Iron and copper wires of the same size are connected in parallel and connected to a power source.

Iron and copper wires of the same size are connected in parallel and connected to a power source. Which one will generate the most heat?

Given:

r1 = 0.018 Ohm * mm2 / m – copper resistivity;

r2 = 0.098 Ohm * mm2 / m – iron resistivity.

It is required to determine which of the wires will generate more heat.

According to the condition of the problem, the dimensions of the wires are the same, they are also connected in parallel.

The type of connection indicates that the voltage at the ends of the wires will be the same. Then, the current on the copper conductor will be equal to:

I1 = U / R1 = U / (r1 * l / s) = U * s / (r1 * l).

On an iron conductor it will be equal to:

I2 = U / R2 = U / (r2 * l / s) = U * s / (r2 * l).

For a period of time t, energy will be released on the copper conductor, equal to:

Q1 = W1 * t = U * I1 * t = U * U * s / (r1 * l) * t = U2 * s * t / (r1 * l).

For the same period of time, energy will be released on the iron conductor, equal to:

Q2 = W2 * t = U * I2 * t = U * U * s / (r2 * l) * t = U2 * s * t / (r2 * l).

Let’s make the replacement: k = U2 * s * t / l, then:

Q1 = k / r1 = k / 0.018.

Q2 = k / r2 = k / 0.098

Since Q1> Q2 (k / 0.018> k / 0.098), more energy will be released on the copper conductor.

Answer: more energy will be released on a copper conductor.