吉林大学：《电工学》课程教学资源（复习习题，第一册）习题答案（一）

1-1P,=-25发出 P.=90W吸收 1-2U=-40I=-4AU=36I=3A 1-3(a)u=3Ik=1.5A p=4.5w P=-3N P 1.5 (b)u=-2P=2WB、=-5WB=3 (c)1=3I2=1.5A2=-1 BR=4.5WP,=10WB=-13WP=-1.5W 1-4电压表、电流表都正偏,输出功率的是A,电压表正偏,电 流表反偏,输出功率的是A2 1-91=-1A,l2=1A,l3=3A,14=-1A,l5=-1A,6=5A 1-11 P=48WP=-721P1=-20H 1-12当R=0时,I=2Ag=1A 当R=∞时,I=5A=4A 131=6A,R=73 1-141=3A,I2=0,13=-3A,14 1-15U 1y P,=6w P 6w 1-16U=7 P=-10形 12R=0.169 2-11=-0.8A,12=2.2A P=2.56WP=29.04WP=-396WP,=8W

1－1 PN1 = −25W 发出 PN2 = 90W 吸收 1－2 U = −40V I = −4A U = 36V I = 3A 1－3 (a) u 3V I 1.5A = R = PR = 4.5W PIS = −3W PUS = −1.5W (b) 2 2 5 3 S S u = − V PR = W PI = − W PU = W (c) u1 = 3V I R =1.5A u2 = −10V PR1 = 4.5W PR2 =10W PIS = −13W PUS = −1.5W 1－4 电压表、电流表都正偏，输出功率的是 A1 ，电压表正偏，电 流表反偏，输出功率的是 A2 1－9 I 1 = −1A, I 2 =1A, I 3 = 3A, I 4 = −1A, I 5 = −1A, I 6 = 5A 1－10 U2 = 4V 1－11 48 72 20 S1 S2 S PU = W PU = − W PI = − W 1－12 当 R = 0 时， I = 2A I E =1A ; 当 R =  时， I = 5A I E = 4A 1－13 I A R , US 90V 3 7 = 6 , =  = − 1－14 3 , 0 , 3 , 1 I 1 = A I 2 = I 3 = − A I 4 = − A 1－15 UA = −1V P1m A = 6W P2m = −6W 1－16 U a = 7V P = −10W 1－17 US =12V R0 = 0.169 1－18 UA开 ＝2V UA闭 ＝－5V 2－1 0.8 , 2.2 I1 = − A I2 = A PR1 = 2.56W PR2 = 29.04W PIS = −39.6W PUS = 8W

2-21=2.5A,12=0.5A,13=2A,I4=-1A 3U=6U"=4IU=10 2-4I=3AI"=5AI=8A 2-5I=190m 2-6I=1.25AI"=-2AI=-0.75A 2-7E=12 2-8155g lⅣ2g 2-94A192 2A20 2-10=0.1A Ⅰ=1A 2-12I=-0.6AI"=-0.5AI=-1.1A 2-13Ⅰ=2.5A 2-14Uak=-10R=0=-1A 2-15U R0=5g=0.4A 2-16C R=99 abk =%3 2-17i3=1.63A4E=16 2-18Uak=2R0=52=6.2A 2-19=1.67A 2-2012=9A,U4=-47,P2=-423W(电源) 2-21=2A 2-22=1.5AI=2A 2-23

2－2 2.5 , 0.5 , 2 , 1 I 1 = A I 2 = A I 3 = A I 4 = − A 2－3 U = 6V U = 4V U =10V 2－4 I = 3A I = 5A I =8A 2－5 I =190mA 2－6 I =1.25A I = −2A I = −0.75A 2－7 E =12V 2－8 15V 5 11V 2 2－9 4A 1 2A 2 2－10 I = 0.1A 2－11 I =1A 2－12 I = −0.6A I = −0.5A I = −1.1A 2－13 I = 2.5A 2－14 Uabk = −10V R0 = 0 I = −1A 2－15 Uabk = 4V R0 = 5 I = 0.4A 2－16 Uabk V R I A 3 4 9 1 = 0 =  = 2－17 i 3 =1.63A E =16V 2－18 Uabk = 21V R0 = 5 I = 6.2A 2－19 I =1.67A 2－20 I x = 9A, U x = −47V, P x = −423W（电源） 2－21 I = 2A 2－22 I开 ＝1.5A I闭 ＝2A 2－23 U3 = −1V

