同样,若由Y变为Z,则有: Y=G+J jB=Y|∠q,Z=R+i=Z|∠q Z=y G-iB G+iB =R+X G2+B2 ∴R= G B G2+B2 Ⅹ= G2+B2 Y y=- R Y G 口z IX DOWN
UP DOWN 同样，若由Y变为Z，则有： j j j j = = − + − = + = = + + − = + = = = + = = + = Z Y G B B X G B R G R jX G B G jB Y G jB Z Y G jB Y Z R jX Z , | | 1 | | , 1 1 | | , | | 2 2 2 2 2 2 º º Z R jX º º Y G jB
§9-2阻抗(导纳)的串联和并联 U=U+U ZEU u,Z2 z1+22 =(Z1+Z2)I Z 十 2 U). Z==LU 同直流电路相似: 串联:z=∑Zk U ∑z DOWN
UP DOWN 同直流电路相似： Z Z1 Z2 + + + - - - • U 1 • U 2 • U • I • • = = : , U Z Z Z Z U k k k 串 联 k • • • U = U1 +U2 §9-2 阻抗（导纳）的串联和并联 Z1 Z2 I U Z = = + • • • • = Z I+ Z I 1 2 • = (Z + Z )I 1 2 • • • = = U Z Z U Z I 1 1 1
h|i2I=1+l2 YDU Y1Y (+1= +I=:=Y ZZ U Z+Z H 1=1U= 十 同直流电路相似: 并联:Y=∑Kk K ∑V
UP DOWN 同直流电路相似： • I Y + - • U Y1 Y2 1 • I 2 • I • • = = : , I Y Y Y Y I k k k 并联 k • • + = + = I Z Z Z I Z Z Z Z Z 1 2 2 1 1 2 1 2 1 2 • • • I = I + I • • U2 Y+ U1 Y= • U) 2 Y+1 Y( = 2 Y 1 Y U I + = = Y • • • • • = = I Y Y I Y U 1 1 1
例:已知Z1=10+6.289,Z2=2031.992,Z3=154579 a 3 求Zab 2 b 2=23+2,+么,=23 +Z Z= (10+j6.28)(20-j319 z1+Z210+16.28+20-139 11.81∠3213°×37.65∠-5761° 3945∠-40.5° =1089+j286 Zab=Z3+Z=15+j15.7+10.89j286 =2589+18.56=31.9∠356°9 DOWN
UP DOWN 例：已知 Z1=10+j6.28, Z2=20-j31.9 , Z3=15+j15.7 。 Z Z Z Z Z Z Z Z = + + = + 3 1 2 1 2 ab 3 Z2 Z1 Z3 a b 求 Zab。 10 6.28 20 31.9 (10 6.28)(20 31.9) 1 2 1 2 j j j j Z Z Z Z Z + + − + − = + = o o o 39.45 40.5 11.81 32.13 37.65 57.61 − − = = 10.89 + j2.86 25 89 18 56 31.9 35.6 Ω 15 15.7 10.89 2.86 o a b 3 = + = = + = + + + . j . Z Z Z j j
例:已知R1=102,L=0.5H,R2=10002,C=10F Us=100V,a=314rd/s,求各支路电流和电庶/no +RI yo +设:Us=100∠0 Us za1=10C2,Zm2=100092 jaC 10 jOL=j157Q2 z=21+Z1+Z2∥Zc C 一j318.5_2 jac =10+j157+ 1000j318.5) Us100∠0° 1000-j318.5 Z167∠-523° 102一j132 =0.6∠523° =167∠-52.3° DOWN
UP DOWN ， ，求各支路电流和电压 。 例：已知 ， ， ， 1 0 1 2 100 314 / 10 0.5 1000 10 • = = = = = = U V rad s U R L H R C F S R2 + R1 - + - jL jC 1 U S • • I 1 • I 2 • I 10 • U = • 设：U S 100 0 ZR1 = 10，ZR2 = 1000 ZL = jL = j157 = = − 318.5 1 j j C ZC Z ZR ZL ZR ZC // = 1 + + 2 1000 318.5 1000( 318.5) 10 157 j j j − − = + + = 102 − j132 =167−52.3 Z U I S • • = − = 167 52.3 100 0 = 0.652.3