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Mutual Inductance Formula Calculation

The mutual inductance M of two coupled inductances L1 and L2 is equal to the mutually induced voltage in one inductance divided by the rate of change of current in the other inductance:

M = E2m / (di1/dt)

M = E1m / (di2/dt)

If the self induced voltages of the inductances L1 and L2 are respectively E1s and E2s for the same rates of change of the current that produced the mutually induced voltages E1m and E2m, then:

M = (E2m / E1s)L1

M = (E1m / E2s)L2

Combining these two equations:

M = (E1mE2m / E1sE2s) (L1L2) = kM(L1L2)

where kM is the mutual coupling coefficient of the two inductances L1 and L2.

If the coupling between the two inductances L1 and L2 is perfect, then the mutual inductance M is:
M = (L1L2)

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