I am confused about derivation of the next formula
The question is about Cm term.
We have coupled inductors.
The voltage across first coil is
And I am ok with it. I understand it.
I know that current I1 causes a flux in the magnetic core
Where c is
But I cannot understand the first formula. How do we get Cm term?
I thought there would must be
My misunderstanding does not relate to the nature of Cm or C1 terms. I do not understand how do we get it mathematically.
Best Answer
I'm not sure what text your pulling this from, but just looking at the first equation you have:
$$V_2 = C_MN_1N_2\frac{di_1}{dt}= M\frac{di_1}{dt}$$
which means that from the equations listed above at the time of writing:
$$M=C_MN_1N_2$$
In other literature (such as this article on mutual inductance or my CRC book) M is the mutual inductance ratio k is the coupling factor which describes the leakage out of each inductor (not all of the magnetic flux lines flow through the other side of the transformer)
$$M=k\sqrt{L_1L_2}$$
or
$$M=\sqrt{k_1L_1k_2L_2}$$
In a problem k or C_M are usually given to you, or they come from another leakage parameter because inductors are not perfect. For iedal transformers, these parameters are 1. For non ideal transformers, between 1 and 0