AC Maximum Power Transfer question

[kozis]

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?

 

[berkeman]

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?

 

[kozis]

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!

 

[berkeman]

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...

 

[kozis]

yeah I can see it now..Thanks a lot !