Finding Currents Using Kirchhoff's Laws

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Homework Help Overview

The discussion revolves around determining the currents I1, I2, and I3 in a circuit using Kirchhoff's Laws, specifically focusing on the junction and loop rules. The problem involves internal resistance of batteries and requires careful application of circuit analysis principles.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the formulation of equations based on Kirchhoff's Laws, with some questioning the accuracy of the original equations derived by the poster. There is a focus on ensuring that all terms are correctly represented, particularly the relationship between resistances and currents.

Discussion Status

Participants are actively engaging in refining the equations, with some providing constructive feedback on the original poster's attempts. There is a recognition of the need for consistency in labeling currents and their corresponding resistances, indicating a productive direction in the discussion.

Contextual Notes

Some participants note the importance of multiplying resistances by their respective currents to accurately reflect potential changes, highlighting a common point of confusion in applying Ohm's Law within the context of Kirchhoff's Loop Rule.

Angie K.
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Homework Statement


P26_34.jpg
a. Determine the currents I1, I2, and I3 in the above figure. Assume the intermal resistance of each battery is r = 2.48Ω.

Homework Equations


Kirchhoff's Laws (Junction Rule and Loop Rule)

The Attempt at a Solution


Using Kirchhoff's Laws,
I ended up with three equations:
i1-i2-i3=0
-12i1-2.48i2=4.48
2.48i2-2.48i3=29

Using matrices to find i1, i2 and i3 I come up with answers but they are wrong. I am wondering if there is a mistake that I made and am not seeing it?
 
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Your KCL equation looks okay, but your KVL equations don't look right. Can you give more detail about how you arrived at them? Perhaps write them out showing all contributing terms as you do your "KVL walk" around the loop.
 
Angie K. said:
i1-i2-i3=0
This looks good.

Angie K. said:
-12i1-2.48i2=4.48
2.48i2-2.48i3=29
How did you get these two equations?
 
The Loop Rule Equations:

(Starting from the top, to the left of the 12V battery and going counterclockwise) -2.48-8+12-2.48i2-10-12i+12=0

(Starting from the junction of the right) 10+2.48i2-12-15+6-2.48i3-18=0
 
Angie K. said:
(Starting from the top, to the left of the 12V battery and going counterclockwise) -2.48-8+12-2.48i2-10-12i+12=0
For one thing, you forgot to multiply the internal resistance by the current to get the voltage drop.
 
Angie K. said:
The Loop Rule Equations:

(Starting from the top, to the left of the 12V battery and going counterclockwise) -2.48-8+12-2.48i2-10-12i+12=0

(Starting from the junction of the right) 10+2.48i2-12-15+6-2.48i3-18=0
I'm seeing a mix of voltage and resistance terms, some resistances multiplied by currents and some not. So as written those equations cannot be correct. You are summing potential changes around the loop, so any resistor value must be multiplied by a current in order to realize its potential change (Ohm's Law). Perhaps you could group the resistance terms for given currents in parentheses?
 
Angie K. said:
The Loop Rule Equations:

(Starting from the top, to the left of the 12V battery and going counterclockwise) -2.48-8+12-(2.48i2)-10-(12i1)+12=0

(Starting from the junction of the right) 10+(2.48i2)-12-15+6-(2.48i3)-18=0
 
(Starting from the top, to the left of the 12V battery and going counterclockwise) -2.48-8+12-(2.48i2)-10-(12i1)+12=0
Aren't 2.48 and 8 and 10 all resistances? What currents multiply them? I see only two voltage sources in the loop (both 12 V).

(Starting from the junction of the right) 10+(2.48i2)-12-15+6-(2.48i3)-18=0
Again, I don't see currents multiplying each resistance.
 
Angie K. said:
The Loop Rule Equations:

(Starting from the top, to the left of the 12V battery and going counterclockwise) -2.48i1-8i1+12-2.48i2-10i2-12i+12=0

(Starting from the junction of the right) 10i2+2.48i2-12-15i3+6-2.48i3-18i3=0
 
  • #10
That looks better! What do you find for your currents?
 
  • #11
Got it, thanks! I just needed to be consistent with labeling which current goes with which resistor.
 

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