?U200/90?2?IC?????jXCXC(A) U2?RI2?200/0?(V)
??I??I??200/90??10/0?ILCRXC∴(A)
??jX?I??j10?(200/90??10/0?)?2000/180??100/90?ULLLXCXC (V)
??U??U??2000/180??100/90??200/0??200?2000?j100U1L2XCXC(V)
又因U1=200
200?(200?故有
20002000?200?173.2X?C200?173.2 XC
则得: XC=5.36(Ω),或XC=74.6(Ω)
2.10 图2.6所示电路中,uS=10sin314tV,R1=2Ω,R2=1Ω,L=637mH,C=637μF,求电流i1, i2和电压uc。
解:ω=314rad/s
XL??L?314?637?200(Ω)
XC?11??5ωC314?637?10?6(Ω) (R?jXL)(?jXC)1000?j5Z1?2???j5.13R2?jXL?jXC1?j195(Ω)
200022000)?1002200???2002?1002XCXC
Z?R1?Z1?2?j5.13(Ω)
?U10/0??I1m?Sm??1.816/68.7?Z2?j5.13(A)
??I??Z?1.816/68.7??(?j5.13)?9.32/?21.3?UCm1m1(V)
?U9.32/?21.3??I2m?Cm??1.86/68.7??jXC?j5(A)
则 i1=1.816sin(314t+68.7°)(A) i2=1.86sin(314t+68.7°)(A) uc=9.32sin(314t-21.3°)(V)
2.11 图2.7所示电路中,已知电源电压U=12V,ω=2000rad/s,求电流I、I1。
解:当ω=2000rad/时s
XL??L?2000?0.5?10?3?1(Ω)
XC?11??2?6ωC2000?250?10(Ω)
R2(?jXC)?j4??1?jR2?jXC2?j2(Ω) Z?R1?jXL?Z1?1?j?1?j?2(Ω) Z1?I?U12??6Z2(A)
UC?I?Z1?6?2?8.49(V)
I1?UC8.49??4.29R22(A)
2.12 图2.8所示电路中,已知R1=40Ω,XL=30Ω,R2=60Ω,Xc=60Ω,接至
220V的电源上.试求各支路电流及总的有功功率、无功功率和功率因数。
解:设U?220/0?(V)
?U220/0??I1???4.4/?36.9??j40?j30R1XL 则 (A) 同理
??I2?U220/0???2.59/45?R2?jXC60?j60 (A)
.
???∵ I?I1?I2?4.4/?36.9??2.59/45??5.41/?8.61?(A) ∴P?UIcos??220?5.41?cos8.61??1.18(KW) Q?UIsin??220?5.41?sin8.61??178.2(Var)
?2.13 图2.9所示电路中,求:(1)AB间的等效阻抗ZAB;(2)电压相量U?;(3)整个电路的有功功率和无功功率。 和UDF
6?(6?j8?j8)ZAB?j4??3?j46?6?j8?j8解:
??cos??cos[0?(?8.61)]?0.99
AF
?U10/0??I???2/?53.1?ZAB3?j4(A)
??I?jX?