3.1已知正弦交流电压U=220V,ƒ=50Hz。写出它的瞬时值式,并画出波形。解:)30314sin(2220)(ttu第3章正弦交流电路-习题课30u,解:Atti)45314sin(10)(3.2已知正弦交流电压Im=10A,ƒ=50Hz。写出它的瞬时值式,并画出波形。45i,3.3比较以下正弦量的相位(1)(2)(3)(4)V)45sin(537V,)90sin(31021tutuA)135π100(50A,)90π100sin(10021titiAcos10V,)30sin(2100tituA1000sin10V,)90100sin(310titu(1)u1超前于u2。(2),u滞后于i。(3)由于u、i不同频,故无法比较相位。(4),i1滞后于i2。604545解:60453.4将以下正弦量转化为幅值相量和有效值相量,并用代数式、三角式、指数式和极坐标式表示,并分别画出相量图。(1)(2)(3)(4)V)90sin(310tuA)60sin(210tiAcos10tiV)30sin(2100tu解:(1)(2)V220902209022022090220V3109031090310310903109090mjsinjcoseUjsinjcoseUjjA2590sin2590cos25259025A1090sin1090cos101090109090mjjeIjjeIjj解:(3)V5035030sin10030cos1001003010030jjeUjV25065030sin210030cos2100210030210030mjjeUj解:(4)A35560sin1060cos1010601060jjeIjV652560sin21060cos2102106021060mjjeIj3.5将以下相量转化为正弦量(1)(2)(3)(4)解:(1)(2)(3)(4)V5050jU4030mjIV210030mjeUA301IV)45sin(100)45sin(2250)(tttuA912650).tsin()t(iV)30sin(2100)(ttuA)30sin(2)(ttiA3.6相量图如图所示,已知频率ƒ=50Hz。写出它们对应的相量式和瞬时值式。解:A60314126012A45314104510V3143100310V603142806080V90314210090100A3142100102m21m1m2211)tsin()t(iI)tsin()t(iItsin)t(uU)tsin()t(uU)tsin()t(uUtsin)t(iIV100A10V80A12V310A10I3.7电路如图所示,电压,,用相量法求每个电阻的电流和吸收的有功功率。解:)V30314sin(3101tu)V603140sin(3102tuW4840)A603140sin(31W4840)A30314sin(3122222111RIPtiRIPti3.8电路如图所示,已知L=10mH,,。求电流i1和i2,并进行比较。解:)V30100sin(1001tu)V301000sin(1002tu)A60100010)A6010010021tsin(itsin(i解:)A1201000sin()A120100sin(1.021titi3.9电路如图所示,已知C=10μF,。求电流i1和i2,并进行比较。)V301000sin(100)V,30100sin(10021tutu3.10求图示电路中未知电压表的读数。解:(a)V的读数为20V(b)V的读数为14.1V(c)V的读数为14.1V(d)V的读数为20V3.11电路如图所示,已知。(1)求电压uR、uL、uC和电流i。(2)求电路的有功功率P、无功功率Q和视在功率S。(3)画出相量图。V100sin141tuμF,100mH,100,Ω10CLR解:VA1000var,0W,1000)90100sin(2100)90100sin(2100)100sin(2100A)100sin(210CLRSQPVtuVtuVtuti3.12求图示电路中未知电流表的读数。解:(a)A的读数为20A(b)A的读数为14.1A(c)A的读数为14.1A(d)A的读数为20A3.13已知图示电路中,求电流i。解:15ΩV,)901000sin(2120RtuμF3.38mH,30CLA)9.1261000sin(210ti解:Z2为电阻,R=10Ω3.14已知图示电路中。试判断阻抗Z2的性质,并求出参数。A)1.5310sin(250StiV10sin2300uA,)9010sin(2401ttiu解:电压表V的读数为141V,电流表A的读数为10A。3.15求图示电路中各未知电压表、电流表的读数。3.16已知图示正弦交流电路中,电源电压。V0220U(1)求电路的阻抗Z;(2)求电流、和。III21解:561105728742594316668521..I..I..Z3.18判别正误。(1)(2)(3)因为,所以(4)因为,所以(5)(6),对应的正弦电压是(×)(√)(×)(√)(√)(×))V45200sin(V2100V10010045tejUj)V45001(sin200)V45001(sin200tt21uuu21UUU21iiimmmIII212121,IIIiiiV30220UV)30sin(220tu)V45001(sin400t3.19有一个电感线圈当给它通入10V直流电时,测得电流是2A。