For the following circuit, find the values of RL and CL that maximize the power extracted from the generator.
Z = R + jX
XL = jωL
XC = 1/jωC
The Attempt at a Solution
Immediately, the impedance of the source can be easily determined, as the source resistor and inductor are in series:
ZS = 50 + j47.879 Ω
Normally, if the load's resistor and capacitor were in series, this could easily be solved by setting the load impedance equal to the complex conjugate of the source impedance:
ZL = 50 - j47.879 Ω
However, I can't do this since the load's resistor and capacitor are in parallel, not in series. I could determine the equivalent impedance of the load with this formula:
ZL = XCRL / XC + RL
Once I have these two equations for the load impedance, I'm kind of stumped on what to do next. I think I'm on the right track, but I've hit a brick wall. Any help would be greatly appreciated!
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