# Equations for three inductors connected together

• anon6912
In summary, you eliminated the intermediary variable VT and wrote the state equations in terms of V1 V2 V3 and I1 and I2.
anon6912
I have a system with three inductors connected together at a common point.
The unconnected ends of each inductor is connected to an independent voltage source.

Basically I want to get three expressions for the dynamics of the currents with V1, V2 and V3 as inputs.
i.e. i need to eliminate the intermediary variable VT.

I want to write the state equations for the system in the following format (state space form):

The system and, how far i got is below:

I don't know how to proceed from here.
Or is it impossible to get it into the format I want?

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anon6912 said:
i.e. i need to eliminate the intermediary variable VT.

anon6912 said:
The system and, how far i got is below:

Here you removed ##V_{T}## from all the equations. You have di/dt (for 1, 2 and 3) in terms of V1,V2... etc without ##VT##.

Maybe I didn't understand your question correctly.

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You are missing an equation. Using the sign conventions from your drawing, i1=i2+i3. That is Kirchoff's Current Law.

Fisherman199
Phylosopher said:
Here you removed ##V_{T}## from all the equations. You have di/dt (for 1, 2 and 3) in terms of V1,V2... etc without ##VT##.

Maybe I didn't understand your question correctly.

At the time I was asking this question I don't think I had grasped the question correctly even myself.

What I initially wanted was to eliminate V_T.
But as a consequence of doing this I found out I had to/ could write I_1 in terms of I2 and I3.
I wasn't sure if this second part of replacing I1 with !2 and I3 was correct because I felt like it would eliminate a state from the system if I did that.
But I think it is correct and can be done.

So now I have a system with VT eliminated and the equations written in terms of V1 V2 V3 and I1 and I2 :)

Phylosopher
anorlunda said:
You are missing an equation. Using the sign conventions from your drawing, i1=i2+i3. That is Kirchoff's Current Law.
Thanks. I ended up integrating kirchhoff law and it worked :)

## 1. What is the purpose of equations for three inductors connected together?

The equations for three inductors connected together are used to calculate the total inductance of the circuit and understand the behavior of the circuit. They are also used in the design and analysis of complex circuits.

## 2. How do you calculate the total inductance of a circuit with three inductors connected together?

The total inductance of a circuit with three inductors connected together can be calculated by using the equations for inductors in series or in parallel, depending on how the inductors are connected. In series, the total inductance is equal to the sum of the individual inductances. In parallel, the inverse of the total inductance is equal to the sum of the inverses of the individual inductances.

## 3. Can the equations for three inductors connected together be applied to circuits with more than three inductors?

Yes, the equations for three inductors connected together can be extended to circuits with more than three inductors by applying the same principles. The total inductance of a circuit with more than three inductors can be calculated by using the equations for inductors in series or in parallel.

## 4. What factors can affect the inductance of a circuit with three inductors connected together?

The inductance of a circuit with three inductors connected together can be affected by the physical properties of the inductors, such as their size, shape, and material. The distance between the inductors and the presence of other components in the circuit can also affect the inductance.

## 5. How can the equations for three inductors connected together be used in practical applications?

The equations for three inductors connected together can be used in practical applications to design and analyze circuits that require specific inductance values. They can also be used to troubleshoot and optimize the performance of existing circuits with inductors. In addition, these equations are important in the study of electromagnetic fields and their effects on circuits.

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