I have no idea how to even start this. All I know about mutual inductances is how to calculate the V of each inductance (taking into consideration the mutual inductance)
V= L di/dt ± M di'/dt
But I don't see how that helps me.
This is a good approximation, but is not perfectly accurate. If you use this method to calculate the effective inductance of two such coupled inductors in parallel, you get "formula 1" for the equivalent inductance of two coupled inductors in parallel:Since the inductors L1 & L2 have mutually aiding flux (according to the dot convention per your diagram) their individual effective inductances are
L1_mutual=L1+M and L2_mutual= L2+M
Inductors in parallel are treated the same as resistors in parallel.
So the effective circuit inductance Lab would be
Lab=L3+(L1_mutual||L2_mutual) where || indicates the parallel combination.
This gives the correct answer of 11.337H (to be exact)
Are you sure the formula didn't also involve M? Without M you can't get the right answer.The solution of this problem is 11.33 and it's done using a formula that only has L1 L2 L3 but I don't know it and it's of the form of a fraction. (I've seen people solving it with the formula but I don't know from where they derived or what it is.)
I'm wondering how Hitman6267, who is apparently a civil engineer (?), could be expected to solve this? He says:Yes Electrician - rather sloppy of me I'm afraid.
Your correct equation for Leq of parallel mutually coupled coils should be applied.
In the loosely coupled case, simply paralleling the inductances is reasonably accurate, but then why would the problem give the mutual inductance if they didn't want the student to use it in the solution?No, all what I've been taught about inductances is how to calculate their equivalent inductance if they're in series/parallel and the formula in my first post.
The solution of this problem is 11.33 and it's done using a formula that only has L1 L2 L3 but I don't know it and it's of the form of a fraction. (I've seen people solving it with the formula but I don't know from where they derived or what it is.)
To help you determine what the proper method is I feel telling you that I'm a civil major and that this is not an advanced electric circuits class might help you.
The expressions you have aren't quite right. See #17 here:When is L(equivalent)= L + L' + M
and when is L(equivalent)= L + L' - M
?