3-1u(0) (0,)=1.5Ai2(0,)=3Ai(0,)=-3A l(∞)=211(∞)=0.5Ai2(∞)=1Aic(∞)=0 2i1(0,)=3A1(0)=18Ai2(0,) 0)=48 i4(∞)=5A1()=3A2(∞)=2A (∞)=0 3-3u2(t)=1332V1(1)=-1.33m4曲线略 3-4C=125/Fi(0,)=0u2(D)=10(1 3-5i1()=11.1+37e833A i2(t)=5.55e 8333t i(1)=1.1-1.85e333 3-6l2(t)=9-e33 3-7l1()=30+20e-130t()=-0.896-1304 曲线略 3-8l(0)=l2(∞)+[(0,)-a(0)e%=201-e t=0.12(0.1)=7.87 S闭合后,l2(t)=20-12.13e 5 3-9l()=-2.5+7.5e5T i()=-0625-0.935e25A i, (t=e a i,(t)=26 i, (t)=ea l()=8-8e2V 3-131()=1-%e 750t l2(t)=1.25

3－1 uC (0− ) = 6V i 1 (0+ ) =1.5A i 2 (0+ ) = 3A iC (0+ ) = −3A uC () = 2V i 1 () = 0.5A i 2 () =1A iC () = 0 3－2 i L (0+ ) = 3A i 1 (0+ ) =1.8A i 2 (0+ ) =1.2A uL (0+ ) = 4.8V i L () = 5A i 1 () = 3A i 2 () = 2A uL () = 0 3－3 uC (t) =13.3e −2 5tV iC (t) = −1.33e −2 5tmA 曲线略 3－4 C F i u t e V C t C 12.5 (0 ) 0 ( ) 10(1 ) 10000 − =  + = = − u t e V t C ( ) 10(1 ) −8 = − 3－5 i t e A i t e A t 8333 t 2 8333 1 ( ) 11.1 3.7 ( ) 5.55 − − = + = i t e A 8333 t 3 ( ) 11.1 1.85 − = − 3－6 ( ) 9 33. 3 u t e V t C − = − 3－7 u t e V i t e A t t C 1.1 2 1 0 1.1 2 1 0 4 4 ( ) 30 20 ( ) 0.896 −  −  = + = − 曲线略 3－8 u t u u u e e V t t C C C C ( ) ( ) [ (0 ) ( )] 20(1 ) −5 − =  + + −  = −  t = 0.1 uC (0.1) = 7.87V ( ) 20 12.13 10 0.1 S2 u t e V t C 闭合后， − （ − ） = − 3－9 ( ) 2.5 7.5 2.5 u t e V t C − = − + i t e A 2.5 t 0 ( ) 0.625 0.935 − = − − 3－10 i t e A i t e A t t 1 ( ) 2 ( ) 2 − − = = 3－11 i t e A u t e V t L t L 4 1 0 4 1 0 2 2 ( ) ( ) 4 −  −  = = − 3－12 ( ) 8 8 25 u t e V t C − = − 3－13 i t e A 750 t 0 6 ( ) 1 1 − = − ( ) 1.25 750 u t e V t L − =

3-14l1()=25-83e"l2(1)=25-167e0 i(1)=83e-30mA 3-15a2()=30+30e2,l2(0.4)=4 (t)=60-19e00 3-16l2(1)=2-2ey l()=4+2e 3-17i1(1)=38-1.8eAi(t)=02+12eA 3-18u(t)=45e-0 i2(t)=60-45emA 3-19u2()=8-2eV1(1)=-067-022e3m 4-1略 4-29=/6mnx U=160 丌,U=40 4-3(1)电感X2=102Q=500arP=0 (2)电阻R=5gQ=0P=8KW (3)电容 14.149Q=17675arP=0 4-4X,=80Z=10∠53.1g 2=176290 U。=132∠0°I=22∠0°A相应图略 4-5C=1.84F 4-6z=447+j337R=4792X=33792串联 并联R=70.22X=9322 4-7i2=2∠90°A,i=2√2∠45A,U=10√2∠-45 U2=2√2∠-6343°V,U2=10∠-3687°V 4-81=10L=7.96mHR1=2.59C=0.6371F

3－14 ( ) 25 8.3 ( ) 25 16.7 5 1 0 2 5 1 0 1 4 4 u t e V u t e V t C t C −  −  = − = − i t e mA 5 10 t 4 ( ) 83 −  = 3－15 u t e V uC V t C ( ) 30 30 , (0.4) 41 2500 = + = − u t e V t t C 2000( ) 1 ( ) 60 19 − −  = − 3－16 u t e V t C 150000 ( ) 2 2 − = − u t e V 150000t 0 ( ) 4 2 − = + 3－17 i t e A i t e A t t L 5 5 ( ) 3.8 1.8 ( ) 0.2 1.2 − − = − = + 3－18 u t e V i t e mA t L t C 10 1000 ( ) 45 ( ) 60 45 4 − − = = − 3－19 u t e V i t e mA t t C 333 333 ( ) 8 2 ( ) 0.67 0.22 − − = − = − − 4－1 略 4－2 U V , U 40V 6 5 , 160 ; 6  =  max =  = −  min = 4－3 (1)电感 XL =10 Q = 500Var P = 0 (2)电阻 R = 5 Q = 0 P = 8KW (3)电容 X C =14.14 Q =176.75Var P = 0 4－4   XL = 8 Z =1053.1  U  L =17690 UR I A    =1320  = 220 相应图略 4－5 C =1.84F 4－6 Z = 44.7 + j33.7 R = 44.7 X L = 33.7 串联 = 70.2 = 93.2 并联 R X L 4－7 2 90 , 2 2 45 , 10 2 45 I2 A I1 A US V     =   =   = − U2 2 2 63.43 V , U3 10 36.87 V    = −  = − 4－8 I =10 L = 7.96mH RL = 2.5 C = 0.637F

