# Writing Kirchhoff Rules for a Multi-Loop Circuit

• carterq
In summary: So the correct equations should be:V1-I1*R1-(I1-I2)*R3-(I1-I4)*R2=0V2-(I2-I3)*R5-(I2-I4)*R4-(I2-I1)*R3=0V3-(I3-I2)*R5-(I3-I4)*R7-I3*R6=0I4*R8-(I4-I1)*R2-(I4-I2)*R4-(I4-I3)*R7=0In summary, the Kirchhoff rules for this circuit involve four loop equations, with each loop having a defined current direction. The equations should be written according to the
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.

## 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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Welcome to PF!
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.

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.

TomHart
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:

CWatters
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.

## 1. What are Kirchhoff's Rules for a Multi-Loop Circuit?

Kirchhoff's Rules, also known as Kirchhoff's Laws, are a set of fundamental principles used to analyze electrical circuits. They are used to calculate the current, voltage, and resistance in a circuit.

## 2. What is the first rule of Kirchhoff's Rules?

The first rule, also known as Kirchhoff's Current Law, states that the sum of the currents entering a node (or junction) in a circuit must equal the sum of the currents leaving that node. This is based on the principle of conservation of charge.

## 3. What is the second rule of Kirchhoff's Rules?

The second rule, also known as Kirchhoff's Voltage Law, states that the sum of the voltages around a closed loop in a circuit must equal zero. This is based on the principle of conservation of energy.

## 4. How do you apply Kirchhoff's Rules to a multi-loop circuit?

In a multi-loop circuit, each loop can be analyzed separately by applying Kirchhoff's Rules to each loop individually. The first rule can be used to calculate the currents in each branch of the circuit, while the second rule can be used to calculate the voltages across each component in the loop.

## 5. What are the advantages of using Kirchhoff's Rules for multi-loop circuits?

Kirchhoff's Rules provide a systematic and accurate method for analyzing complex circuits with multiple loops. They also take into account the effects of all components in the circuit, making it a more comprehensive approach compared to other methods.

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