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.