Using Kirchhoff's laws for multiple batteries and resistors

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SUMMARY

This discussion focuses on applying Kirchhoff's laws to analyze a circuit involving multiple batteries and resistors. The participants emphasize the importance of accurately depicting mid-point connections in circuit diagrams, specifically addressing the need to split the two-ohm and four-ohm resistors at their midpoints for clarity. The initial equations constructed by the user were deemed incorrect due to misleading representations in the circuit drawing. Ultimately, the user confirmed that their loop equations remain valid when applying Kirchhoff's laws to both the left and right loops of the circuit.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Familiarity with circuit diagrams and resistor configurations
  • Knowledge of internal resistance in batteries
  • Ability to construct and solve loop equations in electrical circuits
NEXT STEPS
  • Study the principles of Kirchhoff's Current Law (KCL)
  • Learn how to accurately draw and analyze complex circuit diagrams
  • Explore the impact of internal resistance on circuit performance
  • Practice solving circuit problems using Kirchhoff's laws with various resistor configurations
USEFUL FOR

Electrical engineering students, circuit designers, and hobbyists interested in mastering circuit analysis using Kirchhoff's laws.

Bolter
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Homework Statement
See full question below
Relevant Equations
Kirchhoff 1st and 2nd law
Hey everyone!

Had an attempt at this circuit question, but wanted to check if I got the set up right in order to find the current in the 3rd wire?
Screenshot 2020-04-21 at 12.55.10.png


Here is what I have done
IMG_4655 2.JPG


Thanks!
 
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You have done well, showing the internal resistance in each battery as an explicit external resistor in series.

However, there is a problem with the depiction of the "mid-point" connections. The three ohm wire connects at the midpoints of the two ohm and the four ohm wires. It would be best to split the two ohm "resistor" at its midpoint and to do the same for the four ohm "resistor".

Because the drawing is misleading, the equations you constructed from it are not correct.
 
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jbriggs444 said:
You have done well, showing the internal resistance in each battery as an explicit external resistor in series.

However, there is a problem with the depiction of the "mid-point" connections. The three ohm wire connects at the midpoints of the two ohm and the four ohm wires. It would be best to split the two ohm "resistor" at its midpoint and to do the same for the four ohm "resistor".

Because the drawing is misleading, the equations you constructed from it are not correct.

So would this be a much preferred circuit diagram then?

IMG_4659.JPG


I think my loop equations will be the same as before if I use Kirchhoff's law on left & right loop
 
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Very nice drawing. And now that I look again your equations were correct to start with.
 
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