A generator with an EMF of 150V and an internal resistance of 0.4 Ohm feeds 200

A generator with an EMF of 150V and an internal resistance of 0.4 Ohm feeds 200 lamps with a resistance of 320 Ohm each, connected in parallel. What is the voltage at the terminals of the generator? Disregard the wire resistance.

EMF = 150 V.

r = 0.4 ohm.

n = 200.

R1 = 320 ohms.

U -?

We express the voltage at the terminals of the generator U according to Ohm’s law for the section of the circuit: U = R * I, where R is the external resistance of the circuit, I is the current in the circuit.

With parallel connection of conductors, the total resistance of the circuit R is expressed by the formula: 1 / R = 1 / R1 + 1 / R2 + … + 1 / Rn.

Since all resistors are the same, then 1 / R = n / R1.

R = R1 / n.

We express the current strength I in the circuit according to Ohm’s law for a closed loop: I = EMF / (r + R).

U = R1 * EMF / n * (r + R1 / n).

U = 320 Ohm * 150 V / 200 * (0.4 Ohm + 320 Ohm / 200 = 120 V.

Answer: the voltage at the generator terminals will be U = 120 V.