Hello there, I've been reading about RLC circuits and I'm not understanding the sample excercise.

https://user-images.githubuserconten...2d14e53489.png
So, basically, we have Frequency, Resistance, Inductance,effective current i (we have the effective current of the resistor and the inductor together), and effective total voltage, and we know that the power factor is 0.9, we have to find capacitance

First I started plotting graphs like this

https://user-images.githubuserconten...abacafc6f0.png in order to find an idea or where the result is.

I know from other sources that the Capacitance should be 7.7µF

This is what I've tried, I understand that with the power factor I can get the ratio between real and apparent power, which is the same as the one between real and apparent Impedance, the resistance is 100 Ohms, that means the real part of the impedance is 100.

L from the inductor is 0.3H, the Frequency given is 50Hz that means the angular velocity is 100*Pi, with the angular velocity times L we have the reactance of the Inductor, and that is 30*Pi, Since the inductor and resistance are in series we just add them

100+j(30*Pi) and that's the impedance from the first part of the circuit, what we need is to find capacitance, I know the amplitude of the voltage is 325V, and I know the effective value of the current of i (reistance-inductor) is around 1.67A, I have no idea how to find capacitor other than brute force.

If the power factor is 0.9 and the circuit is a parallel one that means we need to find the admittance that gives us this value, right?

100 is the only real resistance but it is in parallel, so does the total impedance have also 100 as real value?

I suppose I'm confused, about some ideas.