第四章 正弦交流电路习题参考答案

第四章 正弦交流电路习题 参考答案 有机化学期末考试题统计学b答案数学分析3答案计算机必考试卷02新大家的日语参考答案 第四章 正弦交流电路 [练习与思考] ,4-1-1 在某电路中， i,2202sin，，314 t,60A ?指出它的幅值、有效值、周期、频率、角频率及初相位，并画出波形图。 ?如果的参考方向选的相反，写出它的三角函数式，画出波形图，并问?中各项有无改变, i 解:? 幅值 I2202Am I,220A有效值 ,314频率 ,,,fHz5022,, 1周期 Ts,,0.02f 角频率 ,,314/rads 题解图4.01 ,,,rad/s初相位 ,i/A3 波形图如题解图4.01所示 2202A (2) 如果的参考方向选的相反, 则i 2,,,,t，初相位改变了，i,2202sin314 t，A,,3,, ,2,2,rad/s其他项不变。波形图如题解图 ,334.02所示。 题解图4.02 ,,4-1-2 已知， i,10sin(314t,120)Ai,20sin(314t，30)A12 i/A?它们的相位差等于多少, 20A i1iiii?画出和的波形。并在相位上比较和谁121210Ai2超前，谁滞后。 ,t, 解:? 二者频率相同，它们的相位差6 ,2,,,,,,,120:,30:,,150: ii213 ii(2)在相位上超前，滞后。波形图如题解图4.03所示。 题解图4.03 21 of vision Yibin formation in the Center surrounded by, organic dispersion band of bead-space layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a long-term basis in a reasonable space to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multi-center" strategic vision of space frame. Yibin Center City development construction steering extension type extended and connotation type upgrade simultaneously of mode, in Metro construction of while is committed to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urban green space system, promoting the construction of peripheral green space and protection of historical 4-2-1 写出下列正弦电压的相量 ,, ， u,220sin(,t,45)Vu,100sin(314t，45)V12 ,, U,1102，,45:VU,502，45:V解: 12 ,,4-2-2 已知正弦电流和，试用复数计算电流i, 8sin(,t，60)Ai,6sin(,t,30)A12 ，并画出相量图。 i,i，i12 解:由题目得到 ,,,j+I,I，I,8，60:，6，,30:mm1m2,,(8cos60:，j8sin60:)，(6cos30:,6sin30:)Im1 ,,(4，j6.93)，(5.2,j3),9.2，j3.93Im60:,10，23.1:A23.1: +130:,所以正弦电流为 Im2 , i, 10sin(,t，23.1)A1 题解图4.04 相量图如题解图4.04所示。 4-2-3 指出下列各式的错误。 , , I, 10，30AU, 100sin(,t，45)V j30,I, 10eA， I,10sin(314t，20)A , I, 10，30:A 解: 应改为 I, 10，30A ,, 应该为 u, 100sin(,t，45)VU, 100sin(,t，45)V ,:j30j30I, 10eAI, 10eA 应该为 ,, 应该为 i,10sin(314t，20)AI,10sin(314t，20)A 0u4-3-1 已知的电感接在400Hz/100V的正弦电源上，的初相位为20，求电流并画L,1H 出电流、电压的相量图。 , U,100，20:V 解:已知 95green space system, promoting the construction of peripheral green space and protection of historical de city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urbanupgra ation city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features,tted to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimizotation type upgrade simultaneously of mode, in Metro construction of while is commicenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable space to develop, perfect urban district -ank area, the minjiang River area, Golden Sands area on a longict to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bon to expand, Naxi distrspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new visi-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead ,,U100，20: I,,,0.04，,70:A+j,jXj2，400，1L ,电流、电压的相量图如题解图4.05所示。 U 20:4-3-2 指出下列各式哪些是对的，哪些是错的, +170:,,,,UUUuI,X ，,j,L，， ,XIj,,LL,iI,LI,,IdiUUU,,u,L,X,,C C，，，题解图4.05 j,CdtII Uu,XL,X 解: 此式错 应改为 LIi , UU,j,L 此式错 应改为 ,j,L ,II ,, UU,X,jX 此式错 应改为 LL,, II ,,U 此式正确 Ij,,,L diu,L 此式正确dt U,X C此式正确I U1U,,C, 此式错 应改为 I,CI ,,,,IIU,, Uj ,, 此式错 应改为 j,C,C 4-3-3 试列表比较RLC三元件在正弦电源激励下各自表现的特性及其关系。 