电工原理习题答案2269(第三章 8)(46-58)

3―46

???UUUSASBSC??ZZZZ1?2Z1?2Z1?2333???UNNZZZ(Z1?2)?(Z1?2)?(Z1?2)3331???U?)?12040V?(U?USASBSC33

??IA?UAB?U4044SA???8?j4AI??4?j8????45??4?j4AIBCj7?10?j310?j101?j12?Z2?Z2?Z2?Z2U???IA?IB?(IA?IB)??12?4Z2?I1?AB?4A3333Z2??Z2I??Z2I??Z2(I??I?)?Z2?(?12?j12)?Z?(?4?j4)UBCBCBC23333?U??I2?BC?(?4?j4)AZ2??Z2I??Z2I??Z2(I??I?)?Z2?(j12)?Z?(j4)UCACACA23333

?U??I3?CA?j4AZ23―47

??U???Z1?Z2??Im1?Z2?Im2?US1S2??????Z2Im1??Z2?Z3?Im2?US2??Im1??U?US1S2?US2?Z2?Z1??Z2?Z2Z2?Z3??Z2?Z2?Z3?110?110?15??j0.1110?15?1?j0.6?j0.2?j0.1?j0.11?j0.6

?3.75?j28.47?j0.1110?15?1.17?30.96??0.11?j0.2?28.72??82.49?j0.1110?15?1.17?30.96?0.228?118.81?33.06??51.53??11??75?20.9?j26.31?2.85?j10.63???0.228?118.810.228?118.81?18.05?j15.6823.91?40.98?????104.87??77.830.228?118.81?0.228?118.81?1

?Z2?Z1???Im2?Z2?Z1??Z2?Z2??U?US1S2?US2j0.2??j0.128.72??82.49110?15??Z2?Z3??Z20.228?118.81?22?105??2.872?7.51??5.69?j21.25?2.847?j0.357???0.228?118.810.228?118.81??2.843?j21.6321.82?97.49?????95.70??21.32A??0.228?118.810.228?118.81??I??104.87??77.83?A?I1m1??I??I??95.07??21.32??104.87??77.83?I2m2m1?67.04?j67.72?95.29?45.29?A??I??95.70??21.32?AI3m2~??I?*?ZI??*支路1：发出S1?U?26.57。?95.7??21.32??104.87?77.83?1133?I1?1.118?106.99?5.25??104.87?77.83??11220.04?83.08??(1351.83?j11138.31)VA

