Writing Kirchhoff Rules for a Multi-Loop Circuit

AI Thread Summary
The discussion focuses on writing Kirchhoff's rules for a multi-loop circuit in a programming context, with an emphasis on ensuring the accuracy of the equations. Initial equations presented neglect certain resistances, leading to confusion about the correct number of currents and loops. Participants clarify that there are four independent loops, necessitating four loop equations. A key point is the importance of maintaining consistent current direction when applying Kirchhoff's Voltage Law (KVL) to avoid errors. The conversation concludes with an acknowledgment of the need for precise definitions of current directions in the equations.
carterq
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Homework Statement


I need to write Kirchhoff rues for the following circuit. This is not for a physics class, but for a programming class. I can do that part, but I am not sure if the equations are correct.

Homework Equations


upload_2017-4-25_11-6-13.png


The Attempt at a Solution


V1-I1*R1-(I1-I2)R3-I1*R2=0
V2-(I2-I3)R5-I2*R4-(I2-I1)R3=0
V3-I3*R6-I3*R7-(I3-I2)R5=0
These neglect R8, however.
Should I also include:
V1-I1*R1-(I1-I2)R3-(I1-I2)R4-(I1-I3)R7-I1*R8=0
V2-(I2-I3)R5-(I2-I3)R7-(I2-I1)R8-(I2-I1)R2-(I2-I1)R3=0
V3-I3*R6-(I1-I3)R8-(I3-I1)R2-(I3-I2)R4-(I3-I2)R5=0
These last three equations seem really wrong. I am not sure how many currents there even are.
 

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carterq said:
I am not sure how many currents there even are.
For writing KVL, take no of currents= no of meshes (smallest loops). You can see 4 meshes here, so assume four currents.

See this example.
download (1).png

You can now write the current through each resistor in terms of i1, i2 and i3. For example, current through the 25 ohm resistance is i1-i2 downward.
 
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carterq said:

Homework Statement


I need to write Kirchhoff rues for the following circuit. This is not for a physics class, but for a programming class. I can do that part, but I am not sure if the equations are correct.

The Attempt at a Solution


V1-I1*R1-(I1-I2)R3-I1*R2=0
V2-(I2-I3)R5-I2*R4-(I2-I1)R3=0
V3-I3*R6-I3*R7-(I3-I2)R5=0
These neglect R8, however.
So they are wrong. Why did you write them?
carterq said:
Should I also include:
V1-I1*R1-(I1-I2)R3-(I1-I2)R4-(I1-I3)R7-I1*R8=0
V2-(I2-I3)R5-(I2-I3)R7-(I2-I1)R8-(I2-I1)R2-(I2-I1)R3=0
V3-I3*R6-(I1-I3)R8-(I3-I1)R2-(I3-I2)R4-(I3-I2)R5=0
These last three equations seem really wrong. I am not sure how many currents there even are.

These equations are also wrong.
Choose loops and loop currents and draw the currents clearly. Note that you have 4 independent loops, so you need to write 4 loop equations.
This is a possible arrangement:

upload_2017-4-26_7-34-43.png
 
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So these are the new equations that I came up with, but something still is not quite right:
V1-I1*R1-(I1-I2)*R3-(I1-I4)*R2=0
V2-(I2-I3)*R5-(I2-I4)*R4-(I2-I1)*R3=0
V3-(I3-I2)*R5-(I3-I4)*R7-I3*R6=0
I4*R8+(I4-I1)*R2+(I4-I2)*R4+(I4-I3)*R7=0
 
In your third equation you ignored the defined current direction of I3. You did your "KVL walk" around the loop counterclockwise, which is fine, but you wrote the equations as though you were going in the direction if I3 rather than against it. For example, I3 should cause a potential rise as you pass through R5.

Once you've defined the direction of a current and used it in other equations you must stick to what you've defined.
 
Thank you! That makes sense.
 

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