解: 电路 一般关系式 相位关系 大小关系 复数式 U,u,RiR I,,,,,0: ,uiURI, R ,diL U,u,L,,,,90: UuiI, dt,I XLjXL storicalof hi ty of big city. Construction of urban green space system, promoting the construction of peripheral green space and protectionronment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacienvi with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved cityMetro construction of while is committed to old city transformation and built district of perfect, through live and industry otation type upgrade simultaneously of mode, incenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-e to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable spac-n, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a longgang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shaspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lin-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead96 ,1C U, u,idt,,,,,90:Uui, I,C I,XC,jXC 4-4-1 假设R、L、C 已定，电路性质能否确定,阻性,感性,容性, 解:不能。还跟电路的频率有关。 4-4-2 RLC串联电路的是否一定小于1, cos, 解:还可能等于1。 4-4-3 RLC串联电路中是否会出现，，的情况, U,UU,UU,ULCR 解:会出现和的情况，不会出现的情况。 U,UU,UU,ULCR L,CL,C4-4-4 在RLC串联电路中，当时，u超前i，当时，u滞后i，这样分析对吗, 解:在RLC串联电路中，当，电路呈感性，u超前i;当时，电路呈容X,XX,XLCLC性，u滞后i。所以上面的分析是不正确的。 4-4-5 有一RLC串联的交流电路，已知，，试求其两端的电压。 UI,1AR,X,X,10,LC U,IR,1，10,10V 解:此电路为纯阻性，所以 ,,RC4-4-6 有一串联电路，已知，，电源电压，试求电流。 U,100，0ViX,3,R,4,C ,,U100，0:100，0:I,,,,3R,jX4,j3C解: 5，arctan4 100，0:,,20，36.9:A5，,36.9: 4-5-1图4-20所示的四个电路，每个电路图下的电压、电流和电路阻抗模的 答案 八年级地理上册填图题岩土工程勘察试题省略号的作用及举例应急救援安全知识车间5s试题及答案 对不对,各图中给定的电路电压、阻抗是否正确, U,14VU,70VI,8AI,8AZ,7,Z,14,Z,2,Z,2, (a) (b) (c) (d) 图4-17 练习与思考4-5-1图 97green space system, promoting the construction of peripheral green space and protection of historical de city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urbanupgra ation city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features,tted to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimizotation type upgrade simultaneously of mode, in Metro construction of while is commicenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable space to develop, perfect urban district -ank area, the minjiang River area, Golden Sands area on a longict to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bon to expand, Naxi distrspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new visi-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead U,10V解:(a) Z,5, (b)两个元件性质相同，容抗和电压可以直接相加。图中给定的电路电压、阻抗是正确。 (c)图中给定的电路电压、阻抗是正确。 (d)两个元件性质不同，图中给定的电路电压、阻抗是不正确。 4-5-3 两个阻抗串联时，在什么情况下 成立, Z,Z，Z12 111两个阻抗并联时，在什么情况下成立, ,，ZZZ12 解:当两个阻抗的阻抗角相等的时候，上面2个式子成立。 4-5-4 图4-21所示电路中，已知， X,X,R,2,LC 电流表A的读数为3A，试问: 1 ?A和A的读数为多少? 23 ?并联等效阻抗Z为多少? 图4-18 练习与思考4-5-4图 解:?此题为RLC并联电路，，所有各元件中电流X,X,R,2,LC,,ICI2的大小是相等的，即，相量图如题解图4.06所示。 由相量I,I,ILCR 45:, ,UI图知，电流表A所测量的的总电流就是电阻电流I，所以11RIR ,, AI,I,I,3AA，所以电流表的读数为3A。电流表测量的是IILR3LCR2 , A和的总和。由相量图可知的读数为4.24A。 题解图4.06 IC2 11111111,，,,，,,? ZRjXjX22j2j2LC 则并联等效阻抗 Z,2, 4-6-1 对于感性负载，能否采取串联电容器的方式提高功率因数, 解:电容电感串联能够提高电路总的功率因数，但是会改变感性负载的工作状态。 4-6-2 试用相量图说明，并联电容量过大，功率因数反而下降的原因。 解:从题解图4.07相量图上可知，当并联合适的电容时，总电压和总电流的夹角减小，使,得功率因数提高，直到提高到1，这时继续增加并联的电容值，电路由感性变为容性，功率因数 envi with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved cityMetro construction of while is committed to old city transformation and built district of perfect, through live and industry otation type upgrade simultaneously of mode, incenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-e to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable spac-n, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a longgang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shaspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lin-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead98storicalof hi ty of big city. Construction of urban green space system, promoting the construction of peripheral green space and protectionronment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capaci 反而下降。 ,,,,ICIICIC,,,,,,U,UUII ,,,,,, I(I)I(I)I(I)111 (b)(c)(a) 题解图4.07 4-6-3 提高功率因数时，如将电容器并联在电源端(输电线始端)，是否能取得预期效果, 解:电容并联在输电线始端，只能减少电源的无功电流，提高了电源的功率因数，但是连接负载的的输电线路(可能很长)电流并无改变，仍然存在原来的功率损耗，因此达不到提高功率因数的预期效果。 4-6-4 功率因数提高后，线路电流减小了，瓦时计会走的慢些(省电)吗, 解:不会。因为瓦时计测量的是有功功率，提高功率因数后，电路的有功功率不变。 4-7-1 电路基本定律的相量形式是什么, , I,0,解:KCL定理: , U,0,KVL定理: , U,Z欧姆定律: , I 4-7-2分析正弦交流电路一般采用什么方法, 解: 1(根据原电路图画出相量模型图(电路结构不变) C,,jXL,jXR,RCL、、 ,,, u,Ui,Ie,E、 、 2(根据电路基本定律的相量形式，列出相量方程式或画相量图 3(用相量法或相量图求解 4(将结果变换成要求的形式 4-7-3 分析复杂正弦交流电路采用什么方法, 解:同第2章计算复杂直流电路一样，支路电流法、结点电压法、叠加原理、戴维宁定理等 99green space system, promoting the construction of peripheral green space and protection of historical de city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urbanupgra ation city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features,tted to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimizotation type upgrade simultaneously of mode, in Metro construction of while is commicenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable space to develop, perfect urban district -ank area, the minjiang River area, Golden Sands area on a longict to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bon to expand, Naxi distrspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new visi-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead 方法也适用于计算复杂交流电路。所不同的是电压和电流用相量表示，电阻、电感和电容及组成的电路用阻抗或导纳来表示，采用相量法计算。 4-7-4 能否用直流电路中学过的弥尔曼定理和支路电流法分析正弦交流电路,如果能用，使用时应注意什么问题, 解:可以。注意:电压和电流用相量表示，电阻、电感和电容及组成的电路用阻抗或导纳来表示，采用相量法计算。 4-8-1 串联谐振时，电路对外呈电阻性，无功功率为零，能否认为电感和电容的无功功率也为零, 解:不能。电路总的无功功率为零，电感和电容的无功功率大小相等，方向相反。 RLC4-8-2 试说明当频率低于或高于谐振频率时，串联电路是电容性还是电感性的, 解:当时，，电路呈容性; X,Xf,fLC0 当时，，电路发生谐振; X,Xf,fLC0 当时，，电路呈感性。 X,Xf,fLC0 4-8-3 有一2000PF的电容和一个10Ω的电阻及0.2mH的线圈，将它们接成并联谐振电路，求谐振时的阻抗和谐振频率。 117ω,,,1.58，10rad/s 解: 0,15LC0.2，2000，10 3,L0.2，10Z,,,10KΩ 0-12RC10，2000，10 习 题 ,4-1 已知某正弦电压当其相位角为时，其值为5V，该电压的有效值是多少,6 若此电压的周期为10ms，且在t=0时正处于由正值过渡到负值时的零值，写出电压的瞬时值表达式。 u,Usin(,t，,)V解:设正弦电压的瞬时值表达式为 m ,5sinU,7.07V,UU,10V由题目知，所以, 有效值 mm6 100storicalof hi ty of big city. Construction of urban green space system, promoting the construction of peripheral green space and protectionronment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacienvi with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved cityMetro construction of while is committed to old city transformation and built district of perfect, through live and industry otation type upgrade simultaneously of mode, incenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-e to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable spac-n, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a longgang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shaspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lin-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead 1 ,,2,f,2,，,628rad/s,310，10 由t=0时正处于由正值过渡到负值时的零值得: ,,, 得到电压的瞬时值表达式: u,10sin(628t，,)V oo4-2 已知某负载的电流和电压的有效值和初相位分别是6A、-30;48V、45，频 率均为50Hz。(1)写出它们的瞬时值表达式;(2) 画出它们的波形图;(3)指出它们的 u/V,i/A幅值、角频率以及两者之间的相位差。 482V解:(1) ,,2,f,2,，50,314rad/s 62A u,482sin(314t，45:)V,t , i,62sin(314t,30:)A6 ,(2)波形图如题解图4.08所示。 4 (3)幅值，， 题解图4.08 U,482VI,62Amm 314rad/s角频率均为，相位差 ,,,,,,,75:ui ,,j60U,220eV4-3 已知正弦量，试分别用三角函数式、正弦波形及相量图表示它 ,,j60U,,220e们。如V，则又如何, ,,j60U,220eV解:正弦量 三角函数式 u,2202sin(,t，60:)V正弦波形和相量图如题解图4.09所示。 