当给它通入10V工频交流电时测得电流是1.41A。求它的电感L。解:mH9.15L3.20正弦交流电路如图所示,已知而且、同相位。求复阻抗Z。Ω,10CXR,21UUIU解:Ω4525Ω552jZ(5/314H)3.21正弦交流电路如图所示,已知,电源电压,与同相位。求I、R、XL、XC及总阻抗Z。解:V100UA1021IIIUΩ25Ω210Ω25A1.14A210LCXRXZZI解:3.22电路如图所示,当ω=1000rad/s时,若,图(a)与图(b)等效。求C及各为多少?Ω,1000RΩ500'R'CμF2μF1'CC3.23正弦交流电路如图所示,已知,。求I、R2、XL、XC。解:Ω57Ω150A12LC.RXXIA,210A,1021II5ΩV,2001RUL2XR3.25用叠加定理求图示电路的各支路电流。解:A671326A463413A93610321..I..I.I解:A53116022360..IL3.26用戴维宁定理求图示电路的电流。LI3.27电路如图所示,已知。用支路电流并求支路电流的方程组。V,2100901SjeUΩ,1Ω,2Ω,Ω,2V,210021L2L145S2RRjjXjjXeUjΩ59.059.0LjZ解:A58.49LI(1)计算它的功率因数;(2)要使它的功率因数提高到0.9,需要并联多大的电容?电容器的耐压应该多少伏?(3)功率因数提高到0.9以后电流I=?3.30一个感性负载等效为RL串联电路如图所示。测量得到,电流,已知电源频率。V184V,122LRUUmA320IHz50f解:(1)(2)电容的耐压为600V。(3)V,313μF,6.255.054.56coscoscm1UCmA196I3.31已知RLC串联电路在电源频率为500Hz时发生谐振,谐振电流I0=0.2A,电容的容抗XC=314Ω,测得电容电压为电源电压的20倍。求电阻R和电感L。解:H1Ω7.15mLR(1)求电流i2、i3、i4;(2)求电流源提供的有功功率PS;(3)求电容C1。3.32已知。mH,3Ω,1A,1000sin101321SLRRRti0μF,1000mH,1133iCL解:μF3333101W14.25257.12A)901000sin(67.1A1000sin52131S4S32CPtitiii3.33有一台半导体收音机的输入电路电感L=0.5mH,电容器的可调范围是10~270pF。问它是否能满足收听中波段535~1605kHz的要求?解:谐振频率可调范围为433.88~2252.27kHz满足覆盖535~1605kHz要求。kHz272.2252kHz884.4330201ff解:A105314220A135314220A15314220321)tsin(i)tsin(i)tsin(i3.34电路如图所示,已知三相电源对称,三相对称负载。求各相电流的瞬时值式并画出相量图(含线电压、相电压、和相电流、)。V)60314sin(238012tuΩ25.525.5321jZZZ21II12U1U3I3.35图示电路如果联有中性线,中性线上有无电流?为什么?解:因为三相负载对称,则三个相电流亦对称。(2)当联结成图(b)的三相三线制形式,L1开路时求各相电流、、和中电流。此时负载Z2、Z3的工作是否正常?321IIINI(1)当联结成图(a)的三相四线制形式,L1开路时求各相电流、、和中电流。此时负载Z2、Z3的工作是否正常?321IIINI3.36三个单相负载联结在三相对称电源如图所示,已知每相负载的额定电压均为220V。Ω,20Ω,10Ω,5V,)30314sin(238032112ZZZtu解:(a)Z1、Z2能正常工作,因为Z1、Z2上电压仍为220V,是额定电压。(b)Z2、Z3不能正常工作,Z2上电压仅为126.7V,低于额定电压,而Z3上电压253.3V,高于额定电压。1I(2)当联结成图(b)的三相三线制形式,负载Z1短路时求相电流、和中线电流。此时负载Z2、Z3的工作是否正常?32IINI(1)当联结成图(a)的三相四线制形式(每相相线上均接有熔断器进行短路保护)负载Z1短路时求相电流、和中线电流。此时负载Z2、Z3的工作是否正常?32IINI3.37三个单相负载联结在三相对称电源如图所示,已知每相负载的额定电压均为220V。Ω,20Ω,10Ω,5V,)30314sin(238032112ZZZtu解:(a)Z2、Z3能正常工作,因为Z2、Z3上电压仍为额定值。(b)Z3、Z4不能正常工作,因为它们的电压为380V,超出了额定电压220V。3.38三相对称电路如图所示,已知电源。求各线电流和相电流。V,220301jeUΩ8.3312312ZZZ解:相电流线电流A1203100A120100A0100312312IIIA903100A1503100A303100321III解:W9306P3.39电路如图所示,已知三相电源对称,三相对称负载。求负载吸收的有功功率P。V)60314sin(238012tuΩ25.525.5321jZZZ