Mutual inductance / equivalent inductor

[Numbskull]

Homework Statement

Homework 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):

$$L_{eq} = \frac {L_1 L_2 - M^2 } {L_1 + L_2 - 2M }
$$

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 :)

 

[gneill]

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 L_eq.

 

[Numbskull]

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 L_eq.

Thank you. I shall post my attempt for scrutiny!