Inductance: Can L1 and L2 be replaced by an equivalent inductor in Figure 4(b)?

[james123]

Homework Statement

(c) See if you can show that L1 and L2 can be replaced by the

equivalent inductor, Leq, of FIGURE 4(b) where Leq = L1L2-M^2/L1+L2-2M

Homework Equations

The Attempt at a Solution

[/B]
I+I1+I2

Leq = V(L2-M)/jω(L1*L2-M^2) + V(L1-M)/jω(L1*L2-M^2)

= V*(L1+L2)-2M/jω(L1*L2-M^2)

V/jω*Leq = L1*L2-M^2/L1+L2-2M

Can anybody tell me if I'm close with this one or not? Struggling for days with it!

Any advice is appreciated!

 

[gneill]

A search of the Physics Forums' database via the Search tool provides the following thread which should be instructive:

https://www.physicsforums.com/threads/parallel-mutual-inductances.792899/

 

[james123]

Ahh great! So after reading through I presume 'his_tonyness' got part 'C' correct since he wasn't corrected by yourself apart from I=I1+I2?

 

[gneill]

Ahh great! So after reading through I presume 'his_tonyness' got part 'C' correct since he wasn't corrected by yourself apart from I=I1+I2?

I believe that is the case. It's been a while since I took part in that thread (2015).

 

[james123]

Many thanks gneill!