AC circuit power formula question

[bluesteels]

Homework Statement

An L-R-C series circuit is connected to a 120 Hz ac source
that has Vrms = 80.0 V. The circuit has a resistance of 75.0 Ω and an
impedance at this frequency of 105 Ω. What average power is delivered
to the circuit by the source?

Relevant Equations

P=I^2R
P= Irms * Vrms * Power factor
Power factor = R/Z

im kinda confused on why can't you just use the formula P=I^2R.

Can you just use Vrms or Vamp (not sure which one is it) and the value of R which is 105Ω to solve for I

Then just plug it in the formula P=I^2R. But when i did that it the wrong answer so is this formula don't work for AC circuit or am i missing something. The answer for the question is 43.5 W btw

 

[DaveE]

Homework Statement:: An L-R-C series circuit is connected to a 120 Hz ac source
that has Vrms = 80.0 V. The circuit has a resistance of 75.0 Ω and an
impedance at this frequency of 105 Ω. What average power is delivered
to the circuit by the source?
Relevant Equations:: P=I^2R
P= Irms * Vrms * Power factor
Power factor = R/Z

im kinda confused on why can't you just use the formula P=I^2R.

I think you just did it wrong, try again. Your words are good. I don't know what's wrong with your numbers.

But, a couple of ancillary comments:
1) I have no idea what Vamp means. That's OK, you do, plus probably the people in your community too. Most EEs would be left wondering what you're talking about. In my world the standard terms for voltages are Vdc = Vave, Vrms, Vac (which is Vrms plus the assumption the waveforms are sinusoidal), Vpk (the peak voltage of any waveform), and then just the generic V, which is confusing unless you know the context. All of these are different from v(t) because they represent scalar measurements, not a waveform or an instantaneous value.

2) I'm always a bit confused about what people mean when they talk about resistance and impedance in the same context. Some (electricians, mostly) think impedance refers to only the imaginary or reactive component. Which (according to me) is wrong, that would be reactance. Impedance means the real (resistive) plus the imaginary (reactive) portions. In this case they did it correctly, they mean |Z| = 105Ω and Re(Z)=75Ω.

3) I'd leave power factor out of this. It's kind of out of context this time.

Ask again if you're still confused. Show your work so we can see what's wrong.

 

[Delta2]

This is rather simple but I think you are ... overthinking it. I ll just remind you the "easy" equation $$I_{rms}=\frac{V_{rms}}{Z}$$ and I think you can figure out the rest.

Also the value of R is 75 Ohm, the value of Z is 105 Ohm.