How to calculate power from angular frequency of LRC circuit

  • Thread starter MeMoses
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  • #1
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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
 

Answers and Replies

  • #2
gneill
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At resonance (ω = ωo) what is the magnitude of the imaginary component of the impedance? Hint: at resonance, |XL| = |XC|.
 
  • #3
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So the imaginary component would just be 0 and z=R? But what do I use for V?
 
  • #4
gneill
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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?
 
  • #5
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Zero power is dissipated right?
 
  • #6
gneill
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Zero power is dissipated right?
Nope. The supply voltage V still sees the resistor R (since Z = R at resonance).
 
  • #7
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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
 
  • #8
gneill
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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.
 
  • #9
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Yep, wasnt rms. Thanks
 

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