Power absorbed by multiple elements

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Discussion Overview

The discussion revolves around calculating the power absorbed by various elements in a circuit at specific time intervals, particularly focusing on the behavior of a resistor and an inductor when subjected to different voltage inputs. The context includes theoretical and mathematical reasoning related to circuit analysis, specifically in relation to RL circuits.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Participants discuss the voltage function vs(t) = -10u(-t), questioning the behavior of the function at t = 0 and its implications for current through the resistor.
  • Some participants clarify that the inductor does not absorb power but instead stores and discharges energy, focusing the discussion on the resistor's role in power absorption.
  • There is a proposal to calculate the current through the resistor using the equation i(t) = Vs/R(1-e^(-Rt/L))u(-t), with some participants expressing uncertainty about its correctness.
  • Participants explore the implications of the initial current at t = 0- and how it affects power calculations, with some asserting that the current remains constant through the inductor at that moment.
  • There is a discussion about the power calculations at t = 0 and t = 200 ms, with conflicting views on how to approach the problem and whether the initial conditions have been correctly accounted for.
  • Some participants suggest using the principle of superposition to analyze the total current as a function of time, considering both the initial current and the response to the applied voltage.
  • There is a debate about the correct expression for the current at t >= 0, with references to the time constant and the need to account for both the initial current and the response to the voltage input.

Areas of Agreement / Disagreement

Participants express differing views on the correct approach to calculating power absorbed by the circuit elements, particularly regarding the treatment of the inductor and the initial conditions. There is no clear consensus on the final calculations or the correctness of the proposed solutions.

Contextual Notes

Participants note that the behavior of the inductor complicates the analysis, as it does not absorb power but rather affects the current flow. The discussion also highlights the importance of initial conditions and the need for careful consideration of the voltage inputs at different time intervals.

Who May Find This Useful

This discussion may be useful for students and practitioners in electrical engineering or physics, particularly those studying circuit analysis and the behavior of RL circuits under varying conditions.

  • #31
22.24 W at 200mS. For 0 and 0- I get 625 W and for 0+ I get 400 W.
 
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  • #32
DODGEVIPER13 said:
22.24 W at 200mS. For 0 and 0- I get 625 W and for 0+ I get 400 W.

Still part (b), right?

The current is the same for t = 0- and t = 0+. Remember, current can't change instantaneously thru an inductor. So 625W is correct but where did you get 400W?

And how did you get 22.24W? That number is the current at t = 200 ms. What is the power?
 
  • #33
Sweet so I found the power absorbed by the resistor, obviously did not need to for the inductor. But what about the power source I guess that's obvious because it supply's and does not absorb.
 
  • #34
At 200mS I got 494.6176. I got 400 from 20^2 times R which is 1. Obviously since you have questioned this its not correct
 
  • #35
Well I guess then at time 0- and 0+ are both 625 W. that leaves at time 0 which I would guess by looking at everything I have done is 625 W
 
  • #36
DODGEVIPER13 said:
Sweet so I found the power absorbed by the resistor, obviously did not need to for the inductor. But what about the power source I guess that's obvious because it supply's and does not absorb.

Right. Power supplies don't absorb power, they provide it.

Remeber from now on, U(-t) sets up the initial conditions and U(t) starts the input voltage (or whatever) at t = 0+. If the input has neiter U(t) nor U(-t) multiplying it then that input is there from t = -∞ to +∞. Like the 20V in part b.

Also, remember that the input can be time-shifted from t = 0: U(t-τ) means the input is zero until t = τ. And U[-(t - τ)] means the input is zero starting at t = -τ.
 
  • #37
Hey man thanks for all your help I have the problem right now. I really need to work a ton of theses, so I can get used to them. I will add thanks for all your posts later as my ipad won't allow it for some reason.
 
  • #38
DODGEVIPER13 said:
At 200mS I got 494.6176. I got 400 from 20^2 times R which is 1. Obviously since you have questioned this its not correct

494.61W is correct for P(200 ms). The 400 number makes no sense. The idea is, you take your expression for i(t) for which you have worked so hard, plug in t = 0.2s, then square and multiply by 1 ohm. That's for t=200ms. For t=0 you obviously let t=0 in the same i(t) expression.
 
Last edited:
  • #39
Yah 400 was my number for t=0 which I believe to be 625?
 
  • #40
DODGEVIPER13 said:
Yah 400 was my number for t=0 which I believe to be 625?

Right. P(0) = 25^2 = 625. Current at t=0 was 25A.
 
  • #41
DODGEVIPER13 said:
Hey man thanks for all your help I have the problem right now. I really need to work a ton of theses, so I can get used to them. I will add thanks for all your posts later as my ipad won't allow it for some reason.

No prob. Yer' welcome.
 
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  • #42
Heh whoops (b) is actually 20+5u(t) so that would mean at t=0- I would get I(-0)= 20 A and power would be 400 W it would. Also be 400 W at t= 0 and 0+. So at 200 mS it should be 20exp(-.8)+25(1-exp(-.8)) = 22.75 A then P( 200 mS)= 517.71 W.
 
  • #43
DODGEVIPER13 said:
Heh whoops (b) is actually 20+5u(t) so that would mean at t=0- I would get I(-0)= 20 A and power would be 400 W it would. Also be 400 W at t= 0 and 0+. So at 200 mS it should be 20exp(-.8)+25(1-exp(-.8)) = 22.75 A then P( 200 mS)= 517.71 W.

All correct! Good going.
 
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