A rheostat is connected to a 120 V network in series with the lamp. The voltage across the lamp is 45 V.

A rheostat is connected to a 120 V network in series with the lamp. The voltage across the lamp is 45 V. What is the resistance of the rheostat if the current in the circuit is 12A?

Given:
U = 120B,
U1 = 45B,
I = 12A;
Find R2 – rheostat resistance.
Since the lamp and the rheostat are connected in series, the sum of their voltages is equal to the voltage in the network, and the current in them is the same:
U = U1 + U2,
U2 = U – U1 = 120V – 45V = 75V;
Ohm’s law:
R2 = U2 / I = 75V / 12A = 6.25 Ohm.