How will the power of an electric stove change if the length of its spiral decreases by 1.5 times?

Given:

l2 = l1 / 1.5 – the length of the electric hotplate spiral was reduced by 1.5 times.

It is required to determine W2 / W1 – how the power of the electric stove will change with a decrease in the length of its spiral.

Since the problem statement is not specified, we assume that the mains voltage in both cases will be the same and equal to U.

The power of the electric stove in the first case will be equal to:

W1 = U * I1 = U * U / R1 = U ^ 2 / (r * l1 / s) = U ^ 2 * s / (r * l1), where s is the coil specific section area, r is coil resistivity.

The power of the electric stove in the second case will be equal to:

W2 = U * I2 = U * U / R2 = U ^ 2 / (r * l2 / s) = U ^ 2 * s / (r * l2) = U ^ 2 * s / (r * l1 / 1.5 ) = 1.5 * U ^ 2 * s / (r * l1).

Then:

W2 / W1 = (1.5 * U ^ 2 * s / (r * l1)) / (U ^ 2 * s / (r * l1)) = 1.5 times, that is, it will increase one and a half times.

Answer: if the length of the spiral of the electric stove is reduced by 1.5 times, its power will increase by 1.5 times.