Writing Kirchhoff Rules for a Multi-Loop Circuit

[carterq]

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

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.

 

[cnh1995]

Welcome to PF!

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.

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.

 

[ehild]

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?

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:

 

[carterq]

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

 

[gneill]

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.

 

[carterq]

Thank you! That makes sense.