正弦交流电路如图，已知R=Xc=10欧，U1=U2,而且U(相量)、I（相量）同相位。求复阻抗Z
\u6c42\u4e00\u9053\u7535\u8def\u5206\u6790\u9898\u9898\u76ee\u662f\u8fd9\u6837\u7684:\u5df2\u77e5I1 = I2 = 10A ,U=100V ,U(\u76f8\u91cf)\u4e0eI(\u76f8\u91cf)\u540c\u76f8,\u8bd5\u6c42I ,R ,XL ,XC\u4e00\u3001\u89e3\uff1a\u8bbe\u5e76\u8054\u652f\u8def\u7684\u7535\u538b\u4e3aU2\uff08\u76f8\u91cf\uff09=U2\u22200\u00b0V\uff0c\u5219\uff1aI1\uff08\u76f8\u91cf\uff09=10\u222090\u00b0A\uff0cI2\uff08\u76f8\u91cf\uff09=10\u22200\u00b0A\u3002
\u6839\u636eKCL\uff0cI\uff08\u76f8\u91cf\uff09=I1\uff08\u76f8\u91cf\uff09+I2\uff08\u76f8\u91cf\uff09=10\u222090\u00b0+10\u22200\u00b0=10+j10=10\u221a2\u222045\u00b0A\u3002
\u56e0\u6b64\uff0c\u7535\u611f\u4e24\u7aef\u7535\u538b\u4e3a\uff1aU1\uff08\u76f8\u91cf\uff09=I\uff08\u76f8\u91cf\uff09\u00d7jXL=10\u221a2\u222045\u00b0\u00d7jXL=10\u221a2XL\u2220135\u00b0\uff08V\uff09\u3002
\u4ece\u800c\u5f97\u5230\u7aef\u53e3\u7535\u538b\u4e3a\uff1aU\uff08\u76f8\u91cf\uff09=U1\uff08\u76f8\u91cf\uff09+U2\uff08\u76f8\u91cf\uff09=10\u221a2XL\u2220135\u00b0+U2\u22200\u00b0=\uff08-10XL+U2\uff09+j10XL\uff08V\uff09\u3002
\u56e0\u4e3aU\uff08\u76f8\u91cf\uff09\u4e0eI\uff08\u76f8\u91cf\uff09\u540c\u76f8\uff0c\u5373\u4ed6\u4eec\u7684\u76f8\u4f4d\u89d2\u76f8\u7b49\uff0c\u81ea\u7136\u6b63\u5207\u503c\u4e5f\u76f8\u7b49\uff0c\u6240\u4ee5\uff1atan45\u00b0=\uff0810XL\uff09/\uff08-10XL+U2\uff09\uff0c\u4ece\u800c\u5f97\u5230\uff1aU2=20XL\u3002
\u6240\u4ee5\u7aef\u53e3\u7535\u538b\u4e5f\u53ef\u4ee5\u8868\u793a\u4e3a\uff1aU\uff08\u76f8\u91cf\uff09=10XL+j10XL\u3002
\u56e0\u6b64\uff1aU=\u221a[\uff0810XL\uff09²+\uff0810XL\uff09²]=10\u221a2XL=100\u3002
\u6240\u4ee5\uff1aXL=5\u221a2\uff08\u03a9\uff09\u3002\u81ea\u7136\uff1aU2=20XL=100\u221a2\uff08V\uff09\uff0c\u5373\uff1aU2\uff08\u76f8\u91cf\uff09=100\u221a2\u22200\u00b0\uff08V\uff09\u3002
\u7535\u963b\uff1aR=U2\uff08\u76f8\u91cf\uff09/I2\uff08\u76f8\u91cf\uff09=100\u221a2\u22200\u00b0/10\u22200\u00b0=10\u221a2\uff08\u03a9\uff09\u3002
