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Inductance

 

When the current changes in a circuit containing inductance, the magnetic linkage changes and induces a voltage in the inductance:
d
y/dt = e = L di/dt
Note that the induced voltage has a polarity which opposes the rate of change of current.

Alternatively, by integration with respect to time:
Y = òedt = LI

The inductance L of a circuit is equal to the induced voltage divided by the rate of change of current:
L = e / di/dt = d
y/dt / di/dt = dy/di

Alternatively, the inductance L of a circuit is equal to the magnetic linkage divided by the current:
L =
Y / I

Note that the magnetic linkage Y is equal to the product of the number of turns N and the magnetic flux F:
Y = NF = LI

 

Mutual Inductance

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)½ (L1L2)½ = kM(L1L2)½
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)½

 

Inductances in Series

When uncoupled inductances L1, L2, L3, ... are connected in series, the total inductance LS is:
LS = L1 + L2 + L3 + ...

When two coupled inductances L1 and L2 with mutual inductance M are connected in series, the total inductance LS is:
LS = L1 + L2 ± 2M
The plus or minus sign indicates that the coupling is either additive or subtractive, depending on the connection polarity.

 

Inductances in Parallel

When uncoupled inductances L1, L2, L3, ... are connected in parallel, the total inductance LP is:
1 / LP = 1 / L1 + 1 / L2 + 1 / L3 + ...