u/V +j2202V,U ,t60: +1 , 3 题解图4.09 ,,j60utV,,:2202sin(120),U,,220e当V时，三角函数式 ，正弦波形和 相量图如题解图4.10所示 de city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urbanupgra ation city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features,tted to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimizotation type upgrade simultaneously of mode, in Metro construction of while is commicenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable space to develop, perfect urban district -ank area, the minjiang River area, Golden Sands area on a longict to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bon to expand, Naxi distrspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new visi-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead101green space system, promoting the construction of peripheral green space and protection of historical 题解图4.10 U,220V4-4 已知工频电源，设在电压的瞬时值为156V时开始作用于电路，试写出该电压的瞬时值表达式，并画出波形图。 解:设该电压的瞬时值表达式 u,Usin(,t，,)Vmu/V 工频电源，所以 f,50Hz,,2,f,2,，50,314rad/s2202V U,220V，则 U,2202Vm ,t 由题得，所以 ,,30:156,2202sin(314t，,)|t,0 电压的瞬时值表达式: , 6 u,2202sin(314t，30:)V 题解图4.11 波形图如题解图4.11所示。 U,120I,20U,2204-5 一个线圈接在V的直流电源上，A;若接在Hz，Vf,50 I,28.2的交流电源上，则A。试求线圈的电阻R和电感L。 解:接在直流电源上线圈的电感相当于短路，所以线圈的电阻为: U120R,,,6, I20 当线圈接在50Hz的交流电上时，相当于RL串联电路，所以线圈阻抗模为: U2202222ZRXRfL||,，,，(2,),,,7.8, LI28.2 L,15.88mH解得 。 4-6日光灯管与镇流器串联接到交流电压上，可看作为RL串联电路。如果已知某灯管的等效电阻R=260，镇流器的电阻和电感分别为R=40Ω和L=1.65H，电源电压,12 envi with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved cityMetro construction of while is committed to old city transformation and built district of perfect, through live and industry otation type upgrade simultaneously of mode, incenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-e to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable spac-n, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a longgang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shaspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lin-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead102storicalof hi ty of big city. Construction of urban green space system, promoting the construction of peripheral green space and protectionronment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capaci U,220V，试求电路中的电流和灯管两端与镇流器上的电压。这两个电压加起来是 否等于220V? 已知电源频率为50Hz。 解:灯管与镇流器串联电路的总阻抗: Z,(R，R)，j,L,(260，40)，j314，1.65,300，j518,599，59.92:,12 U220电路中的电流 I,,,0.367A|Z|599 灯管两端电压 U,IR,0.367，260,95.42V11 22U,IR，(,L),190.3V整流器两端电压 22 ,,, 注意:，但是 U,U，UU,U，U1212 4-7 图4-38所示，电源电压为，电阻和电容 u 上的电压分别为和u，已知电路阻抗模为 uCR u1000，频率为1000Hz，设与之间的相 u,C ou位差为30，求R和C，并说明在相位上u比 图4-38 习题4-7、4-8图 C超前还是滞后。 ,0U,U，0Vu解:设电压为参考量，，电路中电压和电流相量图题解图4.12所示 , I由相量图可知: , U U,Usin30:RR ,60:U U,Ucos30: 30:C , 两边同除以电流I，可得: UC 题解图4.12 R,|Z|sin30:,1000，0.5,500, X,|Z|cos30:,1000，0.866,866, C 11C,,,0.18,F X2，1000，866,,C u30:u超前。 C green space system, promoting the construction of peripheral green space and protection of historical de city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urbanupgra ation city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features,tted to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimizotation type upgrade simultaneously of mode, in Metro construction of while is commicenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable space to develop, perfect urban district -ank area, the minjiang River area, Golden Sands area on a longict to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bon to expand, Naxi distrspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new visi-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead103 4-8 图4-38是一移相电路。