\u5bb9\u6297\uff1a-jXc=U2\uff08\u76f8\u91cf\uff09/I1\uff08\u76f8\u91cf\uff09=100\u221a2\u22200\u00b0/10\u222090\u00b0=-j10\u221a2\uff0cXc=10\u221a2\uff08\u03a9\uff09\u3002
\u6240\u4ee5\u7b54\u6848\u4e3a\uff1aI=10\u221a2A\uff0cR=10\u221a2\u03a9\uff0cXL=5\u221a2\u03a9\uff0cXc=10\u221a2\u03a9\u3002
\u4e8c\u3001\u7535\u8def\u4e2d\u7535\u963bR\u4e0a\u7535\u538b\u4e0e\u7535\u611fXL\u7684\u7535\u538b\u76f8\u7b49\uff0cjI2*XL=I1*R
\u8bbeI1=10\u2220\u03c61\uff0cI2=10\u2220\u03c62\uff0c\u5219XL=R\uff0c\u03c61=\u03c62+90\u00b0
U\u548cI\u540c\u76f8\u4f4d\uff0cI1*R+(jI2+I1)*-jXC=U\uff0c\uff08R-jXc)*10\u2220\u03c61+XC*10\u2220\u03c62=100\uff0c
10*R*(cos\u03c61+isin\u03c61)+20*XC*(-sin\u03c61+icos\u03c61)=100\uff0c
R=XL=10cos\u03c61/cos2\u03c61\uff0c
Xc=5sin\u03c61/cos2\u03c61
I=10\u221a2
\u6269\u5c55\u8d44\u6599\uff1a
\u76f8\u91cf\u4ec5\u9002\u7528\u4e8e\u9891\u7387\u76f8\u540c\u7684\u6b63\u5f26\u7535\u8def.\u7531\u4e8e\u9891\u7387\u4e00\u5b9a,\u5728\u63cf\u8ff0\u7535\u8def\u7269\u7406\u91cf\u65f6\u5c31\u53ef\u4ee5\u53ea\u9700\u8003\u8651\u632f\u5e45\u4e0e\u76f8\u4f4d,\u632f\u5e45\u4e0e\u76f8\u4f4d\u7528\u4e00\u4e2a\u590d\u6570\u8868\u793a,\u5176\u4e2d\u590d\u6570\u7684\u6a21\u8868\u793a\u6709\u6548\u503c,\u8f90\u89d2\u8868\u793a\u521d\u76f8\u4f4d.\u8fd9\u4e2a\u590d\u6570\u5728\u7535\u5b50\u7535\u5de5\u5b66\u4e2d\u79f0\u4e3a\u76f8\u91cf\u3002
\u4e24\u540c\u9891\u7387\u6b63\u5f26\u91cf\u53e0\u52a0,\u8868\u8ff0\u4e3a:Asin(\u03c9t+\u03b1)+Bsin(\u03c9t+\u03b2)=(Acos\u03b1+Bcos\u03b2)sin\u03c9t+(Asin\u03b1+Bsin\u03b2)cos\u03c9t.\u6613\u77e5,\u53e0\u52a0\u540e\u9891\u7387\u6ca1\u53d8,\u76f8\u4f4d\u53d8\u5316,\u800c\u4e14\u670d\u4ece\u76f8\u91cf(\u590d\u6570)\u8fd0\u7b97\u6cd5\u5219.\u6545\u76f8\u91cf\u76f8\u52a0\u53ef\u4ee5\u63cf\u8ff0\u540c\u9891\u7387\u6b63\u5f26\u91cf\u7684\u53e0\u52a0\u3002
\u76f8\u91cf\u7684\u7684\u4e58\u9664\u53ef\u4ee5\u8868\u793a\u76f8\u4f4d\u7684\u53d8\u5316,\u4f8b\u5982:\u7535\u611f\u0399\u7535\u538b\u8d85\u524d\u7535\u6d4190\u5ea6,\u7528\u76f8\u91cf\u6cd5\u8868\u793a\u4e3aU=j\u03c7I,\u5176\u4e2dj\u4e3a\u5355\u4f4d\u590d\u6570,\u03c7\u4e3a\u611f\u6297\u3002
