So, to do an example problem, consider that L1 is 4 millihenries,

L2 is 9 millihenries, and M is 2mH, or we can simply use this equation to see

that k is equal to m divided by the square root of L1 times L2.

So that equals 2mH divided by 4mH times 9mH.

So that's 36mH squared.

Take the square root of that to give us 6 millihenries under 2 millihenries.

So that means that k is going to be equal to one-third.

This is quite simple to calculate the coefficient of coupling.

It's going to be very important, when we start talking about ideal transformers,

though, because we are going to make a certain assumption about what

this coefficient of coupling happens to be.

In the ideal transformer case, the coupling coefficient k is equal to 1,

which means that these two coils are very tightly coupled.

L2 and L1 are assumed to go to infinity, which means that so

is our mutual inductance.

Now, this is a limit.

It's not that it's equal to the value infinity.

But they're going to approach very, very large numbers.

And the reason that we make this assumption is that it allows the analysis

that leads to the transformer equations.

We're going to skip over the actual analysis.

It's available.

You can find it if you're interested, but we just need to make use of it.

But we clearly know that having this infinite inductance is not possible.

Finally we assume that losses from coil resistances are negligible.

Sometimes when we're doing analysis of transformers,

we're going to stick a resistor here.

And a resistor here to correspond to the resistance of

the two wires that are placed here and here.

It gives a better representation but

in the ideal transformer case we're going to assume that both of those go to zero.

Now the implications of this ideal transformer model are the following.

First of all, v1/N1 = v2/N2 where v1 and

v2 are the voltages across the primary and secondary coils respectively.

And then N1 and N2 are the number of rotations at the coil,

how many wraps of coil in the primary and the secondary coils respectively.

We also have the relationship N1i1 = N2i2.

Now these equations come from the Faraday's Law of Induction.