Simplify the following circuit (all impedances)

In summary, the equivalent impedance about terminals A and B can be calculated by first simplifying the circuit by combining Z1 and Z4 in parallel, then combining that result with Z3 in series. This final result can then be added in parallel with Z2 to find the total equivalent impedance. It is important to draw the circuit with node A at the top and node B at the bottom to avoid confusion. Additionally, drawing circuits in a non-standard organization can make them appear more complicated than they actually are.
  • #1
dphysics
12
0

Homework Statement


Calculate the equivalent impedance about terminals A and B.
[PLAIN]http://img218.imageshack.us/img218/9335/circuits827.png

Z1 = -j2 ohms
Z2 = 1 ohm
Z3 = j2 ohms
Z4 = 2 ohms

Homework Equations


Adding parallel: Zeq = z1*z2/z1+z2
Adding in series Zeq = z1+z2

The Attempt at a Solution


I honestly have been staring at this problem for hours and cannot figure it out. I'm beginning to wonder if you have to perform a Y to Delta transformation about Z1, Z3, and Z4. Without doing that I cannot see how to simplify this problem. Is there another way? Or, is that the only way to solve it by doing a Y to Delta transformation about Z1, Z3, and Z4.

Help / advice much appreciated in advance.
 
Last edited by a moderator:
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  • #2
dphysics said:

Homework Statement


Calculate the equivalent impedance about terminals A and B.
[PLAIN]http://img218.imageshack.us/img218/9335/circuits827.png

Z1 = -j2 ohms
Z2 = 1 ohm
Z3 = j2 ohms
Z4 = 2 ohms

Homework Equations


Adding parallel: Zeq = z1*z2/z1+z2
Adding in series Zeq = z1+z2

The Attempt at a Solution


I honestly have been staring at this problem for hours and cannot figure it out. I'm beginning to wonder if you have to perform a Y to Delta transformation about Z1, Z3, and Z4. Without doing that I cannot see how to simplify this problem. Is there another way? Or, is that the only way to solve it by doing a Y to Delta transformation about Z1, Z3, and Z4.

Help / advice much appreciated in advance.

You are working way to hard.
Z1 & Z4 are in parallel, then in series with Z3, and that result is in parallel with z1.

Just draw the circuit with node A at the top and Node B at the bottom.
 
Last edited by a moderator:
  • #3
Thank you, haha yes I was over analyzing it way too much, I missed that.

Thanks again!
 
  • #4
Drawing circuits in a 'non-standard' organization is a favorite way to confuse.

You should see what you can do to a bridge circuit to make the arms look out of balance.
 

FAQ: Simplify the following circuit (all impedances)

1. What does it mean to "simplify" a circuit?

Simplifying a circuit means reducing the complexity of the circuit by combining or eliminating components in order to make the circuit easier to understand and analyze.

2. What is an impedance in a circuit?

Impedance is a measure of the opposition to the flow of electric current in a circuit. It includes both resistance and reactance, which is the opposition caused by the capacitance and inductance of the circuit.

3. How do you simplify a circuit with multiple impedances?

To simplify a circuit with multiple impedances, you can use techniques such as series and parallel combination of impedances, Thevenin and Norton equivalent circuits, and delta-star transformations. These methods allow you to reduce the number of components in the circuit while maintaining its overall behavior.

4. Why is it important to simplify a circuit?

Simplifying a circuit can make it easier to analyze and understand, which is crucial for troubleshooting and designing circuits. It can also help reduce the complexity and cost of a circuit, making it more practical and efficient.

5. Can simplifying a circuit change its behavior?

Yes, simplifying a circuit can change its behavior, but it should not significantly affect the overall operation of the circuit. The goal of simplifying a circuit is to reduce its complexity while preserving its functionality.

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