Transformers

# Transformers - Mutual Inductance L1 dI Lm 2 dt + + - I1 Lm...

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© Robert York, 2006 Mutual Inductance L m L 1 L 2 + - + - I 1 V 1 + - V 2 I 2 2 m dI L dt 1 L + - 2 L 1 m dI L dt 12 11 22 m m dI dI VL L dt dt dI dI L dt dt + L m L 1 L 2 + - + - I 1 V 1 + - V 2 I 2 2 m dI L dt 1 L + - 2 L 1 m dI L dt Correct sign for mutual inductance found from Lenz’ law and dot convention Dot convention: current flowing into one dot will induce current flow out of second dot

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© Robert York, 2006 Transformers A transformer is just a special case where the mutual inductance is made as large as possible by allowing both coils to share the same flux This is usually achieved by winding them both on a common core of high permeability material (soft iron or ferrite materials) I 1 I 2 + 11 1 2 21 2 2 m m Vj L Ij L I L L I ω ωω = + =+ + V 1 V 2 - - When there is no flux leakage, the mutual inductance is related to the primary and secondary inductances as 12 m L LL = For real transformers this can never be quite achieved, so we write where 0 1 m L kL L k =< < coefficient of coupling
© Robert York, 2006 Ideal Transformer 1:n 11 22

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## Transformers - Mutual Inductance L1 dI Lm 2 dt + + - I1 Lm...

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