~??I?*?106.99?5.25??95.29??45.29??10195支路2：发出 S2?U.08??40.04?22

??7805.31?j6558.72?VA~? ??I?*?106.99?5.25??95.7?21.32??10238支路3：发出S3?U.94?26.5733?9157.59?j4579.78?VA

~~~?S1?S2?9157.14?j4579.59?S3?复功率收恒

3―48

??8VZ5支路所连的二端网络如图（3-48－b）所示，其中：UOC3883???I??0.3528??48.58?A5415?j17?j?5?j732

4Zi??j?3

3―49

由等效电源定理，电压表左边的戴维南等效电路如图(3-49-b)所示，

UOC=120V

Z1?Z2?2?j66.32?108.43??Zi????1.26?55.30??Z1?Z23?j45?53.13Z4?Z5?2?j4??4?j4??5?j8??4?j12?5?j8?Z4?Z52?j4?4?j43?j4Zl?Z3??5?j8?2.5?55.3??5?j8?1.43?j2.055?6.43?j10.055?Z?Zi?ZL?1.26?55.30??6.43?j10.055?0.717?j1.036?6.34?j10.055?7.147?j11.091?13.19?57.2??I?120?9.09A 电流表读数为9.09A13.19

3―50

?、I?、I?设Im1m2m3??11??1?????I?Im2?U??m1S?Gjωωjωω?????11?2??1????I??I?Im3?0?m1m2??jωω?Gjωω??jωω??11?2????I???m2?Gjωω??Im3?0jωω??? 3

11?Gj?C1?j?C0??Im311?Gj?C1?j?C0?1?USj?C12?0Gj?C1?0j?C?01j?C12?Gj?C?1j?C12?Gj?C1?j?C???Im3?1????j?C??US???12??11??1????????Gj?C??Gj?C?????j?C????????3222?12??1????Gj?C?????j?C??????2?11????Gj?C????

?1??j??j?C??US????8R5R24??32R?3?R???????23?32?j?C?????????cj?cj?c?c?????????与U?反向，所以分母实部为?U零2S??8??c?2?R3?2R??C?2?0?6??c?2?R2?0得：R?C?6?1?j???U?c??这时：2??U5R243S??j?cj??c?3j??c?3?R??????16?????295R34R33R3??66666

4

33

3―51

试将图3—49中的各G?1/R与C对调，

分别用节点法、网孔法求?、U?反向时?、G、C的关系。使U2S

节点法：选d为参考点??jωω??jωω???2jωω?G?UUUnanbs????2jωω?G?U??jωω??0UU??jωωnanbnc????jωω?G?U??0?jωωUnbnc???U??U2ncj2?C?j?C0?j?Cωωj2?C?G?jωω0?j?C0j2?C?G?j?Cωω0?j?Cωω0j2?C?G?j?Cωω?j?Cωωj?C?G3??j??C?US??j2?C?G?2?j?C?G???j?C?2?j?Cωω?G???j?Cωω?2?j2?C?G???j??C?3US?32G?6G??C??j5G2?C?j??C?3

?1??j??j?C??US????8R5R24??32R?3?R???????23?32?j?C??c??j??c??????c????j??c???与U?反相，上式分母实部应欲使U为零，则：23G2?6G(?C)2?0??CR?16G2?6G(?C)2G?1R3

5

??－j(?C)UUS2这时，＝?23?Uj5G?C?j(?C)33?(1R61?)3US??1135()2?()RR6R6129

网孔法：??11??1?????I?Im2?U??m1S?GjωωG????1??111??1????I???I??m1?GGjωω?m2GIm3?0G????1??111?????I???m2??Im3?0GGGjωω????Im31?USG21?0Gj?c10?0G?111??0Gj?cG1211???GGj?cG11110???GGGj?c??1?????US?G?211?Gj?c1?G??21????Gj?c????2?11??1????Gj?c????G??????1?????US?G?22?21??1????Gj?c????G?????2?11????Gj?c???????1??1?2?2???????2R?R??R3R??????j?C??j?C?j?C?????R2?UR3?5R2??C?2?6R1?j?Cωωj??C?3S2

6

??1I??RI??而U2m3m3G?R3?USR?35R??c?26R21??j?cj??c?3?与U?反向，故有上式分母虚部为零时,U2S6R21??0j?Cj??C?311得：6R? ?CR?6??C?2?UR3R312这时：??3??3?5R29U3R?30RSR???C?2

3―52 105.8V 1R??10??0L?100?3―53 100?10?3 L?0.1592mHC?159.2pF

Q?100

3―54

22???1100??2?R????1L???????L10???1???22??1100??2????R???3L??L?????10?3???得R?5?1?100?L??8.66?100?C由?1?200?L??8.66200?C?得C?183.8?FL?27.57mH3―55

由1LC解得：C?183.8?F?105L?120?103RCf?70.7HzL?105?100RL?27.57mH 7

3―56

I0?IRLR22R???L?U??1.935A22R???L?U?0.4493AIC???L?IR0?1.882A3―57

谐振时?m?Z??0?1?j?C1L1j?L．j?C21L?a?Z?1???11j?C1j?C1j?L?j?C2L?jj?C2??01j?C2L?j?21L??C2?C1?1得：?0??b?Y??1?j?L11j?L2?j?C1?0谐振时?m?Z??01?j?L11j?L2?j?C1C??L2?L1?

3―58

得：?0?R?j?L?R??L?2?Zi?10?j20???10?2?2?R?j?l?R???L????由谐振条件：?m?Z??0 20??L??R2??L??20R2?02?R2??L???j??20?R2???L?2???R2??L?R???L?22?20?0106L2?500R2?L?R2?0L?500R2??500R?22?4R2?1062?1068

由题意，只有一个L能使电路谐振，所以 500R2得R?4? 则L?4?10?3HR??L?2??2?4R2?106?0?Zi?10?R2???L?2?10?4?4?10.5?16?16 9

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