AC Network?

Question

Find the load impedance 𝑍𝐿 for maximum power to the load and determine that maximum power.

Answer 1

The impedance Zo seen from ZL's terminals:

(10+j10)||(-j10) - j10 =  (10+j10)(-j10)/(10+j10 -j10)   - j10 =

= (10+j10)(-j10)/10 - j10 = 10 - j20 = Zo

By the Maximum Power Transfer Theorem,  ZL = Zo*

ZL = 10 + j20

Current leaving source = 50√2/(10+j10+10-j10) = 5√2/2 A

The reactance of the load cancels that of the output impedance.

i²*R = 25*2/4 *10 = 125W <-----

Answer 2

A voltage source has an impedance of zero ohms, so replace it with a short.  XL is in series with R: convert that to a parallel network.  Now add XC1 to that parallel network and convert to a series network.  Add the XC2 to that network.  You now have a simple series RC driving the load.  The load will be the complex conjugate of the source.