如果C=0.01μF，输入电压V，今欲使输u,2sin6280t 0出电压在相位上前移60，问应配多大的电阻R,此时输出电压的有效值等于uURR多少, 解:由上题的相量图可知: URR ,,tan30:UXCC 1则 R,tan30:，X,tan30:，,9.19K,C,66280，0.01，10 U,U，cos60:,0.5VR1 4-9 在RLC串联电路中，已知端口电压为10V，电流为4A，，V，U,8VU,12RL,,10rad/s，求电容电压及R、C。 U8RR,,,2,解: I4 U12LX,,,3, LI4 U1022ZRXX||,，(,),,,2.5, LCI4 求得 X,1.5,C 11,0.067FC则 = U,IX,4，1.5,6V ,CC10，1.5,XC 4-10 图4-39所示的各电路图中，除A和V外，其余电流表和电压表的读数在图上00 都已标出。试求电流表A或电压表V的读数。 00 (a) (b) 图4-39 习题4-10图 ronment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacienvi with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved cityMetro construction of while is committed to old city transformation and built district of perfect, through live and industry otation type upgrade simultaneously of mode, incenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-e to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable spac-n, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a longgang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shaspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lin-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead104storicalof hi ty of big city. Construction of urban green space system, promoting the construction of peripheral green space and protection 8,XI解:， 6,RIC 22U,ZI,R，XI,10V C 所以，图(a)电压表V的读数为10V 0 由图(b)画出相量模型。 10A,jXC A1,,,I1I,0I1100V,j10,U1,，,A0V1,I0,U1,，,45:UCIj5,5,,,,,U0IU0UC，,V0 题解图4.13 ,,,,,00设为参考相量，超前90，超前90，画出相量图，可得: IUUIUC1110 U1001I,,,102A 22Z5，52 2222A,I,I,I,(102),10,10A 001 U,XI,100ACC0 22V,U,100，100,141.4V 00 4-11 电路如图4-40所示。已知U,200V, R,X，开关闭合前I,I,10A，开关闭L2合后 u，i 同相，求:I、R、X和X。 LC 图4-40 习题4-11图 图4-41 习题4-12图 upgra ation city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features,tted to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimizotation type upgrade simultaneously of mode, in Metro construction of while is commicenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable space to develop, perfect urban district -ank area, the minjiang River area, Golden Sands area on a longict to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bon to expand, Naxi distrspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new visi-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead105green space system, promoting the construction of peripheral green space and protection of historical de city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urban 解:(1)利用相量图题解图4.14计算 开关闭合前后I的值不变。 2 U200200 I,,,,10A222Z2RR，X2L 200? R,X,,102ΩL102 由相量图可求得: 题解图4.14 I,Icos45:,52A2 I,Isin45:,10，sin45:,52A12 U200X,,,202ΩCI521 (2)用相量计算 ，U,200，0:V设: ，? ，? R,XI,10，,45:AL2 ，，Z ,U/I,(200，0:/10，,45:)Ω,20，45:Ω22 ,? R,X,Z，cos45,102ΩL2 ，?开关闭合后 u，i同相 ? I,I，0:A ，，，? ? I，0: ,I，90:，10，,45:III ,，112 由实部相等可得 I,Icos45:,52A2 由虚部相等可得 I,Isin45:,10，sin45:,52A12 U200X,,,202ΩCI521 u,2202sin314tVi,22sin(314t,45:)A4-12 图4-41所示电路中，，， 1 。试求:各表读数及参数R、L和C。 i,112sin(314t，90:)A2 106storicalof hi ty of big city. Construction of urban green space system, promoting the construction of peripheral green space and protectionronment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacienvi with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved cityMetro construction of while is committed to old city transformation and built district of perfect, through live and industry otation type upgrade simultaneously of mode, incenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-e to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable spac-n, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a