r i c i r c u i s 07 R 회로의 응답 7. 병렬 R 회로의 특성방정식 7. 병렬 R 회로의 자연응답 7.3 병렬 R 회로의 계단응답 7.4 직렬 R 회로와 쌍대성 7.5 직렬 R 회로의 자연응답 7.6 직렬 R 회로의 계단응답 7.7* 무손실 회로의 해석 7.8 요약 및 복습 ONTENTS ER c PT e HA l E
07 R HAPTER E l e c r i c i r c u i s R R R R R 3 R 7 0 R 360
HAPTER 07 R i R i i R v R 7 i () 0 = I, v () 0 = V (7) 0 0 7 v R v( ) d i ( ) dv x x 0 0 # = (7) d 0 7 inegrodifferenial equaion d v dv d R d v = 0 (73) 7 R 7 3 7 v () 7 R7 3 36
Elecric ircuis 7 3 7 3 s v () = Ke ( K! 0) (74) K s 7 4 7 3 s Ks e R Kse s Ke s = 0 s Ke s R s b l= 0 (75) 7 5 Ke s s0 0 7 5 s R s = 0 s R s = 0 (76) 7 6 characerisic equaion 7 3 7 6 s, s s, s =! b l (77) R R s s 7 4 v () 36
HAPTER 07 R v () = K e s, v () = K e s v() v() 7 3 d v d d v d dv R d v = 0 (78) dv R d v = 0 (79) 7 8 7 9 d ( v ) ( ) v dv v ( ) d R d v v = 0 (70) v () v () 7 3 lineariy R s s v () = Ke Ke (7) K K 7 v () Ke s = 7 3 s 7 363
Elecric ircuis d y dy a by = 0 a b d d y y y y y y y y Ky 7 6 characerisic roo R complex frequency ~ 0 neper a ~ 0 _ (7) a _ (73) R ~ 0 a s s s, s =a! a ~ (74) 0 364
HAPTER 07 R 7 4 3 a > ~ 0 overdamping a < ~ 0 underdamping a = ~ 0 criical damping R 7 R a > ~ 0 a < ~ 0 a = ~ 0 R v v 5X 6H F 30 v7 3 365
Elecric ircuis 30 d v dv v 0 d 5 d 6 = s s 30 5 0 6 = s 6s 5 = 0 s =, s =5 7 R R R H F 7 6 s R s 0 = Rs s R = 0 4 4( RR ) = 0 R R = ` = X 366
HAPTER 07 R R R R s s R 7 K K R a > 0 ~ 7 4 s s 7 v () s s e s e s v () 0 7 R v() 0 R 367
Elecric ircuis 7 K K 7 3 v(0) i R (0) i (0) i (0) R R 7 v () K K v() 0 7 3 ir() 0 i() 0 i() 0 = 0 i () 0 i () 0 dv R = 0 d = 0 dv d = 0 ir() 0 i() 0 _ vl () 0 = (75) R v () v () K K v() 0 V, dv = 0 = vl () 0 = V (76) d = 0 R 368
HAPTER 07 R R R a > ~ 0 v () K K v() 0 = V, vl () 0 = V 0 v () s s v () = Ke Ke R R v () 0 = 0V, i () 0 = A v () i R i i 5X 6H F 30 v 7 s 6s 5 = 0 ` s =, s =5 369
Elecric ircuis 7 v () 5 v () = Ke Ke K K v() 0 = v () 0 = 0V vl () 0 ir() i() i() = 0 dv =i () i () d R dv ir() 0 i() 0 ` = vl () 0 = d = 0 i () 0 R v() 0 i () 0 0V R = = = A R 5X i () 0 = A vl () 0 vl () 0 = 30( ) =90V/sec K K v() 0 = 0V, vl () 0 =90V/sec v() 0 = K K = 0 vl 5 () =Ke 5Ke vl () 0 =K 5K =90 K= 0, K = 0 v () 5 v () = 0e 0e A, > 0 370
HAPTER 07 R = 0 R > 0 v () = 0 0V 4X 4X X =0 3H 6 F v () < 0 0V 4X 4X i (0 ) X v (0 ) v ( 0 ) 0V i ( 0 ) = i ( 0 ) 0V = =A 4X 4X X 37
Elecric ircuis i ( 0 ) v ( 0 ) i( 0 ) = i( 0 ) =A v ( 0 ) = v ( 0 ) = 0V = 0 4X > 0 i (0)=A X 3H 6 F v () v (0)=0V s 3s = 0 ` s =, s = 7 v () v () = K e K e K K v () 0 = 0V vl () 0 7 5 () () vl ir 0 i () 0 0 = = 6{ ir( 0) i( 0)} i () 0 R v () 0 ir() 0 = = 0A R 37
HAPTER 07 R vl () 0 V/sec = K K v () 0 = 0, vl () 0 = v () 0 = K K = 0 vl () =Ke Ke vl () 0 =K K = K =, K = v () v () = e e A, > 0 R a < 0 ~ 7 4 s s complex conjugae j _ s, s =a! a ~ =a! j ~ a (77) 0 0 7 7 ~ d s, s = a! j~ d (78) ~ _ ~ a (79) d 0 ~ damped resonan frequency d 7 7 7 s s v () = Ke Ke d = Ke Ke d = Ke e Ke e ( a j~ ) ( a j~ d) a j~ a j~ d (70) 373
Elecric ircuis e ji ji e = cos i jsin i (7) e j i = cos i jsin i (7) 7 0 a j~ d a j~ d v () = Ke e Ke e a = e ( Kcos ~ d jksin ~ d Kcos ~ djksin ~ d) a = e {( K K) cos ~ d j( KK) sin ~ d} a = e ( A cos ~ A sin ~ ) d d (73) A A A_ K K (74) A _ j( K K ) (75) 7 3 v () v () 0 7 4 R 374
HAPTER 07 R v() e a 0 e a R a 7 4envelope e a a damping facor a damping facor a = 0 ~ d = ~ 0 ~ 0 undamped resonan frequency ~ d a! 0 damped resonan frequency A A A A 7 4 7 5 7 5j A 7 0 s s K K K K A K K j A 375
Elecric ircuis 7 3 A A v () R R a < ~ 0 v () A A v() 0 = V, vl () 0 = V 0 v () a v () = e ( Acos ~ Asin ~ ) d d = 0 > 0 v () 0 = =0 A X H F v () < 0 376
HAPTER 07 R i (0 ) A X v (0 ) i ( 0 ) A v ( 0 ) 0V i ( 0 ) = v ( 0 ) = i( 0 ) = i( 0 ) = A v ( 0 ) = v ( 0 ) = 0V = 0A > 0 i (0)=A X H F v () v (0)=0V s s = 0 s, s! 6 =! j # = 4 5 4 7 3 v () v () e A cos 5 A sin 5 = 4 d 4 n 4 A A 377
Elecric ircuis v () 0 = 0V vl () 0 7 5 () () vl ir 0 i () 0 0 = =ir() 0 i() 0 i () 0 R v () 0 ir() 0 = = 0A R vl () 0 =V/sec A A v () 0 = 0, vl () 0 = v () 0 = A = 0 vl () e 5 A sin 5 5 A cos 5 = 4 d 4 4 n 4 4 e A cos 5 A sin 5 4 d 4 4 n 4 vl () 0 5 A = A 4 4 = ` A 0, A 8 5 = = 5 v () v () 8 5 e sin 5 = 4 V, > 0 5 4 Euler sin i cos i e! ji e e ji ji = cos i jsin i = cos ijsin i 378
HAPTER 07 R j i j i cos i = ( e e ) ji ji sin i = ( e e ) j f( x) gx ( ) d ( ) { ( ) ( )} df x dg( x) fxgx = gx ( ) fx ( ) dx dx dx 3x hx ( ) = e sin4x hl 3x 3x ( x) = ( e ) lsin 4x e ( sin 4x) l 3x 3x = 3e sin 4x e ( 4cos 4x) 3x = e ( 3sin 4x 4cos 4x) R a = ~ 0 7 4 s s s, s = a = (76) R 379
Elecric ircuis 7 6 7 v () = Ke a Ke a (77) 7 7 K K 7 7 v () = ( K K) e a = Ke a (78) 3 7 8 K 3 7 7 7 9 v () = Ke a Ke a (79) 7 9 a 7 9 e a e 0 a lim e 0 (730) " 3 = 7 9 7 5 380
HAPTER 07 R v() 0 R 7 5 a e a e n e a a e 3 3 a e 3 3 a e 3 a 3 a e e 3 a e 3 a e 0 n lim e 0 " 3 n a = n e a " 3 0 7 9 K K v () 38
Elecric ircuis R R a = ~ 0 v () K K v() 0 = V, vl () 0 = V 0 v () a a v () = Ke Ke v () > 0 4u()A X H 8 F v () < 0 4A i (0 ) 4A X v (0 ) 38
HAPTER 07 R i ( 0 ) 4A v ( 0 ) 0V i ( 0 ) = v ( 0 ) = i( 0 ) = i( 0 ) = 4A v ( 0 ) = v ( 0 ) = 0V = 0 > 0 i (0)=4A X H 8 F v () v (0)=0V s 4s 4 = 0 ` s = s = 7 9 v () v () = K e K e K K v () 0 = 0V vl () 0 7 5 () () vl ir 0 i () 0 0 = = 8{ ir( 0) i( 0)} i () 0 R v () 0 ir() 0 = = 0A R 383
Elecric ircuis vl () 0 =3V/sec K K v () 0 = 0, vl () 0 =3 v () 0 = K = 0 vl () = K e K e K e vl () 0 = K K =3 ` K = 0, K =3 v () v () =3e V, > 0 > 0 R v () 0 = 0V R < 0 =0 0A v () F 8 R H =0 R < 0 384
HAPTER 07 R 0A v (0 ) R i (0 ) R v ( 0 ) R ' R 0RR v( 0 ) = v( 0 ) = ( R' R) 0 = = 0 R R RR R R = > 0 R F 8 H R a = ~ 0 9 _ a = = R R b ~ ` 0 = = 3 b a 9 R = 3 ` R = 3X 385
Elecric ircuis R = 3X v ( 0 ) 3R ` R 6X 3 R = = R R R R 6 R R R R 7 6 I S R 386
HAPTER 07 R I S =0 i R i i R v R 7 6 > 0 ir i i = IS (73) 7 3 i v i () 7 3 v v dv i = I R d S (73) di v = v = d (733) 7 33 7 3 i d i di d R d i IS = (734) 387
Elecric ircuis v () 7 3 v () v dv v( ) d v( 0) I R # x x = d S (735) 0 7 35 dv R d v d v = 0 d d v dv d R d v = 0 (736) 7 347 36 i f v f i n v n forcing funcion 0 0 7 7 7 R 388
HAPTER 07 R R a>~ 0 a=~ 0 a<~ 0 R = 0 R > 0 i() v() 389
Elecric ircuis 0A =0 5X v () i () 6H F 30 < 0 i( 0 ) = i( 0 ) = 0A v ( 0 ) 0V v ( 0 ) = v ( 0 ) = 0V = di v ( 0 ) = = 0 d = 0 di ` = il ( 0 ) = 0 d = 0 7 34 d i d di 6 5i = 50 d s 6s 5 = 0 ( s )( s 5) = 0 ` s =, s =5 i () n i () = K e K e n 5 50 if () = 0A 390
HAPTER 07 R i () = i () i () = 0 K e K e f n 5 i() 0 = 0, il ( 0 ) = 0 K, K i() 0 = 0 K K = 0 il 5 () =Ke 5Ke il () 0 =K 5K = 0 ` K 5, K 5 = = i() v() i () 0 5 e 5 5 = e A, > 0 di v () 6 6 5 e 5 5 5 = = b e 75( e e ) V, > 0 d l = i () i () 0u()A 3X 3H F 6 39
Elecric ircuis < 0 i ( 0 ) = i ( 0 ) = 0A v ( 0 ) = v ( 0 ) = 0V di v( 0 ) = v( 0 ) = = 0 d = 0 di ` = il ( 0 ) = 0 d = 0 7 34 d i d di i = 0 d s s = 0 s, s! 4 8 =! j = i () n i () = e ( A cos A sin ) n 0 if () = 0A i () = i () i () = 0 e ( A cos A sin ) f n i() 0 = 0, il() 0 = 0 A, A 39
HAPTER 07 R i() 0 = 0 A= 0 ` A=0 il () = e ( Asin Acos ) e ( Acos Asin ) il () 0 = A A = 0 ` A = A =0 i () i () = 0 0e ( cos sin ), > 0 v () 6u()A X H v () F 8 < 0 v( 0 ) = v( 0 ) = 0V i( 0 ) = i( 0 ) = 0A = 0 ir( 0 ) i( 0 ) i( 0 ) = 6 v ( 0 ) dv i( 0 ) = 6 R d = 0 dv ` 6 = = 48V/sec d = 0 7 36 d v d dv 4 4v = 0 d 393
Elecric ircuis s 4s 4 = 0, s = s = v () n v () = K e K e n 0 vf () = 0 v () = v () v () = K e K e f n v() 0 = 0, vl() 0 = 48 K, K v () 0 = K = 0 vl () = K e K e K e vl () 0 = K K = 48 ` K = 48 v () v () = 48e V, > 0 v () < 0 394
HAPTER 07 R 9u()A v F 8 6X H =0 3X 4u()A < 0 i (0 ) 9A v (0 ) 6X 3X v ( 0 ) 6X 3X v ( 0 ) ( 6 3 ) 9A 6 3 # # = X ' X = # 9A 8V 6 3 = i ( 0 ) i ( 0 ) 3X = # 9A = 3A 6X 3X v( 0 ) = v( 0 ) = 8V i ( 0 ) = i ( 0 ) = 3A > 0 9A 6X 395
Elecric ircuis i F 8 v i i R H 3X 4A 7 36 d v d dv 6 9v = 0 d s 6s 9 = 0, s = s =3 v () = K e K e n 3 3 0 vf () = 0 v () = v () v () = K e K e f n 3 3 v 0 = ir( 0 ) i( 0 ) i( 0 ) = 4 v ( 0 ) dv i( 0 ) = 4 R d = 0 dv ` v ( 0 ) 8 4 8 = l = b 3 90 d 3 l= = 0 396
HAPTER 07 R v() 0 = 8, vl() 0 =90 K, K v () 0 = K = 8 vl 3 3 3 () = 3K e K e 3K e vl () 0 = 3K K = 90 ` K =36 v () v () = 8e 36e V, > 0 3 3 v () 0 i() 0 v i i ( 0 )! i ( 0 ) v ( 0 )! v ( 0 ) i dv = d dv dv i ( 0 ) i ( 0 ) = = d d = 0 = 0 dv dv i ( 0 ) i ( 0 ) = = d d = 0 = 0 dv dv `! vl( 0 )! vl( 0 ) d d = 0 = 0 v di = d 397
Elecric ircuis di di v( 0 ) v( 0 ) = = d d = 0 = 0 di di v( 0 ) v( 0 ) = = d d = 0 = 0 di di `! i ( 0 )! i ( 0 ) d d l l = 0 = 0 v i R R RR 7 80 R R v R i v v R 7 8 i () 0 = I, v () 0 = V (737) 0 0 398
HAPTER 07 R 7 8 Ri di i( x) dx v ( 0) 0 d # = (738) 0 7 38 d i R di d d i = 0 (739) 7 39 s Rs = 0 s R s = 0 (740) 7 40 s, s s, s R R =! b l (74) R ~ 0 a ~ 0 _ (74) a _ R (743) R ~ 0 a s s 399
Elecric ircuis s, s = (744) a! a ~ 0 R R 7 44 3 a > ~ 0 a < ~ 0 a = ~ 0 R R 3 R i 5X H i 6 F i7 39 d i di 5 6i = 0 d d 400
HAPTER 07 R s 5s 6 = 0 ` s =, s =3 a ~ 0 a R 5, = = ~ 0 = = 6 a > ~ 0 R R dual R7 3 d v dv d R d v = 0 (73) R7 39 d i R di d d i = 0 (739) 7 3 7 39 R v R i (745) 7 45 R 40
Elecric ircuis R R R RR 7 R R R R R dv dv d R d v 0 = d i R di d d i 0 = s R s = 0 s R s = 0 a ~ 0 R R 7 R a R R a a 7 40 R R R R R s s 3 40
HAPTER 07 R R a > 0 ~ 7 44 s s RR s s i () = Ke Ke (746) K K R i () i() 0 I, di = 0 = I (747) d = 0 > 0 i () 5X H i() 0u()V 6 F < 0 403
Elecric ircuis 5X i(0 ) 0V v (0 ) i( 0 ) = 0A, v ( 0 ) = 0V v ( 0 ) i( 0 ) i( 0 ) = i( 0 ) = 0A v ( 0 ) = v ( 0 ) = 0V > 0 R 7 40 s 5s 6 = 0 ` s =, s =3 7 46 i () 3 i () = Ke Ke K K vr( 0 ) v( 0 ) v( 0 ) = 0 Ri( ) di 0 v ( 0 ) 0 d = = 0 di v ( 0 ) ` = =0A/sec d = 0 K K i() 0 = 0, il ( 0 ) =0 404
HAPTER 07 R i() 0 = K K = 0 il 3 () =Ke 3K e il () 0 =K 3K =0 K= 0, K = 0 i () 3 i () = 0e 0e A, > 0 R a < 0 ~ 7 44 s s s, s =a! a ~ =a! j ~ a (748) 0 0 7 48 ~ d s, s = a! j~ d (749) ~ _ ~ a (750) d 0 ~ d RR a i () = e ( Acos ~ Asin ~ ) (75) d d A A R i () 7 47 405
Elecric ircuis = 0 A BR < 0 A > 0 i () A X H 6V B =0 i() F < 0 A X i(0 ) 6V v (0 ) i( 0 ) = 0A, v ( 0 ) = 6V i( 0 ) v ( 0 ) i( 0 ) = i( 0 ) = 0A v ( 0 ) = v ( 0 ) = 6V 0 = B 406
HAPTER 07 R X H B i() F 7 40 s s = 0 s, s = j! i () 7 5 i () = e ( Acos Asin ) vr( 0 ) v( 0 ) v( 0 ) = 0 Ri( ) di 0 v ( 0 ) 0 d = = 0 di ` = {Ri( 0 ) v ( 0 )} =6A/sec d = 0 A A i() 0 = A = 0 il () = e ( Asin Acos ) e ( Acos Asin ) il () 0 = A A = 6 ` A =6 i () i () 6e sin A, > 0 = 407
Elecric ircuis R a = ~ 0 7 44 s s s, s R = = (75) a RR i () = Ke a Ke a (753) K K R i () 7 47 > 0 i () v () 6X i() H v () 8u()V F 3 < 0 408
HAPTER 07 R 6X i(0 ) 8V v (0 ) i( 0 ) = 0A, v ( 0 ) = 8V i( 0 ) v ( 0 ) i( 0 ) = i( 0 ) = 0A v ( 0 ) = v ( 0 ) = 8V > 0 R 7 40 s 8s 6 = 0 ` s = s =4 7 53 i () 4 4 i () = Ke Ke K K vr( 0 ) v( 0 ) v( 0 ) = 0 Ri( ) di 0 v ( 0 ) 0 d = = 0 di ` = {Ri( 0 ) v ( 0 )} =4A/sec d = 0 i() 0 = 0, il () 0 =4 i() 0 = K = 0 il 4 4 4 () = 4Ke Ke 4Ke il () 0 = 4K K = 4 ` K =4 409
Elecric ircuis i () i () 4e A, > 0 = 4 v () v () di 4 4 = = ( 4e 6e ) V, > 0 d 7 3 R R R [v()] R [i()] ( a > ~ 0 ) ( a < ~ 0 ) ( a = ~ 0 ) s Ke s Ke Kes K es e a( Acos ~ d Asin ~ d) ea ( Acos ~ d Asin ~ d ) Kea K ea Kea K ea a a = R a R = R R overdamping underdamping criical damping 40
HAPTER 07 R R R 7 3R R R 7 9 V S R R V S =0 v R v v R 7 9 > 0 vr v v = VS (754) 7 54 i v 4
Elecric ircuis i () 7 54 i () di Ri i ( ) d v ( 0) V d # x x = S (755) 0 7 55 di d i R d d i = 0 d i R di d d i = 0 (756) v () 7 54 Ri di v V d = S (757) dv i = i = (758) d 7 58 7 57v d v d R dv d v VS = (759) 7 567 59 i f v f i n v n R 7 7 4
HAPTER 07 R A 0 = B R > 0 v () B 5X H 0V A =0 5V i () v () F 6 < 0 i ( 0 ) = 0A, v ( 0 ) = 5V i( 0 ) = i( 0 ) = 0A v( 0 ) = v( 0 ) = 5V dv i( 0 ) = i( 0 ) = = 0 d = 0 dv ` = vl ( 0 ) = 0 d = 0 = 0 B 7 59 d v d dv 5 6v = 60 d s 5s 6 = 0 ` s =, s =3 v () n 43
Elecric ircuis v () = K e K e n 3 60 v () f vf () = 0V v () v () = v () v () = K e K e 0 n f 3 v() 0 = 5, vl ( 0 ) = 0 K K v () 0 = K K 0 = 5 vl () =Ke 3K e vl () 0 =K 3K = 0 ` K = 5, K = 0 3 v () v () = 5e 0e 0V, > 0 3 R > 0 v () X H 46u()V i () v () F 44
HAPTER 07 R < 0 4V X i (0 ) 4V v (0 ) i ( 0 ) = 0A, v ( 0 ) = 4V i( 0 ) = i( 0 ) = 0A v( 0 ) = v( 0 ) = 4V dv i( 0 ) = i( 0 ) = = 0 d = 0 dv ` = vl ( 0 ) = 0 d = 0 > 0 6V 0V R 7 59 d v d dv v = d s s = 0 s, s = j! v () n v () = e ( A cos A sin ) n 0 v () f 45
Elecric ircuis vf () = 0V v () v () = v () v () = e ( A cos A sin ) 0 n f v() 0 = 4, vl ( 0 ) = 0 A A v () 0 = A 0 = 4 ` A=6 vl () = e ( Asin Acos ) e ( Acos Asin ) vl () 0 = A A = 0 ` A = A =6 v () v () = 6e ( cos sin ) 6V, > 0 A = 0 B > 0 i () 4X A B 6X H 0V 6X =0 F 3 i () 0V < 0 A 46
HAPTER 07 R v ( 0 ) 6X = # 0V = V 4X 6X i ( 0 ) = 0A v( 0 ) = v( 0 ) = V i ( 0 ) = i ( 0 ) = 0A > 0 vr( 0 ) v( 0 ) v( 0 ) = 0 di 6i( 0 ) = 0 d = 0 di ` i ( 0 ) 0 = l = A/sec d = = 0 = 0 B > 0 0V R 7 56 d i di 8 6i = 0 d d s 8s 6 = 0 ` s = s =4 i () n i () = K e K e n 4 4 0 0 i () i () = K e K e 4 4 i () 0 = 0, il ( 0 ) = K K 47
Elecric ircuis i() 0 = K = 0 il 4 4 4 () = 4Ke Ke 4Ke il () 0 = 4K K = ` K = i () i () e A, > 0 = 4 7 9 = 0 R > 0 v () < 0 0V =0 i X 3i 3X H i () v () F < 0 i( 0 ) 0V = = 5A X i ( 0 ) = 0A, v ( 0 ) = 3i 0 =5V 48
HAPTER 07 R i( 0 ) = i( 0 ) = 0A v ( 0 ) = v ( 0 ) =5V > 0 0V X i() 3i 3X H i () v () F dv i( 0 ) = i( 0 ) = = 0 d = 0 dv ` = vl ( 0 ) = 0 d = 0 di 3i v i 3i = 0 d dv dv i = i = =, i =i d d d v dv v = 0 d d s s = 0 ` s = s = v () n 49
Elecric ircuis v () = K e K e n 0 0 v () v () = K e K e v () 0 = 5, vl ( 0 ) = 0 K K v () 0 = K =5 vl () = Ke Ke Ke vl () 0 = K K = 0 ` K = K =5 v () v () =5e 5e = 5e ( ) V, > 0 7 0 R R i i R 3 R v 40
HAPTER 07 R i() 0 v () 0 i () 0 = I, v () 0 = v() 0 = V (760) 0 0 7 0 i i = 0 (76) v( ) d i ( 0) dv # x x = 0 (76) d 0 7 6 d v d v = 0 (763) 7 63 s = 0 (764) s, s j =! =! j~ 0 (765) v () = Acos~ Asin~ (766) 0 0 7 60 v () i( 0 ) i( 0 ) = 0 i ( ) i ( ) dv 0 = 0 = d = dv i( 0 ) I0 ` = = d = 0 0 (767) 4
Elecric ircuis A A v() = A = V (768) 0 0 vl () = ~ A sin~ ~ A cos~ (769) 0 0 0 0 vl I0 I0 () 0 = ~ 0A = ` A = (770) ~ 0 v () I0 v () = V0cos~ 0 sin~ 0 (77) ~ 0 7 7 v () = ( ~ 0V 0 ) ~ 0 I cos( ~ z) (77) 0 0 I0 z = an e o (773) ~ V 0 0 7 7 v () undamped v () 7 0 7R 0 R 4
HAPTER 07 R R i R 0 v i() 0 v () 0 i () 0 = I, v () 0 = V (774) 0 0 7 v v v = 0 (775) di dv =, i i d = = (776) d 7 76 7 75 d v d v = 0 (777) 7 63 v () 7 0 7 43
Elecric ircuis = 0 R > 0 v () < 0 0X F 4 0V =0 v () 5X H < 0 i ( 0 ) = 0A, v ( 0 ) = 0V i( 0 ) = i( 0 ) = 0A v( 0 ) = v( 0 ) = 0V dv i( 0 ) = i( 0 ) = = 0 d = 0 dv ` = 0V/sec d = 0 = 0 7 64 s 4 = 0 ` s, s =! j v () 44
HAPTER 07 R v () = A cos A sin A A v () 0 = A = 0 vl () = Asin Acos vl () 0 = A = 0 ` A = 0 v () v () 0 cos V, > 0 = acos x bsin x a a b cos x b acos x sin x bsin x = e o a b a b a b z cos z a = a b sin z b = a b an z b = a a b z a b 45
Elecric ircuis acos x bsin x = a b ( cos zcos x sin zsin x) a b cos( x z), z an b = = b a l z sin z = cos z = an z = a b a a b b a b a b z b a acos x bsin x = a b ( sin zcos x cos zsin x) = a b sin( x z) 7 0 7 46
HAPTER 07 R R 3 R a > ~ 0 s, s,, =a! a ~ 0 a _ ~ 0 _ R s s v () = Ke Ke a < ~ 0 s, s =a! j~ d, ~ d _ ~ a a v () = e ( Acos ~ Asin ~ ) 0 d d a = ~ 0 s= s =a v () = Ke a Ke a 47
Elecric ircuis R R R I S i d i d di R d i IS = v d v d dv R d v = 0 R R a > ~ 0 s, s, R =a! a ~ 0 a _, ~ 0 _ s s v () = Ke Ke a < ~ 0 s, s =a! j~ d, ~ d _ ~ a a v () = e ( Acos ~ Asin ~ ) 0 d d 48
HAPTER 07 R a = ~ 0 s= s =a v () = Ke a Ke a R R R R v R i a R R a a R R R V S i d i d R di d i = 0 49
Elecric ircuis v d v d R dv d v VS = R R R v() 0 430
HAPTER 07 R E X E R I S E. = 0 R > 0 v () = 0 3H X =0 3X v () 6 F 0V > 0 v () i () i () 4u()A X 7 H 0 F 7 v () 43
Elecric ircuis 3. = 0 R > 0 v () = 0 5 H =0 A X v () 0 F 4. = 0 R > 0 i() = 0 3 H 4X =0 i () F X 8V 5. = 0 R < 0 v () H 5A X v () F 8 3X =0 43
HAPTER 07 R 6. = 0 R < 0 i () v () 5X 5V =0 30 F v () i () 6H 7. A 0 = B > 0 v () X A B 6X H =0 0A 4X 4X v () F 3 5V 8. R > 0 v () 5X H 50u()V v () 6 F 433
Elecric ircuis 9. A = 0 B R > 0 v () i() X B 3X 3 H 8V A =0 5V i () v () 3 6 F 0. > 0 i () X H i () 6u()V F. = 0 R > 0 v () < 0 X =0 v x X H 0V v x 3X v () F 434
HAPTER 07 R. 0 = > 0 v () X 6 H 8V =0 3X v () 3 F 3. = 0 R > 0 i () ir() < 0 =0 4X 5A i () i R () i () H 4X v F 8 0u()V 4. > 0 v () 30X 4u()A 3H v () 30 F u()a 435
Elecric ircuis 5. > 0 i () i () 5u()A H 6 F 436