How does the current in the circuit change if the voltage is increased by 3 times, and the resistance is decreased by 3 times?

Given:

U2 = 3 * U1 – the voltage in the electrical circuit was increased by 3 times;

R2 = R1 / 3 – the resistance in the electrical circuit was reduced by 3 times.

It is required to determine I2 / I1 – how the current strength in the electrical circuit will change.

The current strength in the first case will be (Ohm’s law):

I1 = U1 / R1.

The current strength in the second case will be equal to:

I2 = U2 / R2 = 3 * U1 / (R1 / 3) = 9 * U1 / R1.

Then:

I2 / I1 = (9 * U1 / R1) / (U1 / R1) = 9 * U1 * R1 / (U1 * R1) = 9 times.

Answer: the current in the electrical circuit will increase 9 times.