longgang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shaspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lin-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead 图4-43 习题4-15图 解:(1) 求各表读数 ? ? V的读数为220V U,220V 22? I,,15.6AI,11A122 ，，，? I,I，I,15.6，,45:，11，90:A,11A12 11A即A的读数为 也可以根据题解图4.15相量图求得: 22I,15.6,11A,11A 题解图4.15 (2)求参数 R、L、C 方法1: ，220，0:UZ,,Ω,14.1，45:Ω,10，j10Ω1，15.6，,45:I1 XLL,,0.0318H? R,X,10ΩL2πf ，220，0:UZ,,Ω,20，,90:Ω2，11，90:I2 11? C,,,159μF 题解图4.16 2πfX314，20C 方法2:利用题解图4.16阻抗三角形 UZ,,14.1Ω1I1 R,Zcos45:,10ΩX,Zsin45:,10Ω? 1L1 upgra ation city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features,tted to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimizotation type upgrade simultaneously of mode, in Metro construction of while is commicenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable space to develop, perfect urban district -ank area, the minjiang River area, Golden Sands area on a longict to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bon to expand, Naxi distrspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new visi-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead107green space system, promoting the construction of peripheral green space and protection of historical de city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urban XL L,,0.0318H2πf U? 即: X=20Ω Z,,20ΩC2I2 11? C,,,159μF2πfX314，20C C,50μFRLCR,50,4-13 在串联电路中，, L=150mH，，电源电压 ,f,50u,2202sin(,t，20)V，电源频率Hz。 (1)求X、X、Z; LC (2)求电流I并写出瞬时值的表达式; i ,(3)求各部分电压有效值并写出其瞬时值表达式; UL(4)画出相量图; 108.4:,,(5)求有功功率P和无功功率Q UIR ,3解:(1) X,,L,2,fL,2,，50，150，10,47.1,71.6:L 111X ,,,,63.7,C,,6CfC,,2,2，50，50，10UC Z,R，j(X,X),50,j16.6, 题解图4.17 LC U,220V(2) 电源电压有效值 ,,U220，20: I,,,4.18，arctan0.332,4.18，38.4:A Z50,j16.6 I,4.18A则: i,5.9sin(314t，38.4:)A U,IR,4.18，50,209V(3) R U,IX,4.18，47.1,197V LL U,IX,4.18，63.7,266V CC u,2092sin(314t，18.4:)VR 108storicalof hi ty of big city. Construction of urban green space system, promoting the construction of peripheral green space and protectionronment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacienvi with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved cityMetro construction of while is committed to old city transformation and built district of perfect, through live and industry otation type upgrade simultaneously of mode, incenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-e to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable spac-n, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a longgang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shaspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lin-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead u,1972sin(314t，108.4:)VL u,2662sin(314t,71.6:)VC (4) 相量图如题解图4.17所示。 22(5) 有功功率 P,IR,4.18，50,873.6W 22 无功功率 Q,IX,IX,4.18，4.18，(,16.6),,290VarLC 4-14 在图4-42的电路中，欲使电感和电容器上的电压有效值相等，试求R值及各部分电流。 图4-42 习题4-14图 解:依题意电感和电容器上的电压有效值相等，则有电容的阻抗模与并联之路的阻抗模相等，即 ,j4Rj2.4, R,j4 R,3,解得: ,, UU设电感上电压为，并联部分电压为 L// ,,j2.4,j2.4U,，10，0:,，10，0:,11.4，118:V则 L,j4R,j12，j2.4，j2.4R,j43,j4 , U,11.4，,65:A 同理 // ,U11.4，,65:// I,,,2.85，25:AC,j4,j4 ,,U11.4，,65://I,,,3.8，,65:A R33 de city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urbanupgra ation city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features,tted to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimizotation type upgrade simultaneously of mode, in Metro construction of while is commicenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable space to develop, perfect urban district -ank area, the minjiang River area, Golden Sands area on a longict to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bon to expand, Naxi distrspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new visi-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead109green space system, promoting the construction of peripheral green space and protection of historical ,,U11.4，118:L I,,,2.4，28:Aj2.4j2.4 ,,U,220，0V4-15 在图4-43的电路中，已知，试求: (1)各元件上的功率; (2)电路的总功率因数、有功功率、无功功率及视在功 ,率。 