Resistors with resistance 10-20 and 30 ohms are connected in parallel and connected to a constant voltage

Resistors with resistance 10-20 and 30 ohms are connected in parallel and connected to a constant voltage source of 60 V. What is the current in each of the resistors? in the whole chain?

R1 = 10 ohms.

R2 = 20 ohms.

R3 = 30 ohms.

U = 60V.

N1 -?

N2 -?

N3 -?

N -?

The current power N is determined by the formula: N = U ^ 2 / R, where R is the resistance of the resistor, U is the voltage at the ends of the resistor.

N1 = U1 ^ 2 / R1.

N2 = U2 ^ 2 / R2.

N3 = U3 ^ 2 / R3.

For parallel connection of resistors, the following formulas are valid: I = I1 + I2 + I3, U = U1 = U2 = U3.

N1 = (60V) ^ 2/10 ohm = 360W.

N2 = (60V) ^ 2 / 20Ω = 180W.

N3 = (60V) ^ 2/30 ohm = 120W.

Since U = U1 = U2 = U3, then according to Ohm’s law for the circuit section we express: I1 = U / R1, I2 = U / R2, I3 = U / R3.

I1 = 60 V / 10 Ohm = 6 A.

I2 = 60 V / 20 Ohm = 3 A.

I3 = 60 V / 30 Ohm = 2 A.

I = 6 A + 3 A + 2 A = 11 A.

We will find the power of the entire circuit by the formula: N = I * U.

N = 11 A * 60 V = 660 W.

Answer: N1 = 360 W, N2 = 180 W, N3 = 120 W, N = 660 W.