How Do You Solve a Norton Equivalent Circuit with a Dependent Source?

[rafehi]

Homework Statement

See picture:

http://img88.imageshack.us/img88/8319/87671967.jpg

The answer is given as phasors
I = 0.3536$$\angle$$45
Z = 2.828$$\angle$$-45

Homework Equations

The Attempt at a Solution

Z_L = jwL = 2j Ohms
Z_C = -j/(wC) = -4j Ohms

Can't do it by zeroing the sources as there's a dependent source (if it's possible, we haven't been taught it).

So then we'll have to find both the open source voltage V_OC and the short circuit current I_SC, correct?

Starting with V_OC with a node b/w the inductor and resistor (which is equal to V_OC because there is no voltage drop through the resistor due to no current going through it):
(groud at bottom node)
V_OC: $$\frac{Voc}{-4j}$$ + $$\frac{Voc - 2}{2}$$ = 1.5I_L

I_L = $$\frac{Voc - 2}{2}$$

Subbing in and arranging gives:

$$\frac{Voc}{-4j}$$ = $$\frac{Voc - 2}{4}$$

Solving gives:
V_oc = -1.414$$\angle$$45,

however I'm fairly sure it's wrong given the answers ( IZ != V).I'm not sure how to find I_SC because of the dependent current source. Have tried and can't get the correct answer - not sure if I'm going about it the right way.
i₁ = top loop current
i₂ = left loop
i₃ = right loop

Taking positive to be CW,
i₁ = 1.5i_L
i_L = i₁ - i₂

Therfore,
i_L = 2i₂

Loop two (left):
-2i₂ - 4j (i₂ - i₃) = 2$$\angle$$0

Loop three (right):
2i₃ - 4j (i₃ - i₂) = 0

Solving the two linear equations gives
i₃ = i_N = 2j

which isn't the correct answer.Any help would be greatly appreciated...

 

[Jhero]

your approach to solving this problem should be systematic and based on fundamental principles and equations. Here are some steps you can follow to solve this problem:

1. Identify the unknown quantities in the circuit: In this case, the unknown quantities are the current I and the impedance Z.

2. Write down the equations that relate these unknown quantities to the given information: In this case, the equations are I = 0.3536∠45 and Z = 2.828∠-45.

3. Use the given information to solve for the unknown quantities: In this case, you can use the given equations to solve for I and Z. Note that the given values for I and Z are in phasor form, so you need to convert them to Cartesian form before solving for the unknown quantities.

4. Check your solution: Once you have solved for I and Z, you can check your solution by substituting the values into the given equations. Your solution should satisfy the given equations.

5. If your solution does not satisfy the given equations, check your calculations and make sure you have not made any mistakes. If you are unable to find the mistake, you may need to approach the problem from a different angle or seek help from a classmate, tutor, or instructor.

6. If your solution satisfies the given equations, then you have successfully solved the problem! Congratulations!