Power dissipation in a circuit (Kirchoff's Laws)

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Homework Help Overview

The discussion revolves around a circuit problem involving three resistors connected in a multiloop configuration, where participants are tasked with determining the power dissipated in the resistors using Kirchhoff's Laws.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the application of Kirchhoff's Junction and Loop Rules, attempting to set up equations based on current and voltage relationships. Some express difficulty in reducing the equations to a single variable, while others suggest substituting known values to simplify the problem.

Discussion Status

There is an ongoing exploration of the equations set up by the original poster, with some participants questioning their validity and suggesting alternative approaches. A few participants have identified potential arithmetic errors in their calculations, indicating a productive direction in the discussion.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is also a mention of an electromotive force (emf) in the circuit that may affect the analysis.

Renaldo
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Homework Statement



Three resistors, R1 = 27 Ω, R2 = 42 Ω, and R3 = 53 Ω, are connected in a multiloop circuit, as shown in the figure. Determine the amount of power dissipated in the three resistors.



Homework Equations



Junction Rule
Loop Rule


The Attempt at a Solution



I am getting mired in the math.

i2 + i3 = i1

V2 + i2R2 - i1R1 = 0

V1 + i1R1 - i3R3 = 0

I try using these equations to reduce it down to one variable, but I can't get there.
 

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Substitute the values for the voltages and resistors. You have three equations and three unknowns. You should be able to solve this system (try using Cramer's rule after making the substitutions)
 
SteamKing said:
Substitute the values for the voltages and resistors. You have three equations and three unknowns. You should be able to solve this system (try using Cramer's rule after making the substitutions)

Substituting the values helped me reduce it, but it produced the wrong answer. This leads me to believe my original equations are wrong. Is there anything that looks bad about them?
 
i believe the 1st equation will be i1+i2+i3=0... try using that
 
That isn't working. I'm not saying it isn't right, but if it is, then something else is messed up.
 
the third equation is completely wrong! how did u arrive at that first tell me
 
I'm going around the circuit. Other than that, I don't have a good rational. How do you determine it?
 
i don't think that's going to work... there's a cell and emf in the middle... instead of that, try considering the bottom loop...
 
So it would be:

V1 + V2 +i2R2 - i3R3 = 0

Is that right?
 
  • #10
yeah... doo they work out?
 
  • #11
I get something sort of close to the final answer, but it isn't right.

For power, I use:

P = i^2(R)
 
  • #12
Hold up. I found an arithmetic error in my process. I think this will work.
 
  • #13
Yep, it worked. Thanks for your help.
 
  • #14
good job
 

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