8. Determine the value of R and C which when conntected as shown maximize the average power absorbed from the source. Determine the optimum average power.

My approach for this problem was to first solve for the Thevenin equivalent impedance for the circuit, and then use this to solve for the capacitance and resistance.

The problem is the capacitor and resistor are in parallel so I get a enormous ridiculous equation relating the two impedances.... any help?

Zth = 10 + 5j Ω
Veff = 10V

 

I got very reasonable values. First, your Z thevenin is 10 ohms in parallel with j10. After you calculate that value, then you can add 5 ohms to it. Second, your thevenin voltage is found as a voltage divider.

By the way, don't be afraid to switch back and forth between Z and Y when it is convenient.

Updated: I just realized your Zth is correct after you add the 5 ohms to the parallel combination. Now you need to find the right Vth at the terminals.

 

R = 12.5Ω
c = 40μf

 

R = 12.5Ω
c = 40μf

That's what I got too.