# Energy in a coupled circuit

Discussion in 'Homework Help' started by p75213, Mar 17, 2012.

1. ### p75213 Thread Starter Member

May 24, 2011
39
0
The author is establishing an upper limit for the mutual inductance M.

The missing text is:
"The energy stored in the circuit cannot be negative because the circuit is passive."

Can somebody explain equation 13.34 where he completes the square. This has me scratching my head. He pulls iii2√L1L2 out of the blue. I can't see how this is completing the square.

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2. ### vvkannan Active Member

Aug 9, 2008
138
11
Let a=i1√L1 b=i2√L2

In 13.33 we have 1/2(a²+b²) .To write this in (a+b)² [to get the coefficient of coupling relation] we need an extra 2ab.so we add and subtract 2ab.But since we have 1/2 multiplying (a-b)² it is enough to add 'ab' to cancel the extra -2ab we have introduced to make a²+b² --->(a-b)².

so a²-b² becomes (a-b)² and ab (i1√L1 * i2√L2) has been added to get the relation for coefficient of coupling.