Maximum Power Transfer Ideal Transformer

In summary, the conversation discusses finding the value of ZL for maximum average power transfer and the maximum power in a given circuit. The method of moving ZL from the secondary to the primary coil is used, along with the formula for calculating power dissipated in the load. The final answer is the real component of SI, which represents the maximum power.
  • #1
OmniNewton
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5

Homework Statement


upload_2016-12-13_10-26-7.png

Given the following circuit find the value of ZL for maximum average power transfer and find the maximum power.

Homework Equations


n = N2/N1
V2/V1 = N2/N1
I2/I1= N1/N2

The Attempt at a Solution


move ZL from the secondary coil to the primary coil using Zs* = ZL/n^2
ZL = 4(3+2j) = 12 +8j
P = (12)^2/ [(8)(12)] = 1.5W

I want to verify if this is the right method
 
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  • #2
OmniNewton said:
ZL = 4(3+2j) = 12 +8j
Right.
OmniNewton said:
P = (12)^2/ [(8)(12)] = 1.5W
This is incorrect. Looking at the equivalent circuit referred to primary, which formula will you use for calculating power dissipated in the load?
 
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  • #3
cnh1995 said:
Right.

This is incorrect. Looking at the equivalent circuit referred to primary, which formula will you use for calculating power dissipated in the load?

I see thank you for the response. When dealing with this problem would you determine the current I by dividing the given voltage by the sum the 2 impedances. Then we can say that S= I^2Z so P = the real component of S
 
  • #4
OmniNewton said:
I see thank you for the response. When dealing with this problem would you determine the current I by dividing the given voltage by the sum the 2 impedances. Then we can say that S= I^2Z so P = the real component of S
Right.
Note that the power you get will be the real power since there is no reactive power in the circuit. So, S=P.
 
  • #5
And this would be the maximum power?
 
  • #6
OmniNewton said:
And this would be the maximum power?
Yes.
 
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  • #7
Thank you sir!
 

1. What is the maximum power transfer theorem?

The maximum power transfer theorem states that maximum power is transferred from a source to a load when the impedance of the load is equal to the complex conjugate of the source impedance. This is known as the "maximum power transfer condition."

2. What is an ideal transformer?

An ideal transformer is a theoretical device that can transfer electrical energy from one circuit to another without any losses. It consists of two coils of wire, known as the primary and secondary coils, which are magnetically coupled but electrically isolated. The ratio of the number of turns in the primary and secondary coils determines the voltage and current levels in the secondary circuit.

3. How does an ideal transformer affect the maximum power transfer theorem?

An ideal transformer does not affect the maximum power transfer theorem as it is designed to have no losses. This means that the complex conjugate of the source impedance will still be equal to the load impedance, resulting in maximum power transfer.

4. What is the efficiency of an ideal transformer in maximum power transfer?

Since an ideal transformer has no losses, its efficiency in maximum power transfer is 100%. This means that all the power from the source is transferred to the load without any losses.

5. What are the practical limitations of an ideal transformer in maximum power transfer?

In real-world applications, ideal transformers do not exist, and there will always be some losses due to factors such as resistance in the coils and magnetic hysteresis. Additionally, the load impedance may not always be equal to the complex conjugate of the source impedance, making it difficult to achieve maximum power transfer. These practical limitations can reduce the efficiency of an ideal transformer in maximum power transfer.

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