4-9=2AUa=1021=5A12=3AU1=10 U2=101=10∠90°A1=1+2=10∠0°A U1=1007U0=1002 4-10U,=10 TU,=10 U=10√2U=102 4-11R2=29.699=0.144H 4-12/=2∠-15.33°1=164∠-60.3°12=145∠37.8° U1=82∠-7°,Uz=4∠1468° 4-13i=442sin(3141-53.1)A 2=22√2sin(3141+369°)4 =492√2sin(314-2656°)A cosQ=cos2656°=0.9P=97416W Q=48406arS=10824A相量图略 4-14R=10gL=0.172H 4-151=5.6∠40.2°12=1.12∠-866U=58:5∠-40° 4-16U,=220∠135°U=220√2∠0° 4-17=5.2A22=275∠-652° 4-181=4∠-53.13°412=825∠2283°A U=81.42∠9°P=804.2 4-19U=17.26U=236.5P=2373.23B=119W 4-20I=22.46A 4-2111=2∠-60°12=2∠60°=2∠0°U=6020°

4－9 I0 = 2A U0 =10 2V I1 = 5A I2 = 3A U1 =10V U V I A I I IR A   2 =10  1 =1090  0 =  1 +  =100 U1 =100V U0 =100 2V 4－10 10 20 10 U2 = V U3 = V U4 = V U5 =10 2V U6 =10 2V 4－11 RL = 29.69 L = 0.144H 4－12 2 15.33 1 1.64 60.3 2 1.45 37.8    I  = − I  = − I  =  8.2 7 , 4 14.68 1   U  = − U  Z =  4－13 44 2sin(314 53.1 ) i 1 t A  = − i 2 22 2sin(314t 36.9 )A  = + i 49.2 2sin(314t 26.56 )A  = − cos = cos 26.56 = 0.9 P = 9741.6W   Q = 4840.6Var S =10824VA 相量图略 4－14 R =10 L = 0.172H 4－15 1 5.6 40.2 2 1.12 86.6 58.5 40    I  =  I  = − U  = − 4－16 220 135 , 220 2 0   U  L =  U  C =  4－17  I = 5.2A Z2 = 275− 65.2 4－18 4 53.13 8.25 22.83 I 1 A I 2 A    = −  =  U = 81.429 V P = 804.2W   4－19 U1 =17.26V U = 236.5V P2 = 2373.23W P1 =119W 4－20 I = 22.46A 4－21 2 60 2 60 2 0 60 0 1 2     I  = − I  =  I  =  U  a b = 

4-22P=22686WP=1731.4W 4-23i=2si(200+45)Ai=√2sin(2000+90)A l2=2002si(2000 U,=200√2∠135°U=200∠90°V cos=0.707P=200Wg=200ar S=28284VA相量图略 4-24X=91.39 4-25f=593.135kHQ=44.71z=10gI=1mA Un=10mU,=447.lmU=447.lmP=10W 5-1星形连接=11∠-30°A1=11∠-150°A =11∠90°A相量图略 5-2将120只日光灯均匀接在三相上,每相40只(并联) ==1454A 5-3角形连接 10∠-45°A,=10∠-165°A my=10∠75°Ai=103∠-75°4 i=103∠-195°4i=10√3∠45°A 相量图略 5-4Z=782∠2836 5-5=5∠90°A 14.88∠-40°A 4.88∠140°A 5-61=22∠0°A1=22-6687A =22∠-210°A =14.8∠-38.9°A l,=3.67∠-30°l,=367∠-180° 3.67∠60°

