How does the release of heat in the circuit change if the current strength in it is reduced by 3 times

How does the release of heat in the circuit change if the current strength in it is reduced by 3 times and the resistance is increased by 3 times?

Given:

I2 = I1 / 3 – the current in the electric circuit was reduced by 3 times;

R2 = 3 * R1 – resistance increased by 3 times.

It is required to determine Q2 / Q1 – how the amount of released heat has changed.

Since the condition of the problem is not specified, we assume that the voltage of the electrical network was the same in both cases and equal to U. Let us compare the released heat for the same period of time t.

In the first case, the heat will be equal to:

Q1 = W * t = U * I1 * t = I1 * R1 * I1 * t = I12 * R1 * t.

In the second case, the heat will be equal to:

Q2 = W * t = U * I2 * t = I2 * R2 * I2 * t = I2 ^ 2 * R2 * t = (I1 / 3) ^ 2 * 3 * R1 * t = I1 ^ 2 * R1 * t / 3.

Then:

Q2 / Q1 = (I1 ^ 2 * R1 * t / 3) / (I1 ^ 2 * R1 * t) = 1/3, that is, it will decrease by 3 times.

Answer: after changes in current strength and resistance, the amount of heat released will decrease by 3 times.