Self - Inductance
• Faraday postulated that a magnetic field
consists of lines of force surrounding the
current-carrying conductor.
• Think of these lines as elastic bands that
close on themselves.
• As the current increases and decreases,
the bands expand and collapse about the
conductor.
ECE 201 Circuit Theory I
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Self – Inductance continued
Compress for decreasing
magnetic field (due to
decreasing current).
Faraday’s Law : the
voltage induced into the
conductor is proportional
to the number of lines
that cut the conductor.
Expand for increasing
magnetic field (due to
increasing current).
ECE 201 Circuit Theory I
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Faraday’s Law
d
v
dt
λ is called the “flux linkage” and is measured in weber-turns
ECE 201 Circuit Theory I
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Magnetic field linking an N-turn coil
  N
  PNi
ECE 201 Circuit Theory I
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Permeance, P
• Permeance describes the magnetic
properties of the space occupied by the
flux.
• Linear for non-magnetic materials
• Units are webers/ampere-turn.
ECE 201 Circuit Theory I
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d  d ( N )
v

dt
dt
d
d
vN
 N (PNi )
dt
dt
di
di
2
vN P L
dt
dt
LN
2
Self - Inductance
ECE 201 Circuit Theory I
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Voltage Polarity
• When i increases, di/dt is + and v is +.
– Energy produces the magnetic field
ECE 201 Circuit Theory I
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Voltage Polarity
• When i decreases, di/dt is - and v is -.
– i is still +
– Magnetic field collapses
-
+
ECE 201 Circuit Theory I
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