# 2 lamps with a power of 40 and 60 W, designed for a voltage of 220 V included in this network

2 lamps with a power of 40 and 60 W, designed for a voltage of 220 V included in this network afterwards What power does each lamp consume?

Let us express the resistance of the lamps R in terms of power and voltage:
P = U * I, where P is the power, U is the voltage, I is the current in the circuit.
I = P / U.
Ohm’s law:
I = U / R;
R = U / I;
Substitute I:
R = U / (P / U) = U ^ 2 / P.
Resistance of 40 W lamp:
R1 = 220 ^ 2 V / 40 W = 1210 Ohm.
Lamp Resistance 60W:
R2 = 220 ^ 2 V / 60 W = 806.7 Ohm
Total resistance of lamps connected in series:
R3 = 2 * R1 + R2 = 2 * 1210 Ohm + 806.7 Ohm = 3226.7 Ohm.
Circuit current:
Ip = U / R3 = 220 V / 3226.7 Ohm = 0.068 A.
Lamp power 40 W:
P1 = Ip ^ 2 * R1 = (0.068 ^ 2 A ^ 2) * 1210 Ohm = 5.6 W.
Power for 60 W lamp:
P2 = Ip ^ 2 * R2 = (0.068 ^ 2 A ^ 2) * 806.7 Ohm = 3.7 W.
Answer: 5.6 watts; 5.6 watts; 3.7 watts

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