Unbalanced star connected load with neutral

[boileroo]

Homework Statement

An unbalanced, star connected load with a neutral connection has resistances of value 2,4,1 in the a,b,c lines, and a resistance of 3 in the neutral.
Find the current flowing in each line and in the neutral

Homework Equations

I think:
Va = ZaIa + Zn(Ia+Ib+Ic)
Vb = ZbIb + Zn(Ia+Ib+Ic)
Vc = ZcIc + Zn(Ia+Ib+Ic)

The Attempt at a Solution

.'. Va = 5Ia+3Ib+3Ic
Vb = 7Ib+3Ia+3Ic
Vc = 4Ic+3Ia+3Ib

if this is right so far, i am unsure where to go next! THANK YOU!

 

[mark726]

I would approach this problem by first understanding the concept of an unbalanced star connected load. This means that the resistances in each line are not equal, and the neutral connection also has a resistance.

To find the current flowing in each line, I would use Ohm's Law (V = IR) and the equations provided in the post. I would also take into consideration that in a star connected load, the voltage across each line is the same.

Next, I would use Kirchhoff's Current Law to determine the total current flowing through the neutral connection. This law states that the sum of all currents entering a node must equal the sum of all currents leaving that node.

Using the equations provided, I would solve for the currents in each line and the neutral by setting up a system of equations and solving for the unknown variables. Once I have the values for the currents, I would verify my solution by checking if the sum of all currents entering the neutral is equal to the sum of all currents leaving the neutral.

In summary, to find the current flowing in each line and in the neutral of an unbalanced star connected load, I would use Ohm's Law, Kirchhoff's Current Law, and solve for the unknown variables using a system of equations.