Power dissipation in a circuit (Kirchoff's Laws)

In summary, three resistors with values of 27 Ω, 42 Ω, and 53 Ω are connected in a multiloop circuit. Using the Junction Rule and Loop Rule, the equations i2 + i3 = i1, V2 + i2R2 - i1R1 = 0, and V1 + i1R1 - i3R3 = 0 were utilized to determine the amount of power dissipated in the resistors. After substituting the values and solving the system of equations, the final answer was obtained using the formula P = i^2(R). There were some initial errors in the process, but after correcting them, the final answer was found.
  • #1
Renaldo
58
0

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.
 

Attachments

  • Untitled.png
    Untitled.png
    2.9 KB · Views: 539
Physics news on Phys.org
  • #2
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)
 
  • #3
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?
 
  • #4
i believe the 1st equation will be i1+i2+i3=0... try using that
 
  • #5
That isn't working. I'm not saying it isn't right, but if it is, then something else is messed up.
 
  • #6
the third equation is completely wrong! how did u arrive at that first tell me
 
  • #7
I'm going around the circuit. Other than that, I don't have a good rational. How do you determine it?
 
  • #8
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...
 
  • #9
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
 

1. What is power dissipation in a circuit?

Power dissipation in a circuit refers to the amount of energy that is converted to heat in a circuit due to the flow of electric current. This heat can be dissipated through resistors, wires, and other components in the circuit.

2. How is power dissipation related to Kirchoff's Laws?

Kirchoff's Laws, specifically Ohm's Law and the Conservation of Energy, are used to calculate power dissipation in a circuit. Ohm's Law states that the amount of current in a circuit is directly proportional to the voltage and inversely proportional to the resistance. The Conservation of Energy states that energy cannot be created or destroyed, only converted from one form to another. Therefore, the power dissipated in a circuit must equal the energy input to the circuit.

3. What factors affect power dissipation in a circuit?

The main factors that affect power dissipation in a circuit are the voltage, current, and resistance. The higher the voltage and current, the more power will be dissipated. Additionally, the higher the resistance in a circuit, the more energy will be converted to heat, resulting in higher power dissipation.

4. How can power dissipation be minimized in a circuit?

To minimize power dissipation in a circuit, the voltage and current can be reduced, and the resistance can be increased. This can be achieved by using components with lower resistance values, such as thicker wires and larger resistors. Additionally, using efficient components and avoiding excessive current can also help reduce power dissipation.

5. What are the implications of high power dissipation in a circuit?

High power dissipation in a circuit can lead to overheating of components, which can cause damage and decrease the lifespan of the circuit. It can also result in energy wastage and inefficiency. Therefore, it is important to consider power dissipation when designing and using circuits to ensure their safe and efficient operation.

Similar threads

  • Introductory Physics Homework Help
Replies
18
Views
2K
  • Introductory Physics Homework Help
Replies
22
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
683
  • Introductory Physics Homework Help
Replies
16
Views
3K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
919
Replies
2
Views
726
Back
Top