance using Ohm's Law: ΔR = ΔV / I, where ΔV is the change in potential difference. Since the supply voltage remains unaltered, the change in potential difference is 0. We plug in the values and solve for ΔT:

ΔT = 0.05 A / (4.28×10⁻³/°C * 1.0 Ω) = 11.68 °C.

The mean temperature of the coil is 20°C + 11.68°C = 31.68°C.