84-1 the inductor A current-carrying conductor produced a magnetic field(1800°) A changing magnetic field could induce a voltage in a neigh boring circuit(1820) q .DEL +D(t) dr p= Li dt (L→>pN2A/s) L--inductance(H)
§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 di Li L dt d = = = L--inductance (H) ( L N A / s) 2 → + (t) − i(t) L
The electrical characteristics (1)Inductor as a"short circuit to DC"; (2)We can not permit an inductor current to change suddenly. i(t)3H +D() i(4) i(4) r(s)-01 t(s) t(s) 22 AUC ▲D ( 30 t(s) t(s) pulses impulses 脉冲 冲激
The electrical characteristics: dt di = L i(A) t(s) 0 1 2 1 i(A) t(s) 0 1 2 1 − 1 3 i(A) t(s) 0 1 2 1 − 0.1 2.1 (V ) t(s) 0 1 2 pulses 30 + (t) − i(t) 3H (1) A inductor as a ''short circuit to DC"; (V ) t(s) 0 1 2 pulses 3 脉冲 (V ) t(s) 0 1 2 impulses 冲激 (2) We can not permit an inductor current to change suddenly
Ldi di dt i(t) DdT i(t)-i(t0) DdT i(to L or i(t)=i(to)+odt i(to)--initial current L 0 Let: to =0 and t (0+=0=0) 0 Udt+i(0)→>i(0)=i(0) L J0 0 The current, which flows through a linear time-invariant inductor, must always be a continuous function
d i t initial current L or i t i t t t = + − − ( ) 1 ( ) ( ) 0 0 0 − + Let : t 0 = 0 and t = 0 The current, which flows through a linear time-invariant inductor, must always be a continuous function. = i( t ) i( t ) t t d L di 0 0 1 − = t t d L i t i t 0 1 ( ) ( ) 0 dt L di 1 = dt di = L + 0 − 0 0 t 0 (0 ) (0 ) (0 ) 1 (0 ) 0 0 + − + − = + → = + − dt i i i L i ( ) + − 0 = 0 = 0
The power p(accepted) by the inductor i P=u= Li dt The energy W(t) i i(t) dw,=l pdt=Ll idt=Ll idi=Li(t)-i(to) HL(0) dt i(to) 2 Or w1(t)-w(t0)=L{i(t)-i(t0) 2 J:i(t0)=0w1(t)=L 2
The power p (accepted) by the inductor: The energy : dt di p =i = Li { ( ) ( )} 2 1 0 2 2 ( ) ( ) ( ) ( ) 0 0 0 0 dt L idi L i t i t dt di dw pdt L i i t i t t t w t w t t t L L L = = = = − 2 0 2 1 If : i(t ) 0 w ( t ) Li = L = w ( t ) w ( t ) L{ i ( t ) i ( t )} or L L 0 2 2 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
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
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. 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 (Fh) function or response (HaM) 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 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
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 D,(0*),(0+) t○pen=0 n05 20 (0) ①al000b i08 i(0+)=i0)=12A U1(01)=-24-36=-60 (0)=-3Q
Drill problem 1: Find i (0 + ) and (0 ), . + L (0 ) 1 + R R1 (0 ) = −36V + L (0 ) = −24− 36 = −60V + i(0+ )= i(0- )=1.2A V 24 0 3 − + (t) L 0 2 − + ( ) 1 t R mH 50 i − + + ( ) L 0 − + + ( ) R 0 1 i( ) + 0 20 30