IZ1 ，,3，j4,,I3I2 ,Z2UZ3解:题解图如图4.18所示 5,,j5,, ,j5，5电路总阻抗 Z,，3，j4,5.5，j1.5,5,j5 ,,U220，0:220，0:(1) 题解图4.18 I,,,,38.6，,15.3:AZ5.5，j1.55.7，15.3: ,,,j5 I,I，,27.3，120:A25,j5 ,,5 I,I，,27.3，60:A35,j5 2222P,I，3,38.6，3,4470WQ,I，4,38.6，4,5960Var ZZ11 22P,I，5,27.3，5,3726WQ,0Var ZZ222 2 P,0WQ,,I，5,,3276VarZZ333 ) 电路的总功率因数 (2 cos,,cos15.3:,0.96 P,P，P，P,4470，3726，0,8196W 有功功率 ZZZ123 Q,Q，Q，Q,5960，0,3276,2684Var 无功功率 ZZZ123 S,UI,220，38.6,8492VA 视在功率 ,,, UU4-16 计算图4-44a中的电流和各阻抗元件上的电压与，并作相量图;计算图I21 ,,, II4-44b中的各支路电流与和电压，并作相量图。 U12 110storicalof hi ty of big city. Construction of urban green space system, promoting the construction of peripheral green space and protectionronment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacienvi with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved cityMetro construction of while is committed to old city transformation and built district of perfect, through live and industry otation type upgrade simultaneously of mode, incenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-e to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable spac-n, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a longgang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shaspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lin-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead (a) (b) 图4-44 习题4-16图 解:图(a)电路中: ,,U10，0:I,,,2，,36.9:A Z，Z2，2，j312 ,,Z21 U,U,，10，0:,,4，,36.9:V1Z，Z2，2，j312 ,,Z2，j32U,U,，10，0:,7.21，19.4:V2Z，Z2，2，j312 图(b)电路中: ,,Z1,j2I,I,，2，0:,2，,45:A1Z，Z1，j，1,j12 ,,Z1，j1I,I,，2，0:,2，45:A2Z，Z1，j，1,j12 ,, U,ZI,(1，j)，2，45:,2，0:V11 相量图如题解图4.19(a)、(b)所示 , I2 ,,,19.4:IU45:U,36.9:R I,45:,U1I1 (a) (b) 题解图4.19 4-17 已知一感性负载的额定电压为工频220V，电流为30A，cosφ=0.5，欲把功 率因数提高到0.9，应并多大的电容器, P,220，30，cos,,220，30，0.5,3300W解: 111green space system, promoting the construction of peripheral green space and protection of historical de city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urbanupgra ation city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features,tted to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimizotation type upgrade simultaneously of mode, in Metro construction of while is commicenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable space to develop, perfect urban district -ank area, the minjiang River area, Golden Sands area on a longict to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bon to expand, Naxi distrspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new visi-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead ,,2,f,2,，50,314rad/s P3300,1,1,,C,(tan,tan),[tan(cos0.5),tan(cos0.9)]122ωU314，220 ,4,4,2.2，10，(tan60:,tan25.8:),2.2，10，(1.73,0.48),67.6,F cos,,0.884-18 一照明电源，已知电源电压为220V、50Hz，总负载为6kVA，，负载有白炽灯和日光灯，已知日光灯本身的功率因数为0.5，计算白炽灯和日光灯各有多少瓦, 解:电路中的无功功率是有日光灯产生的，所以有 P日光灯22Q,，1,0.5,6000，1,cos,,2850Var 日光灯0.5 解得 P,1645W日光灯 P，P,6000，cos,,5280W日光灯白炽灯 则 P,5280,1645,3635W白炽灯 4-19 有一电感性负载，额定功率，额定电压，额定功率因P,40kWU,380VNN 数,,0.4，现接到50Hz、380V的交流电源上工作。求: N ?负载的电流、视在功率和无功功率; ?