# Kichoff Simultaneous Equations

• jase951
In summary: Whenever you have a node, assume that each segment intersecting that node has its own current. So, for the first node, I would assume I1 = 10A, I2 = 0, and I3 = 10A. And for the other nodes, I would use those same values, but add in the corresponding current for each segment intersecting the node.
jase951

## Homework Statement

I what to know how I form an equation for the middle loop, as there is no EMF in that part. Or, how do I go about forming the equations? Also, am I right to say that I should have 3 equations?

## Homework Equations

http://www.theground.co.uk/CCF18012009_00000.jpg

Thanks!

Jase

Last edited by a moderator:
In any loop, the sum of the voltage drops (IR) and the EMFs must be zero.

One way is to assign each branch its own current. You'll need as many equations as branches.

Thanks!

So the middle section, we'd have 0V = (Ix20) + (Ix10) + (Ix8) + (Ix20)?

jase951 said:
So the middle section, we'd have 0V = (Ix20) + (Ix10) + (Ix8) + (Ix20)?
Yes, but each segment of that loop will have a different current. And take care with signs when you add up the voltage drops.

I'm trying it again. I've updated the image.

I have managed to have do this with 2 loops, but the the 3 loops. Using Kichoff's second law, I'll have 3 equations I understand.

What I am confused about is where I need to lable the current changes to enable me to use Kichoff's first law.

Thanks!

I would label each segment of the circuit with its own current. I see six separate segements, thus I'd have six currents. Then I'd use 3 loops and 3 nodes to produce my equations. (It's not as hard as it sounds.)

Another thing I found helpful when I took this class is, once you follow Doc Al's advice, to set up all the equations in a matrix. It helps make the algebra easier!

I would assume that the 6 currents would be that of where the resitors are. where would the 6th be?

For the first loop on the left I have:
200V = 10.I1 (thus I1 = 10A).

2nd loop I have:
0V = 8.I2 + 10.I1 + 20.I3 + 20.I5

3rd:
-125V = 30.I4 + 20.I5

For the nodes, and K's 1st Law:

I3 + I4 = I5

And I don't understand how to get the other 2 when I have 2 currents coming out of the node: I5 = I4 + I2 ?

I've got to understand this, doing a Product Design degree. Thanks.

jase951 said:
I would assume that the 6 currents would be that of where the resitors are. where would the 6th be?
The 6th current will be through E1.

For the first loop on the left I have:
200V = 10.I1 (thus I1 = 10A).
Good.

2nd loop I have:
0V = 8.I2 + 10.I1 + 20.I3 + 20.I5
Good.

3rd:
-125V = 30.I4 + 20.I5
Good.

For the nodes, and K's 1st Law:

I3 + I4 = I5
Good.

And I don't understand how to get the other 2 when I have 2 currents coming out of the node: I5 = I4 + I2 ?
That works.

Get one more node equation (which will involve the 6th current).

Thanks!

So I6 + I2 = I1.

I should be able to do the algebra from these.

Could you tell me why you would have I6 there, because of the EMF? As I thought that that current through the EMF would be the same as I1 - or is it because the bottom node is split?

Thanks again!

jase951 said:
So I6 + I2 = I1.
That works.
Could you tell me why you would have I6 there, because of the EMF? As I thought that that current through the EMF would be the same as I1 - or is it because the bottom node is split?
Because the current splits. (From the above equation, the only way that I6 = I1 would be if I2 = 0.)

Whenever you have a node, assume that each segment intersecting that node has its own current.

I'm understanding it now. Many Thanks again! :)

## 1. What are Kichoff Simultaneous Equations?

Kichoff Simultaneous Equations, also known as Kirchhoff's Circuit Laws, are a set of fundamental principles used to analyze electrical circuits. These laws state that the total current flowing into a node is equal to the total current flowing out of the node, and the sum of voltage drops in a closed loop is equal to the sum of voltage rises.

## 2. What is the difference between Kirchhoff's Current Law and Kirchhoff's Voltage Law?

Kirchhoff's Current Law (KCL) deals with the conservation of charge at a node in a circuit. It states that the algebraic sum of currents entering and leaving a node must equal zero. On the other hand, Kirchhoff's Voltage Law (KVL) deals with the conservation of energy in a closed loop circuit. It states that the sum of all voltage drops in a closed loop must equal the sum of all voltage rises.

## 3. How are Kirchhoff's Laws used in circuit analysis?

Kirchhoff's Laws are used to solve for unknown currents and voltages in a circuit. By applying KCL and KVL at different points in a circuit, a set of simultaneous equations can be formed. These equations can then be solved using algebraic methods to determine the unknown values.

## 4. Can Kirchhoff's Laws be applied to both DC and AC circuits?

Yes, Kirchhoff's Laws can be applied to both DC and AC circuits. However, some modifications may need to be made for AC circuits, such as taking into account impedance and reactance.

## 5. Are there any limitations to Kirchhoff's Laws?

Kirchhoff's Laws are based on ideal circuit components and may not give accurate results in real-world circuits. Additionally, these laws assume linear behavior of components, which may not always be the case. They also do not take into account the effects of electromagnetic interference or non-ideal connections in a circuit.

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