AC Maximum Power Transfer question

In summary, the goal is to determine the value of a resistor and a capacitor in a parallel circuit that will ensure maximum power is received by the load impedance. The complex impedance of Zl must be equal to the complex conjugate of the source impedance, and the impedance of a parallel RC circuit can be written as ZcZR/Zc+Zr. By substituting values and simplifying, the resistor and capacitor values can be determined.
  • #1
kozis
11
0

Homework Statement



In the circuit attached the load impedance ZL comprises a resistor in parallel with a capacitor. Determine the value of the resistor and the capacitor to ensure that the maximum power is received by the load impedance.


The Attempt at a Solution


So,if components in ZL were in series i would say that the series impedance must be equal with the conjugate of ZL take real parts and imaginary parts seperately and easily find the solutions.I think so,so correct me if I am wrong. But now I don't know what to do. I thougt that i could find the current through ZL and then the Voltage so resistor and capacitor would have same voltage across them,but with the current through each of them being different and unknown how I could calculate them?
 

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  • #2
kozis said:

Homework Statement



In the circuit attached the load impedance ZL comprises a resistor in parallel with a capacitor. Determine the value of the resistor and the capacitor to ensure that the maximum power is received by the load impedance.


The Attempt at a Solution


So,if components in ZL were in series i would say that the series impedance must be equal with the conjugate of ZL take real parts and imaginary parts seperately and easily find the solutions.I think so,so correct me if I am wrong. But now I don't know what to do. I thougt that i could find the current through ZL and then the Voltage so resistor and capacitor would have same voltage across them,but with the current through each of them being different and unknown how I could calculate them?

You are on the right track that the complex impedance of Zl has to be the complex conjugate of the source impedance (the series R & L). What is the value of Zs? And write the impedance of a parallel RC circuit for Zl. Can you then match up components in a conjugate fashion?
 
  • #3
Value of Zs should be 20 + jωL which comes up to be 20+10j so the impedance of ZL must be 20 -10j right? Is it correct to assume that this must be equal to the parallel combination, eg. ZcZR/Zc+Zr? I am a bit confused!
 
  • #4
kozis said:
Value of Zs should be 20 + jωL which comes up to be 20+10j so the impedance of ZL must be 20 -10j right? Is it correct to assume that this must be equal to the parallel combination, eg. ZcZR/Zc+Zr? I am a bit confused!

That's correct. No need for confusion!

So now just do the substitutions into your last equation and simplify it into the form a+bi and equate...
 
  • #5
yeah I can see it now..Thanks a lot !
 

What is AC maximum power transfer?

AC maximum power transfer is the concept that states when a load resistance is equal to the source resistance, the maximum power will be transferred from the source to the load.

What is the formula for calculating AC maximum power transfer?

The formula for calculating AC maximum power transfer is P = (V^2 / 4R), where P is power, V is voltage, and R is the load resistance.

Why is AC maximum power transfer important?

AC maximum power transfer is important because it allows for the efficient transfer of power from a source to a load, minimizing energy loss and maximizing the use of available power.

What factors affect AC maximum power transfer?

The factors that affect AC maximum power transfer include the source voltage, the load resistance, and the impedance of the circuit components. The length and type of transmission lines can also impact power transfer.

How can AC maximum power transfer be applied in real-world situations?

AC maximum power transfer is commonly applied in electrical engineering and power systems, where it is used to optimize power distribution and minimize energy waste. It is also used in audio systems to ensure maximum power is delivered to speakers. In telecommunications, AC maximum power transfer is utilized to improve signal strength and reduce noise.

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