§ 4-1 the inductor
A current-carrying conductor produced a magnetic
field (1800’).
A changing magnetic field could induce a voltage in
a neighboring circuit (1820’).
dt
diLLi
dt
d ???? ????
L--inductance (H)
)s/ANL( 2??
?? )( t?
)(ti L
The electrical characteristics:
dt
diL??
)(Ai
)(st
0 21
1
)(Ai
)(st
0 21
1
1? 3
)(Ai
)(st
0 21
1
1.0?
1.2
)(V?
)(st
0 21
pulses
30
?? )( t?
)(ti H3
(1) A inductor as a ''short circuit to DC";
)(V?
)(st
0 21
pulses
3
脉冲
)(V?
)(st
0 21
impulses
冲激
(2) We can not permit an inductor current to change suddenly.
c u r r e n ti n i t i a ltidLtitior tt ???? ? )(1)()( 00
0
??
?? ?? 00,0 ta n dtL et
The current,which flows through a linear time-invariant
inductor,must always be a continuous function.
? ??)t(i )t(i tt dLdi0 01 ?? ???
t
t dLtiti 0
1)()(
0 ??
dtLdi ?1?
dt
diL???
?0?0
0
t
0
)0()0()0(1)0( 00 ???? ???? ? ?? iiidtLi ?
)( ?? ?? 000
The power p (accepted) by the inductor:
The energy,
dt
diLiip ?? ?
)}()({21 022)( )()( )(
000 0
titiLi d iLdtdtdiiLp d tdw ti titttw tw ttLL
L
????? ??? ?
2
0 2
10 Li)t(w)t(i:If
L ??
)}t(i)t(i{L)t(w)t(w
or
LL 0
22
0 2
1
???
Some of important characteristics of a inductor are
now apparent:
1,There is no voltage across an inductor if the current
through it is not changing with time,An inductance is
therefore a short circuit to dc.
2,A finite amount of energy can be stored in an
inductor even if the voltage across the inductance is
zero such as when the current through it is constant.
An inductor resists an abrupt change in
the current through it in a manner analogous to the way a mass
resists an abrupt change in its velocity.
3,It is impossible to change the current through an
inductor by a finite amount in zero time,for this requires
an infinite voltage across the inductor.
4,The inductor never dissipated energy,but only stores it,
Although this is true for the mathematical model,it is not
true for a physical inductor.
It will be
advantageous later to hypothesize that such a voltage may
be generated or applied to an inductor,but for the present
we shall avoid such a forcing (激励 ) function or response
（响应）, An inductor resists an abrupt change in the
current through it in a manner analogous to the way a
mass resists an abrupt change in its velocity.
Drill problem 1,Find i (0+) and,),0( ?
L?
)0(1 ?R?
VR 36)0(1 ???? VL 603624)0( ???????
i(0+)= i(0-)=1.2A
V 24 ?03
?
?
)(tL?
?02
?
?
)(1 tR?
mH50
i
?
?
? )(
L 0??
?
? )(
R 01?
)(i ?0
20
30