2 Port Networks - Impedance Parameters

[p75213]

Homework Statement

see attached

Homework Equations

The Attempt at a Solution

$$\eqalign{
& {V_1} = {Z_{11}}{I_1} + {Z_{12}}{I_2} \cr
& {V_2} = {Z_{22}}{I_2} + {Z_{21}}{I_1} \cr
& {\rm{ - - - - - - - - - - - - - - - - - - - - - - - - - - - }} \cr
& 2\angle 30 = 8{I_1} - j4{I_2} \cr
& 0 = - j4{I_1} + 8{I_2} & \to {I_1} = {{8{I_2}} \over {j4}} = - j2{I_2} \cr
& 2\angle 30 = - j16{I_2} - j4{I_2} \cr
& {{2\angle 30} \over {20\angle - 90}} = {I_2} \cr
& {I_2} = 0.1\angle 120{\rm{ A}} \cr} $$

As I2 is incorrect I haven't bothered with I1. Can somebody point out where the error is?

 

[NascentOxygen]

[strike]Z₁₁ is 6 ohms. EDIT: Oops, I failed to notice you'd included the 2 ohms there.[/strike]

Where it says 2∠30°, change it to 20∠30°.

 

[rude man]

Check the relation between I₁ and I₂. There's a sign error there!

Plus the magnitudes are wrong anyway unless you change the input to 20V or reduce the answers by a factor of 10 ...

Plus, the angle of I₁ is off by 10 deg.

Not a good day for the quizmaster.

 

[p75213]

Thanks guys.

I have learned a lot from this book in spite of the many errors.

 

[rezeew]

I would like to point out that the equations and calculations provided in the attempt at a solution are not completely accurate. The first two equations are correct, but the values used for Z11, Z12, Z21, and Z22 are not given in the problem and cannot be assumed. Additionally, the second to last line is incorrect as the division should be between 2∠30 and 20∠-90, not 2∠30 and 20∠90. This results in a different value for I2, which then affects the value of I1. Therefore, both I1 and I2 would need to be recalculated using the correct values for Z11, Z12, Z21, and Z22. It is important to carefully check all equations and values before proceeding with calculations to ensure accuracy.