Power Factor for Circuit and Frequency

[I Love Pi]

For the first question, I found the power factor to be 1. Could you please help me identify what I’m doing wrong? I think I’m on the right track with drawing my circuit.

For the second question, I am trying to determine what the frequency is.

Any and all feedback is very much appreciate. Thank you!

 

[Cubist]

On your first page (which shows a power factor of 1) you're applying V=IR across the resistor only... however you aren't given the voltage across the resistor. You're given the voltage across a resistor, capacitor and inductor in series. Therefore, the first step is to calculate the impedance of the 3 series components. Then you can use Ohm's law (with the impedance).

 

[I Love Pi]

For question #1, thank you for your feedback. This was very helpful. How does my revised work look?

For question #2, I am really lost. I tried to solve it a different way but I could use some assistance.

Thank you very much!