Calculating Impedance for a Source: Solution Attempt

[eehelp150]

Homework Statement

Find the impedance as seen by the source.

Homework Equations

The Attempt at a Solution

-j2||j1 = 2i
Z = 2-j1+j2+(1^2)/(j2+2+j2)
Ztotal = 2.1+0.8i
Is this correct?

 

[NascentOxygen]

What do you understand is meant by the j2 Ω on each side of the transformer? What does the j1 Ω referring to both sides indicate?

 

[eehelp150]

What do you understand is meant by the j2 Ω on each side of the transformer? What does the j1 Ω referring to both sides indicate?

Mutual inductance?

 

[cnh1995]

Mutual inductance?

Well, I don't know the direct formula for finding impedance in such coupled circuits, but you can use mesh analysis on both the sides and find the current on the source side. Source voltage/source current will be the impedance seen by the source.

 

[gneill]

Homework Statement

Find the impedance as seen by the source.
View attachment 109038

Homework Equations

The Attempt at a Solution

-j2||j1 = 2i
Z = 2-j1+j2+(1^2)/(j2+2+j2)
Ztotal = 2.1+0.8i
Is this correct?

The final result looks okay, but whether or not your work is correct is hard to say. Since all the values in the circuit are 1's and 2's, they become somewhat anonymous when we can only see digits.

The Relevant equations part of the template is there for a good reason. Could you not have quoted or referenced the equation that you employed?

 

[NascentOxygen]

What do you understand is meant by the j2 Ω on each side of the transformer? What does the j1 Ω referring to both sides indicate?

Mutual inductance?

I asked two questions, and you gave only one answer?

 

[eehelp150]

I asked two questions, and you gave only one answer?

j1 is mutual inductance
j2 on each side is the self inductance

The final result looks okay, but whether or not your work is correct is hard to say. Since all the values in the circuit are 1's and 2's, they become somewhat anonymous when we can only see digits.

The Relevant equations part of the template is there for a good reason. Could you not have quoted or referenced the equation that you employed?

Z(total left) + M^2/Z(total right)
Z on left side:2-j1+j2
M=1-> M^2 = 1
-j2||j1 = 2j
Ztotalright = (j2+2+j2)

 

[gneill]

Okay. Now I can state that you've achieved the correct result in a valid manner.

For completeness, if the mutual inductance has impedance $Z_m = 1j$ as it was specified on the circuit diagram, and letting $Z_p$ and $Z_s$ be the total primary and secondary circuit impedances, then you can write:

$Z_in = Z_p - \frac{Z_m^2}{Z_s}$

The "j" of the mutual inductance squares out to -1, cancelling with the "-" of the term.

 

[rude man]

Homework Statement

Find the impedance as seen by the source.
View attachment 109038

Homework Equations

The Attempt at a Solution

-j2||j1 = 2i+

Z = 2-j1+j2+(1^2)/(j2+2+j2)
Ztotal = 2.1+0.8i
Is this correct?

I did:
load impedance Z_L = (j1 || -j2) + 2 = 2 + j2
for the input impedance to the xfmr including the load: (-7 + j4)/(2 + j4)
then add source impedance Z_s = 2 - j1 giving total input impedance = (-7 + j4)/(2 + j4) + 2 - j1 = 2.1 + j0.8
which agrees with your result also. You seem to have come up with a faster way, to your credit!