Maximal effect in an AC circuit

[David331]

Homework Statement

Determine R1 and C2 so that the power in A-B is maximal.

Relevant Equations

See below

Hello again, I have a solution for the question, but as it is my first time solving these types of exercises I am uncertain if I my solution is correct. The first picture represents the exercise with the circuit and the second is the just some rewrites of the circuit, in swedish. Picture 3 and 4 is my solution, in english. Any help is much appreciated.

 

[alan123hk]

This question requires long calculations to get the answer. My calculation result is R1=170 Ohm, C2=6.5uF.
I don’t know if I did something wrong that caused the calculation result to be inaccurate, but according to my calculation result is similar to yours, so I believe your calculation process is basically no problem.

 

[David331]

Thanks for the answer! So, you got exact values of R1 and C2? Maybe there is just some rounding errors in prior computations? I will doublecheck my numbers once more.

 

[alan123hk]

This is probably due to rounding errors caused by my calculations being too sloppy, because in the calculation process, I used a very limited number of significant figures many times to write down the results displayed by the handheld calculator.

 

[The Electrician]

David331, here's what I got: