DIPOL rlc

1. ? ?ا???RLC ةراد ?? ة???ا ت???????ا :??ا???ا ???RLC ةراد ?? ة???ا ت???????ا (I :????? (1 .L??????? ?????و r ????و??? ?? !وو C "??# $%&?و R "??و??? ??وأ ?(?? )? ن?&?? ةراد ?ه ??ا???ا ???RLCةرا,?ا ? ????? - ??,.? ?? $%&/?ا ?? ?0و12/?ا ?3?4?ا ا,??? ?3?4?? ر,5? يأ ن??7/?ا ? !"?#??ا ر!??$? ???% يأ &$' (??)? * ة .( ة راد ?? ة?8 ت???????ا ??????ا ?? ?????ا غ???? ??? ). :????و ?? ???% -???? (2 ن?&? RLC ا??ا نأ يأ ر 9 ? : ,? . ?????ا ?."?% /?" ?????ا ب1"1??ا 23ار ??!? &$' /?!?4و ، /?" ?????ا ب1"1??ا 23ار ??!? &$' /?!?4و ، 267???ا &?إ 9:;ر<4 2= ?????ا /:)? ???!آ ???%ز ة??? 167???ا ?? ر!???ا 6A!B 6C4 د??E?ا ??F4أ &$' (G:?? . R ?% و!H??ا ???B 6??" تا?% ة?' ?"?J??ا ???4 :د??E?ا ??F4أ (3 2 ) ? . ?????ا ?."?% ?=4/?ا ?????ا @3?.?? ???????و ?.?7?ا @3?.?? ، ةرا,?ا ?? ى??E? ??? د,=?? ?3?4?ا )? ء1: ب?????ا لHI ).ة,/2?و ة?8 ت???????ا نL? ، ةرا,?ا ?? ,??/?ا ب? M? ا?;0و . ة,/2? ت???????ا نأ ل??0 ، $%&/?ا ?4??? ??و??/?ا د?:?? ا?;0و ، " #?=? ) ? ب????? $%&/?ا ?.?!، AB?/?ا ?? ر? ??ا AC?3 ABو ,.? ل?: ل??O/? ??را?8 .( ?3?C ? &! ??? ??وNا ?(?/?ا :??F4أ ثL= M??4 ةرا??ا ?%و!H% ???B NO?و .(ةرا,?? ? ?&?ا ?3?4?ا PO?.? ?????ا Q?ه ??) .ة,/2? ? Rو ة?8 ت???????ا ن?&?،??,?.? ةرا,?? ? ?&?ا ??و??/?ا ن?&? ??,.? :يرود م?;0* ?هو).م???? نأ &?إ !#?3و RB!??? ??!:?ا S1ه ???،ة??E% و ة?? ت!"1"1??ا ،ة??TU ةرا?$? ??$??ا ?%و!H??ا ن??? !%??' :يرود 9V? م!F4* ???C .( ?ا د??E?ا ??!? .ب1"ذ1? نود ?$??A ???%ز ة?% ??" /?? 9??:? ?????ا ?H??.ي?B د??E?ا نY ت!"1"1??ا ???E? ??!:?ا S1ه ?? ، ة??Vآ ?%و!H??ا :يرود* م!F4* .RLC ةرا?? ??$7!???ا ??د!???ا (4 ??!??ا N?آ???ا ?V??? : : تا?????ا ???!7إ ن?4!B NO? du c ⇐ du dq = = = = c . c . uR R i u R i c 6% R dt dt dt 1

2. di و = . + uL i r L dt 2 2 d u du du d u ⇐ + + = + + + = c c c c 0 ( ) 0 Lc R c u u R r c Lc نذإ : . t c c 2 2 dt dt dt dt 2 d u R du 1 + + = c t c RLC???ا??% ةرا?? ??$7!???ا ??د!???ا &$' (G:4و . . 0 u : c 2 L dt LC dt R du t. c .( د??E?ا لوM? 9%ا??4!" د??E?ا ة?ه!Z /' [?!4 ) : را?H??ا L dt .LC ???!?% ةراد ?? ة??E??ا ??] ت!"1"1??ا( II LC ???!???ا ةرا??ا ?3ارد (1 L !#C??:? (%!?% ????وو ،C 9??3 ???% /% ن????ا ??!??ا N?آ???ا ?V??? : N?آ???ا (أ .!?V??J? 9H?H:? N?G? ??!?% N?آ?? ا1#? ??!??!"و ?$?#% ??] !#?%و!H% ن^? ??????ا _4!آ !???آ 94Y ???!?% ةراد S1ه.?%???% !#?%و!H%و :??$7!???ا ??د!???ا(ب ) 1 ( + L c u u = 0 ?J4 تا?????ا ???!7إ ن?4!B NO? : cu d dt 1 = + c u c L q :ب 2 ( ) d u du dq di L= = = = uL= c c c . . c L u i c L : نذإ 6% : 2 dt dt dt dt 2 d u uc?????ا !#HH:? ???ا ??$7!???ا ??د!???ا ?هو (2) ?$? !?آ `VG? : (1), و c . 0 . ?????ا ?."?% /?" 2 . dt 2 2 1 d q d q q + = +c = + = c u a????" :?Z?:$% . 0 0 0 ) 1 ( ?BL??ا ، c q L u u :يأ : `VG? L c 2 2 . L c dt dt .q ?? !"?#??ا ??:)?ا !#HH:? ???ا ??$7!???ا ??د!???ا ?هو :??$7!???ا ??د!???ا (? (ج 1 2 + c u c L dt cos( ) ( ω + = t U t u o m c 2 d u = c 0 : ?$? !?آ N??? 9?V?; ??اد /' ةر!V' ، (a) ??$7!???ا ??د!???ا (? : . π 2 ϕ ) ω = . ص!E?ا aV??ا 6% : o T O ω U rad / 9???و ،LC . s . ?"1"1???ا ةرا?$? ص!E?ا aV??ا ????$? ???GH?ا ???H?ا ?هو : : O c u ت!"1"1??ا 63و m (t ) π 2 T ϕ + ( ) .t t d?ر!??ا تاذ ?F:$?ا ??' ?????ا ر?A : ϕ T .(rad ن!?دا??!" . ) d?را???ا (Uأ ??' ر?.?ا ت!"1"1?$? ص!E?ا رو??ا . : : O /???"!??ا c u ????$? ?? ?V?ا طو?)?ا ل!???3!" ناد?:? ϕ و ) ϕ :?.?,? :ص!E?ا رو??ا ??V?? ???:? ( 2 du c ⇐ .i ? !"?#??ا ر!???ا ة??و U m = + ω ( ) . cos( . u t U t c m o 2 d u 2 2 = − . ω ω + ϕ = − ω × = − . ω ω + ϕ c . cos( . ). ( ) . sin( . ). : نذإ U t u t U t m o o o c m o o 2 dt dt 1 1 1 2= 2 ω = ω ⇐ − ω + = ? ?B????ا ??د??/?ا ?? W??????? ) a ( ,X0 . . 0 ص?Z2?ا W=.?ا : u u o o o c c C . . L L C C . L .??4!??ا ?ه ?H"!O?ا ?BL??ا ?? رو??ا ة??و ن?آ /% ?آf?4 ??? د!?"Yا ??د!?% (???O?? 2

3. (s ) T ??4!??ا يأ ، /%M?ا ة??و : ?ه ة??و نذإ O L τ = τ = : RLوRCN.H?ا ? !?= /% (?? /%M?ا ??"!= ????? لLg /% :ى?gأ ?H??." وأ RC . و R ر!???ا ة ??و q??:)?ا ??V?? (3 . cos( ϕ ω + = t q O m (t ) ) i ϕ . . t = U . q c = × = ω + ( ) ( ) . U c cos( ) q t c u t :?????ا ??:? * :6% m m m O :??????او ?????ا /?" ?B!.?ا ل!H?4ا(III .LC ???!???ا ةرا?$? ??$??ا ?B!.?ا ??V?? ( 1 e ξ?????ا ?? ?4وME??ا ?? !"?#??ا ?B!.?ا ع??J% ?F:? (آ ?? يو!O? LC ?B!.?او ??!???ا . ةرا??ا ?? ?4وME??ا ??$??ا ?B!.?ا ??????ا ?? ?4وME??ا ξ ??O?A!?T??ا m 2 1 1 q ξ = ξ + ξ = + 2 Li t e m 2 2 c dq = ω . ⇐ = = − . ω ω + ϕ = ω + ϕ . sin( . ) . cos( . ) I q i q t q q t نذإ : : !???? m m o m o o m o dt : ?$? !?آ N??? ?????ا ?? ?4وME??ا ?? !"?#?? ا ?B!.?ا ??V??و 2 I 1 2 2= 2 2= = ⇐ ω ⇐ = ω . ; نأ !?"و : m L . C . q I : A? q I q m m o m m m o ω C . L o 2 1 2 2 . . q I L C 1 1 2 ξ = × = × = m C m . . ,X0 ????E?ا ?3H??ا ?? W???????و : L I T m 2 2 2 C 3

4. 2 q 1 1 2 = × = ξ :LC LC? ??%/?ا ةرا,?? ? ?&?ا ?3?4?ا ???!?% ةرا?? ??$??ا ?B!.?ا m C . . . ????[ L I T m 2 2 .j???او ??????ا ?? ??O?A!?T% ?B!A &?إ ?????ا ?? ?? !"?#??ا ?B!.?ا ل?:?? ة??E??ا ??] ت!"1"1??ا لLg :ج!???3ا ⇐ q = ϕ ⇐ q = = π ω + ϕ ϕ = ϕ = . 2 ( ، t=0 ?F:$?ا ??' : !???? : ?Z?:$% 0 . cos 1 π . cos . . cos( . ) q q q q t : نذإ m m m m o 2 q . 2 ξ = ω = = ω 2 9?%و : m . cos ) . t . cos . q q t : ????$? ?? !"? # ??ا ?B!.?ا نذإ 6% : e o m o . 2 c T T o o t Ee To/4 To/2 0 3.To/4 To 0 0 2 2 2 qm . 2 qm . 2 qm . 2 c c c o T T = LC ???!?% ةراد ?? . ت!"1"1? $? ص!E?ا رو? ?ا ?G4 يو!O? ??????او ?????ا /?" ?B!.?ا لد!V??ا رود 2 . RLC ???ا????ا ةرا??ا ?B!A ( 2 2 1 1 q ξ = + 2 Li ???ا????اةرا??ا ?B!A /' ??V???ا /??? RLC : ?$? !?آ ????% ?F:? ?? t 2 2 c ξ d   q dq di q di = + = + t . . Li i L نذإ :   dt c dt dt c d dt tξ ξ d < ⇐ = − ?BL??ا ر!V?'!" ) ١ ( 2 t 0 .i R . ?%و!H??ا د?;و &?إ k?ذ ىM??و ??GB!?? ?B!.?ا نذإ dt dt . ل?; ل???% NVO" !?J?ر?? ةرا?$? ??$??ا ?B!.?ا RB!??? :ت!"1"1??ا ?4!?U (IV ت!"1"1??ا ?4!?U /?? ?? ???ا??% ةراد ةرا?$? ??$??ا ?%و!H??ا ى??O% . G ???% ل!???3!" k?ذ 2??و ، RLC ? &$' ل?; ل????" ةذ1V??ا ?B!.?ا ض??? ?B!." ةرا??ا دوM? 4

5. = + = G ????ا ? Ro R r . ( 6% ) . ةرا??ا ?V?? ي1?ا ? !"?#??ا ر!???ا ة?? 6% N3!??? ????" ةرا??ا ادا?Aا .?V?!3 ?%و!H?آ ف?G?? ?هو !7إ ن?4!B n?V.?" تا?????ا ??? : دوM? u R i g o = + + u u u u g R c L di di + = ⇐ + = + + + 0 ( ) . . L c u R r i R i u i r L ) ١ ( : يأ c dt dt 2 d u du di dq = = = c c c i c : ن^? نأ !?"و : 2 dt dt dt dt 2 d u + = c 0 Lc u `VG? k?1"و ، ?$?#??ا ?%و!H??ا تاذ ???!???ا ةرا?$? ةM????ا ??$7!???ا ??د!???ا ?هو ت!"1"1??ا : `VG? ( ١ ) نذإ c 2 dt . ?4!G% 5