# Finding impedance in an ideal transformer circuit

• Engineering
• m453438
In summary, the conversation is about a challenging review question for a test. The problem is to find the impedance ab using the equation Zin = 1/a^2 * ZL. The attempt at a solution involved writing 3 KCL equations for 3 nodes and using an AC voltage source at the left feeding terminals ab. The correct answer according to the instructor is 210 - j2700 ohms.
m453438

## Homework Statement

This is a review question for my test, but I can't get the right answer, the problem is to find the impedance ab.

Zin = 1/a^2 * ZL

## The Attempt at a Solution

The 10 ohm resistor and the capacitor are in parallel and then add the 50 ohm resistor times 1/9. Doing this, I get 60-0.333j, but it is not the correct answer.

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m453438 said:

## Homework Statement

This is a review question for my test, but I can't get the right answer, the problem is to find the impedance ab.

Zin = 1/a^2 * ZL

## The Attempt at a Solution

The 10 ohm resistor and the capacitor are in parallel and then add the 50 ohm resistor times 1/9. Doing this, I get 60-0.333j, but it is not the correct answer.

Challenging question! I'd approach it by writing the 3 KCL equations for the 3 nodes. Put an AC voltage source at the left feeding terminals ab, label the upper left of the xfmr "1", the bottom of the xfmr "2", and the upper right of the xfmr "3". Write those 3 KCL equations, and see if you can solve for the voltages and currents in the circuit. Once you have those, you should be able to solve for Zin = ______

berkeman said:
Challenging question! I'd approach it by writing the 3 KCL equations for the 3 nodes. Put an AC voltage source at the left feeding terminals ab, label the upper left of the xfmr "1", the bottom of the xfmr "2", and the upper right of the xfmr "3". Write those 3 KCL equations, and see if you can solve for the voltages and currents in the circuit. Once you have those, you should be able to solve for Zin = ______

Thank You!, I would never thought of that...

The Electrician said:

I haven't tried solving yet, but the correct answer according to my instructor should be 210 - j2700 ohms. And thank you everyone for helping me out.

## 1. What is impedance in an ideal transformer circuit?

Impedance in an ideal transformer circuit refers to the total opposition to current flow in the circuit. It is a combination of resistance, inductance, and capacitance, and it is measured in ohms.

## 2. How is impedance calculated in an ideal transformer circuit?

In an ideal transformer circuit, impedance can be calculated by taking the ratio of the square of the number of turns on the secondary winding to the square of the number of turns on the primary winding, multiplied by the impedance of the load on the secondary side.

## 3. What is the relationship between impedance and voltage in an ideal transformer circuit?

In an ideal transformer circuit, the impedance on the primary side is equal to the impedance on the secondary side multiplied by the square of the turns ratio. This means that as the voltage increases on the secondary side, the impedance also increases proportionally.

## 4. How does the frequency of the input voltage affect impedance in an ideal transformer circuit?

In an ideal transformer circuit, the frequency of the input voltage has a direct impact on the impedance. As the frequency increases, the impedance also increases. This is because the inductance and capacitance in the circuit are directly proportional to frequency.

## 5. What factors can affect the impedance in an ideal transformer circuit?

The main factors that can affect impedance in an ideal transformer circuit are the number of turns on the primary and secondary windings, the frequency of the input voltage, and the type and value of the load connected to the secondary side. Additionally, the physical properties of the transformer, such as the core material and size, can also impact the impedance.

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