若与负载并联一电容，使电路总电流降到120A，则此时电路的功率因数提高到多少,并联的电容是多少, P40000NI,,,263.2A解:(1)负载的电流 ,U380，0.4NN P40000NS,,,100KVA 视在功率 ,0.4N 22Q,S，1,,,100000，1,0.4,91.7KVar 无功功率 N P40000'N,,,,0.88(2)并联电容后电路功率因数为 N'380，120UIN P40000,1,1C,(tan,tan),，[tan(cos0.4),tan(cos0.88)],,122ωU314，380 ,4,4,8.8，(tan66.4:,tan28.4:),8.8，10，(2.29,0.54),15.7，10F 112storicalof hi ty of big city. Construction of urban green space system, promoting the construction of peripheral green space and protectionronment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacienvi with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved cityMetro construction of while is committed to old city transformation and built district of perfect, through live and industry otation type upgrade simultaneously of mode, incenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-e to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable spac-n, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a longgang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shaspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lin-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead 4-20 某收音机输入电路的电感约为0.3mH，可变电容器的调节范围为25,360pF。试问能否满足收听中波段535,1605kHz的要求。 解:收音机选台是通过调节可变电容的参数值使得调谐回路在某一电台频率下发生串联谐振。 , I21, 由串联谐振频率 f,0,I90:2,LCUab得到 , I1 当时，电路的谐振频率为 C,360pF 1f,,484KHz,535KHz 1,3,12,20.3，10，360，10 当时，电路的谐振频率为 C,25pF 1f,,1838KHz,1605KHz 2,3,12,20.3，10，25，10 所以能否满足收听中波段535,1605kHz的要求。 4-21 在图4-45的电路中，。今调节电容C值使电路发生并联谐振，此R,5,1 时测得:，，，电路总I,10AI,6AU,113V12Z 功率P=1140W。求阻抗Z。 解:调节电容C使并联电路发生谐振时， u电流与 同相，且达到最小值，可画出电路的iab 相量图，如题解图4.20所示。 由相量图可得 图4-45 习题4-21图 2222I,I,I,10,6,8A 12 Z,R，jX设 22则 P,IR，IR,1140W11 113green space system, promoting the construction of peripheral green space and protection of historical de city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urbanupgra ation city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features,tted to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimizotation type upgrade simultaneously of mode, in Metro construction of while is commicenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable space to develop, perfect urban district -ank area, the minjiang River area, Golden Sands area on a longict to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bon to expand, Naxi distrspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new visi-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead 22PIR,1140,10，511所以 R 题解图4.20 ,,,10,22I8 U11322Z而 |Z|,R，X,,,14.13, I8 2222X,,|Z|,R,,14.13,10,,10, 所以可得 Z,R，jX,10,j10, 114storicalof hi ty of big city. Construction of urban green space system, promoting the construction of peripheral green space and protectionronment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacienvi with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved cityMetro construction of while is committed to old city transformation and built district of perfect, through live and industry otation type upgrade simultaneously of mode, incenter" strategic vision of space frame. Yibin Center City development construction steering extension type extended and conn-e to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multiterm basis in a reasonable spac-n, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a longgang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shaspace layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lin-of vision Yibin formation in the Center surrounded by, organic dispersion band of bead