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Unformatted text preview: nductances. 67 EE1002 Introduction to Circuits and Systems i1 (t ) i2 (t ) i3 (t ) i(t )
di1 (t ) di2 (t ) di3 (t ) di (t ) dt
dt
dt
dt
v1 (t ) v2 (t ) v3 (t ) v(t ) L1
L2
L3
Leq
As all the voltages are equal, v1 v2 v3 v
1 1 1 v
1
1 1 1 v Leq L1 L2 L3 L1 L2 L3 Leq Mutual Inductance When several coils are wound on the same form, the magnetic flux from one coil links all other coils on the form. Then, a time varying current in one coil induces voltages in the other coils. These coils are said to have a mutual inductance. The total voltage induced in each coil will be sum of self‐induced voltage and the mutually induced voltage: di1 (t )
di (t )
M 2
dt
dt di2 (t )
di1 (t )
v2 (t ) L2
M
dt
dt v1 (t ) L1 The voltage and current polarities and directions follow the passive reference convention. The two black dots being on the same end indicates that the flux due to the two coils aid each other. If the dots were at two opposite ends as shown in Fig. (b), then the magnetic fields due to the two fields would oppose each other and voltage equations would change. The sign of the mutual terms in the voltage equation depends on how the currents are referenced with respect to the dots. If both the 68 EE1002 Introduction to Circuits and Systems curr...
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 Winter '14

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