Find V2 in Single Phase Transformer

[jsammut]

1. Homework Statement
Find V2. Everything else is available in the picture

Homework Equations

r1=r1+a^2*r2
x1=x1+a^2*r2
z2=a^2*r2
I1=vp/z2+r1+x1

The Attempt at a Solution

So I have used the first three formulas but it's the last one I am getting stuck on.
Since my x1 is an imaginary number how do I do this?
I'm currently stuck at I1=1200/192+4+j16
Can someone help me?

EDIT: VP=1200 NOT 1000 LIKE THE PICTURE STATES. EVERYTHING ELSE IS THE SAME

 

[cnh1995]

I'm currently stuck at I1=1200/192+4+j16

The impedance 192+4+j16 can be written as 196+j16.
Convert this into polar form. For multiplication and division of two phasors, you need their polar forms.

 

[jaus tail]

I'm currently stuck at I1=1200/192+4+j16

You can also solve as:
I1 = 1200/(196 + j6). Multiply numerator and denominator by 196 - j6.
This will remove 'j' from denominator and then you can proceed.
j * j = -1.

 

[jsammut]

Okay I got.

You can also solve as:
I1 = 1200/(196 + j6). Multiply numerator and denominator by 196 - j6.
This will remove 'j' from denominator and then you can proceed.
j * j = -1.

But then wouldn't I still have "j" in my numerator?

 

[cnh1995]

Okay I got.But then wouldn't I still have "j" in my numerator?

Yes. If you want to keep the answer in complex form, you should keep it in the form
I_real+jI_reactive. Or you can simply convert it into polar form.

 

[jsammut]

Yes. If you want to keep the answer in complex form, you should keep it in the form
I_real+jI_reactive. Or you can simply convert it into polar form.

Okay. It's my first time working with Complex numbers. Just to confirm.
In order to do 1200/196+j16 I have to convert the numerator into polar form first. Reason for this is because 1200 is basically 1200∠0 which is polar form. You can not divide polar by rectangular.

Can you divide rectangular by polar?

 

[cnh1995]

It's my first time working with Complex numbers. Just to confirm.
In order to do 1200/196+j16 I have to convert the numerator into polar form first. Reason for this is because 1200 is basically 1200∠0 which is polar form

Right.

You can not divide polar by rectangular.

Can you divide rectangular by polar?

Yes and no.

 

[jsammut]

T

Right.

Yes and no.

Thank you, been a big help?

 

[jaus tail]

It's easier to convert into polar form when dividing or multiplying, and to convert to rectangular form when adding or subtracting. But if the denominator has simple terms like 1 + i or 1 - i then multiplying num and den by 1- i or 1 + i respectively is quicker than using calculator.