The average power consumed -- where is my mistake

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Discussion Overview

The discussion revolves around calculating the average power consumed by various elements in a circuit, including a source and resistive loads. Participants are analyzing the results of their calculations against those provided in a textbook, exploring the implications of circuit components such as inductors.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • The initial poster presents their calculations for average power using nodal analysis and expresses confusion over discrepancies with textbook values.
  • Another participant questions the calculation of the angle θ in the presence of an inductor, suggesting that it may not be zero.
  • A different participant challenges the textbook's result for the power consumed by the source, proposing that it should deliver more power based on their calculations involving RMS values and load impedance.
  • One participant shares a resource for load impedance, indicating that their own calculations did not align with the textbook answer either.
  • Another participant references educational materials that discuss multiple types of power in circuits, suggesting complexity in understanding power calculations.

Areas of Agreement / Disagreement

Participants express disagreement regarding the calculated average power values, with no consensus reached on the correct interpretation or results. Multiple competing views on the calculations and assumptions are present.

Contextual Notes

There are unresolved assumptions regarding the circuit's configuration, the role of the inductor, and the definitions of power being used. The calculations depend on interpretations of voltage and current relationships in the circuit.

Who May Find This Useful

This discussion may be useful for students and practitioners interested in electrical engineering, circuit analysis, and power calculations, particularly those grappling with discrepancies between calculated and textbook values.

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Homework Statement


We have the circuit in the figure.I have to find the average power consumed by all the elements and the source.
PmGUCOu.png

Homework Equations


P=0.5*(I^2)*R
P=-VmImcosθ/2

The Attempt at a Solution


The inductor consumes zero inductive power.
I apply nodal analysis at node Vo

We have (6-Vo)/3=Vo/6
Vo=4
Here I find that I1=(6-4)/3=2/3
So the average power dissipated by 3 ohm
P=0.5*(4/9)*3=2/3 W
Current through 6 ohm is Vo/6=4/6
P=0.5*(16/36)*6=4/3..problem is ,in my book power dissipated by 6 ohm is 10/3...
Now,the power consumed by the source is
P=P=-(2/3)(6)cos0/2=-2 W...but the result in my book is -4W
Where is my mistake?
 
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How do you calculate ##\theta = 0## if there is an L in the circuit ?
 
Your book's result of -4 W for the average power "consumed" by the source looks very mysterious to me. I think the source should be delivering more than 4 W to the load.

Assuming that the source voltage function 6cos(t) implies a 6V peak value, then the RMS value would be 6/√2, and the frequency of the source would be ω = 1 rad/sec. Taking the equivalent impedance Z of the load and using the RMS value of the source voltage I find a real power in the load of closer to 6 W. (I say "closer to" because I'm not going to give away actual results here).
 
Here is a cheat sheet. Look here for your load impedance (its complex). I needed it to dust off what I used to know. Didn't end up with the book answer either
 
Elaia still there ?

Imperial college slides are nice too ! You learn about no less than four different Powers (one complex, the other three Re, I am and modulus) and a power factor to boot.
 
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