# How to calculate power from angular frequency of LRC circuit

## Homework Statement

A voltage Δv = (120 V) sin ωt (in SI units) is applied across a series combination of a 2.13 H inductor, a 12.8 μF capacitor, and a 15.0 Ω resistor.

a) Determine the angular frequency, ω0 at which the power delivered to the resistor is a maximum. = 192
b) Calculate the power at that frequency.
c) Determine the two angular frequencies ω1 and ω2 at which the power delivered is one-half the maximum value. [The Q of the circuit is approximately ω0/(ω2 - ω1).] Enter the smaller one first.

## Homework Equations

Not sure
P = Irms^2 * R
P = IV

z = sqrt(R + (wL - 1/(wC)))
z = V/I

## The Attempt at a Solution

I got part a as 192, but I'm not sure where to go with part b. I calculated z to equal 15.0685 but how do I calculate I? Do i have to use z=V/I, but then what value do I use for V? Would it just be 120V? I'm not sure where to take this, so any help would be great. Thanks

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gneill
Mentor
At resonance (ω = ωo) what is the magnitude of the imaginary component of the impedance? Hint: at resonance, |XL| = |XC|.

So the imaginary component would just be 0 and z=R? But what do I use for V?

gneill
Mentor
So the imaginary component would just be 0 and z=R? But what do I use for V?
At resonance, yes. So, given that the impedance at resonance is purely real (and equal to R), what is the power dissipated?

Zero power is dissipated right?

gneill
Mentor
Zero power is dissipated right?
Nope. The supply voltage V still sees the resistor R (since Z = R at resonance).

Ok, but won't I = V/R and then P=V*I? but i'm not getting the correct answer, unless im not supposed to use 120 for V

gneill
Mentor
Ok, but won't I = V/R and then P=V*I? but i'm not getting the correct answer, unless im not supposed to use 120 for V
What value did you get for the power? Do you know what the correct value should be?

It could be that the 120V is a peak value rather than rms.

Yep, wasnt rms. Thanks