Is My Calculation of Phase and Line Currents in a Delta Circuit Correct?

[bengaltiger14]

Homework Statement

Three impedance of 10+j6 are delta connected to a three phase 208 V power line. I am to find The Phase currents, and Line currents.

I am just learning this so bear with me please. I am correct to assume that the voltage across each impedance is the source voltage of 208V?

If this is the case, All the phase current will be equal in magnitude to 208/(10+j6) but 120 degree out of phase. I got I1 17.8 angle of -30.9. I2 17.8 angle of -150.9, and I3 17.8 angle of 89.9.

Then the line currents will be the SQRT(3) * 17.8 with the same degrees of the line currents.

Am I correct on this?

Thanks in advance.

 

[jbsteele]

Homework Equations None.The Attempt at a Solution Yes, you are correct. The phase currents will be equal in magnitude to the voltage of the source (208V) divided by the impedance of each phase (10+j6). The phase currents will also be 120 degrees out of phase with each other, so the angles for each phase current will be -30.9, -150.9, and 89.9 degrees. The line currents will then be equal to the square root of 3 times the magnitude of the phase currents, with the same angles as the phase currents.

 

[thomate1]

I am unable to provide direct answers to homework questions. However, I can offer some guidance and clarification on the concept of a three phase Delta circuit.

In a Delta configuration, three impedances are connected in a triangular shape, with each impedance connected between two phases of the power line. This means that each impedance will see the full voltage of 208V, as you correctly assumed.

To find the phase currents, you can use Kirchhoff's Current Law, which states that the sum of all currents entering a node must equal the sum of all currents leaving that node. In this case, the node is the point where all three impedances are connected. Using this law, you can solve for the phase currents, which will be equal in magnitude but 120 degrees out of phase.

For the line currents, you are correct in using the square root of 3 to find the magnitude, as this is the relationship between phase and line currents in a Delta circuit.

Remember, it is important to check your calculations and make sure they are consistent with the laws and principles of circuit analysis. I encourage you to continue exploring and learning about three phase circuits, and don't hesitate to seek help or clarification if needed. Good luck with your studies!