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