How to Divide Complex Numbers in a Balanced Load Star Connected Circuit

[davidcowling]

When finding the current in a 4+j3 balanced load star connected circuit. with 400V line voltage at 50Hz.

Do you find the current by dividing the phase voltage approx. 230V by 4+j3 ohms?

and if so. how do you divide normal numbers with complex numbers?

your help is appreciated.

 

[vk6kro]

You put the 230 volts over 4 + j3 then multiply by 4 - j3 over 4 - j3. (You can multiply anything by 1 and it stays the same.)

So, the top line becomes 920 - j690

The bottom line becomes 16 + 9 (because J = sqrt of -1 ). =25

Dividing by 25, Current = (36.8 - J 27.6) amps

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Another way is to convert to polar notation.

4 + j 3 is 5 ohms at an angle of +36.87 degrees { 5= SQRT(16 + 9) 36.87 = tan-1 of 3 on 4}

so divide 230 by 5 and take the angle to the top line as a negative

so the current is 46 amps at an angle of - 36.87 degrees.

 

[davidcowling]

you mentioned in the first part of the question that the current is 36.8-J27.6 =

is the 27.6 the angle?

and what is the 46A magnitude?

cheers

 

[waht]

you mentioned in the first part of the question that the current is 36.8-J27.6 =

is the 27.6 the angle?

and what is the 46A magnitude?

cheers

no, just flip the complex number to polar form

 

[vk6kro]

Dividing by 25, Current = 36.8 - J 27.6 = 46 amps magnitude.

This was just a crosscheck on the second part.
The magnitude is sqrt ( 36.8 * 36.8 + 27.6 * 27.6) =46 amps
The angle of this is the inverse tan of -27.6 / 36.8 which is -36.87 degrees.

I find it helps to picture this as a right angled triangle with sides of 36.8 and 27.6 with the right angle between these.
The magnitude is the length of the 3rd side of the triangle. This works out to be 46. (you get this with Pythagoras's Theorem)
The angle is the angle between the 46 and the 36.8 sides of the triangle.

 

[╔(σ_σ)╝]

Convert everything to the phasor domain and carry on division as usual in the phasor domain.

 

[berkeman]

Thread moved from EE to Homework Help.

Please be careful, folks, responding to misplaced questions like this one. Ask youself if it might be a misplaced homework/coursework question, and if it could be, then most likely it will get moved out of the general technical forums, and the normal HH rules apply. So the OP should be doing all of this work, not you guys.