Equivalent Impedance: Find Z=84.907-j20.12 ohms

[Cursed]

Homework Statement

Find the input impedance $$Z$$. (i.e. Find $$Z$$ equivalent.)

Answer in the back of the book: $$Z=84.907-j20.12$$ ohms

[PLAIN]http://img834.imageshack.us/img834/8508/circuit.png

Homework Equations

n/a

** $$j=sqrt(-1)$$

The Attempt at a Solution

I combined the 60-ohm, 50-ohm, and -j90 ohm resistors in parallel to get:

$$\frac{29700}{1189}-\frac{9000 j}{1189}$$Then, I combined that impedance with the j50 to get:

$$\frac{2700}{184009199}+ \frac{3681000 j}{184009199}$$Adding that to the 15- and 100-ohm resistors, I get the wrong answer.

 

[skeptic2]

Can you find the current in each of the three loops?

 

[Cursed]

yes, but what dose that have to do with finding the equivalent impedance?

to find the equivalent impedance, you must combine the resistors in the phasor domain. I'm having difficulty doing that.

 

[gneill]

The equivalent impedance is also equal to the ratio of the input voltage to the input current. In this case, if you assume that the input voltage in the first loop is V, then if you can solve for the current in the first loop, I1, the input impedance will be V/I1.

So, write the KVL equations for the circuit and solve for the current in the first loop.

 

[skeptic2]

In order to find the input impedance for the whole circuit, you need to find the total current for the whole circuit, not just the first loop.

 

[gneill]

In order to find the input impedance for the whole circuit, you need to find the total current for the whole circuit, not just the first loop.

That's not true. The input impedance is *defined* to be the ratio of the input voltage to the input current. The only loop current that passes through the input voltage in this circuit is the current in the first loop.

Note that you still need to write all three loop equations in order to solve for the first loop's current, since they are interrelated.

 

[skeptic2]

You are correct, I misinterpreted your previous answer.