\u5b9a\u7406
\u76f8\u91cf\u5f62\u5f0f\u7684KCL\u5b9a\u5f8b\u8868\u793a\u5bf9\u4e8e\u5177\u6709\u76f8\u540c\u9891\u7387\u7684\u6b63\u5f26\u7535\u6d41\u7535\u8def\u4e2d\u7684\u4efb\u4e00\u7ed3\u70b9\uff0c\u6d41\u51fa(\u6216\u6d41\u5165)\u8be5\u7ed3\u70b9\u7684\u5168\u90e8\u652f\u8def\u7535\u6d41\u76f8\u91cf\u7684\u4ee3\u6570\u548c\u7b49\u4e8e\u96f6\u3002
\u76f8\u91cf\u5f62\u5f0f\u7684KVL\u5b9a\u5f8b\u8868\u793a\u5bf9\u4e8e\u5177\u6709\u76f8\u540c\u9891\u7387\u7684\u6b63\u5f26\u7535\u6d41\u7535\u8def\u4e2d\u7684\u4efb\u4e00\u56de\u8def\uff0c\u6cbf\u8be5\u56de\u8def\u5168\u90e8\u652f\u8def\u7535\u538b\u76f8\u91cf\u7684\u4ee3\u6570\u548c\u7b49\u4e8e\u96f6\u3002
\u7279\u522b\u6ce8\u610f\u7684\u662f\u4efb\u4e00\u7ed3\u70b9\u5168\u90e8\u652f\u8def\u7535\u6d41\u6700\u5927\u503c\uff08\u6216\u6709\u6548\u503c\uff09\u548c\u6cbf\u4efb\u4e00\u56de\u8def\u5168\u90e8\u652f\u8def\u7535\u538b\u632f\u5e45\uff08\u6216\u6709\u6548\u503c\uff09\u7684\u4ee3\u6570\u548c\u5e76\u4e0d\u4e00\u5b9a\u7b49\u4e8e\u96f6\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u76f8\u91cf
U\u5e76=P2/\uff08I*cos\u03c6)=50(1-j\uff09
I2=U\u5e76/\uff0810+10j\uff09=-5j
I1=I-I2=1.414+(1.141-5)j
Z=U\u5e76/I1
Z\u5e76=U\u5e76/I
\u8ba1\u7b97\u8fc7\u7a0b\u4f60\u5728\u770b\u770b\uff0c\u601d\u8def\u5c31\u662f\u8fd9\u6837\u3002
看图
绛旓細鐢电鑳 鍗曞悜瀵奸
绛旓細鐢甸樆鎶梈=R+锛圶L-XC锛夛紝位 =cos蠄=R/鈭歊²+锛圶L-XC锛²=0.707 锛岀劧鍚庢湁宸茬煡R=XL=10惟锛屾墍浠ユ帹瀵煎嚭XC=10惟锛屽簲璇ユ槸杩欐牱鍋氬惂锛屾垜涓嶆槸寰堢‘瀹氾紝鏈涚粰浜堟壒璇勬寚姝
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绛旓細鏍规嵁鐩搁噺鍥撅紝I1锛堢浉閲忥級鍜孖2锛堢浉閲忥級鐩稿樊90掳锛屾墍浠ヤ緷鎹甂CL锛殀I1锛堢浉閲忥級+I2锛堢浉閲忥級|=鈭氾紙I1²+I2²锛=鈭氾紙I1²+1²锛=I=鈭2銆侷1=1锛圓锛夈Xc=U1/I1=4/1=4锛埼╋級銆鐢佃矾闃绘姉锛歓=Z1+Z3=4鈭ワ紙-j4锛+4鈭4=锛-j4锛/锛1-j1锛+j4/锛1+j1锛=2-...
绛旓細I=U/X X=R+J(XL-XC) 鏃燲L 灏变负0 X=R-J10 I=10/10-J10
绛旓細璁R涓Xc骞惰仈鍚庣殑绛夋晥闃绘姉涓篫锛岀湅鍥俱
绛旓細锛1锛夋荤數娴両锛濃垰2/2A 锛2锛夐樆鎶梈锛濃垰锛XC锛2+R锛2锛夛紳鈭氾紙10*10+10*10锛夛紳10鈭2锛埼╋級鏍规嵁娆у瀹氬緥I锛漊/Z鍙煡 鐢佃矾鐨勬荤數娴両锛漊/Z锛10/10鈭2锛濃垰2/2锛圓锛
绛旓細浜ゆ祦鐢佃矾鐨勮绠
