If the current through a resistor is increased by a factor of 4, by what factor does the voltage change?

4.

Explanation:

If we apply Ohm's law to the resistor, the voltage between its terminals can be expressed as follows:

V = I*R

If the current is multiplied by 4, provided that the resistor remains in the linear zone of operation (which means that Ohm's law is still applicable), the voltage will increase in the same factor, i. e., 4.