4－22 P1 = 2268.6W P2 =1731.4W 4－23 2sin(2000 45 ) 2 sin(2000 90 ) i 1 t A iC t A   = + = + u 200 2sin(2000t)V R = UL US V    = 200 2135  = 20090 cos = 0.707 P = 200W Q = 200Var S = 282.84VA 相量图略 4－24 X C = 91.3 4－25 f 0 = 593.135kHz Q = 44.71 Z =10 I =1mA UR =10mV UL = 447.1mV UC = 447.1mV P =10W 5－1 星形连接 I 11 30 A I 11 150 A U V    = −  = − IW A   =1190 相量图略 5－2 将 120 只日光灯均匀接在三相上，每相 40 只（并联） I L =I P =14.54A 5－3 角形连接 I 10 45 A I 10 165 A UV VW    = −  = − I 10 75 A I 10 3 75 A WV U    =   = − I 10 3 195 A I 10 3 45 A V W    = −  =  相量图略 5－4  Z = 7.8228.36 5－5 IW A IU A IV A     = 590  =14.88−40  =14.88140 5－6 IU A IV A    = 220  = 22−66.87 IW A IN A    = 22−210  =14.8−38.9 5－7    I  U = 3.67−30 I  V = 3.67−180 I  W = 3.6760

Utn=3674∠0Ul=3674∠-120°Um=3674∠120° 5-81=l=44A1,=/2=76A 5-9(4)=658 A COSo=0.8P=34656W 5-10i=10∠-60°A2=103∠-60°Ai=2732∠-60 5-11Y:1=732-36A=732-1569A n=7.3∠83.1A △:U,=220U,=220∠0° l=7.3∠-369°Am=7.3∠-1569°A 1m=73∠83.1°A 5-12Z=100∠36.9°9 5-13(U)=220 5-14coq=0.8P=3Q=2.3kmrS=3.77A 5-15 coS=0.8 P=7.74kw 0=5.kvAr S=9.68kVA 5-16U,=220U=127S=9.68kA R=129X,=99 5-17I=9.15∠-758°A 5-18(A1)=0.914(A2)=0455A (A3)=0.455A(4)=0 7-1n21=1500 P=2S,=0.033 mIn 7-4P=3S=0.047=2984NmTn=59.68Nm T=6565NmP、=3.6kWS=4.74kA 7-5TN=494NmI=104.3AT=692Nm

   U  UV  = 367.40 U  VW  = 367.4−120 U  WV  = 367.4120 5－8 I I 4.4A I I 7.6A U = W = V = L = 5－9 (A) = 65.8A cos = 0.8 P = 34.656kW 5－10 10 60 10 3 60 27.32 60 1 2    I  = − A I  = − A I  = − 5－11 Y : I 7.3 36.9 A I 7.3 156.9 A U V    = −  = − IW A   = 7.383.1  : UL = 220V U  U = 2200 IUV A IVW A    = 7.3−36.9  = 7.3−156.9 IWU A   = 7.383.1 5－12 =    Z 100 36.9 5－13 (U) = 220V 5－14 cos = 0.8 P = 3kW Q = 2.3kVar S = 3.77kVA 5－15 cos = 0.8 P = 7.74kW Q = 5.8kVar S = 9.68kVA 5－16 U 220V U 127V S 9.68kVA L = P = = =12 = 9 R XL 5－17 I A   = 9.15− 75.8 5－18 ( ) 0.91 ( ) 0.455 A1 = A A2 = A (A3 ) = 0.455A (A4 ) = 0 7－1 2 0.033 min n1 =1500 r P = SN = 7－4 P = 3 SN = 0.04 TN = 29.84N.m Tst = 59.68N.m T max = 65.65N.m P1N = 3.6kW S = 4.74kVA 7－5 TN = 49.4N.m I st =104.3A Tst = 69.2N.m

1n=34.774Ty=23NmT∝l 494NmT"=x2T=494Nmx=0.845 380×0845=321.l 7-6(1)n=689Nm(2)m=3215Nm>0.37x∴能 7-8cosq=0.84cosq=0.48 7-97,=13.36NmT,=63Nm 7-10T=194.9 Nm coS o、=0.881=4025A 1n=134.17AT=7796N T=11694Nm不能 T=48.725Nm能 7-11=738NmI=17AT=147.6Nm T=1476NmⅠ=110.5A TT能短时运行 T>T但ln>1004不能直接起动

34.77 23 . 2 I stY = A TstY = N m Tst U 49.4 . 49.4 . 0.845 2 TL = N m T st = x Tst = N m x = Umin = 3800.845 = 321.1V 7－6 (1)TN = 68.9N.m (2)TstY = 32.15N.m  0.3TN 能 7－8 cos = 0.84 cos = 0.48 7－9 TN1 =13.36N.m TN 2 = 63N.m 7－10 TN =194.9N.m cos N = 0.88 I st = 402.5A I 134.17A T 77.96N.m stY = stY = TL =116.94N.m 不能 TL = 48.725N.m 能 7－11 T 73.8N.m I 17A T 147.6N.m N = N = st = T max =147.6N.m I st =110.5A TN  TL 不能长期运行 T max  TL 能短时运行 Tst  TL 但I st 100A 不能直接起动