Homework Help: Mutual inductance / equivalent inductor

1. Oct 31, 2016

Numbskull

1. The problem statement, all variables and given/known data

2. Relevant equations
See if you can show that L$_1$ and L$_2$ as in (a) can be replaced by the equivalent inductor L$_{eq}$ as in (b):

$$L_{eq} = \frac {L_1 L_2 - M^2 } {L_1 + L_2 - 2M }$$
3. The attempt at a solution
Um, I don't really know where to start because I don't really understand what the question is asking. Am I supposed to provide some 'proof' in algebraic form? Thus I don't know the form that the answer should take, as in what equals what.

A gentle nudge would get me moving :)

2. Oct 31, 2016

Staff: Mentor

Just like reducing a resistor network to a single equivalent resistance, they want you to reduce the inductor network to a single equivalent inductor. The tricky bit is handling the mutual inductance. How you go about it is up to you, but consider driving the circuit with ac test voltage V and finding the resulting current it supplies. Then compare to the expression for the current if the load was just a single inductor Leq.

3. Oct 31, 2016

Numbskull

Thank you. I shall post my attempt for scrutiny!