A rheostat is connected to a 120 V network in series with the lamp. The voltage across the rheostat is 75 V.

A rheostat is connected to a 120 V network in series with the lamp. The voltage across the rheostat is 75 V. What is the resistance of the lamp if the current in the circuit is 12 A?

Initial data: U (mains voltage) = 120 V; U1 (voltage across the rheostat) = 75 V; I (current in the circuit) = 12 A; lamp and rheostat are connected in series (I = I1 = I2).

1) Determine the voltage across the lamp from the formula for the total voltage in series connection: U = U1 + U2, whence U2 = U – U1 = 120 – 75 = 45 V.

2) Let’s calculate the resistance of the lamp: R2 = U2 / I = 45/12 = 3.75 Ohm.

Answer: The resistance of the lamp is 3.75 ohms.