首先附上视频链接,讲得真的很好
首先看题目 进行分析,选定回路{43i1+4(i1−i2)−ei=04(i2−i1)+3(i2−i3)+2i2=01c∫0ti3dt+3(i3−i2)=0\begin{cases} \frac{4}{3}i_1+4(i_1-i_2)-e_i=0 \\ 4(i_2-i_1)+3(i_2-i_3)+2i_2=0 \\ \frac{1}{c}\int ^{t}_0 i_3 dt + 3(i_3-i_2)=0 \end{cases} ⎩⎪⎨⎪⎧34i1+4(i1−i2)−ei=04(i2−i1)+3(i2−i3)+2i2=0c1∫0ti3dt+3(i3−i2)=0另外显然
eo=2i2e_o=2i_2eo=2i2首先由第一个式子得
163i1−4i2=ei\frac{16}{3}i_1-4i_2=e_i316i1−4i2=ei
i1=316(ei+4i2)=316ei+34i2i_1=\frac{3}{16}(e_i+4i_2)=\frac{3}{16}e_i+\frac{3}{4}i_2i1=163(ei+4i2)=163ei+43i2
i1′=316ei′+34i2′{i_1}^{'}=\frac{3}{16}{e_i}^{'}+\frac{3}{4}{i_2}^{'}i1′=163ei′+43i2′由第二个式子得
−4i1+9i2−3i3=0-4i_1+9i_2-3i_3=0−4i1+9i2−3i3=0
i3=−43i1+3i2i_3=-\frac{4}{3}i_1+3i_2i3=−34i1+3i2
i3′=−43i1′+3i2′{i_3}^{'}=-\frac{4}{3}{i_1}^{'}+3{i_2}^{'}i3′=−34i1′+3i2′由第三个式子得
i3=3Ci2′−3Ci3′{i_3}=3C{i_2}^{'}-3C{i_3}^{'}i3=3Ci2′−3Ci3′代入
i3=−43i1+3i2i_3=-\frac{4}{3}i_1+3i_2i3=−34i1+3i2
i3=3Ci2′−3Ci3′{i_3}=3C{i_2}^{'}-3C{i_3}^{'}i3=3Ci2′−3Ci3′
−43i1+3i2=i3=3Ci2′−3Ci3′-\frac{4}{3}i_1+3i_2={i_3}=3C{i_2}^{'}-3C{i_3}^{'}−34i1+3i2=i3=3Ci2′−3Ci3′再由
i3′=−43i1′+3i2′{i_3}^{'}=-\frac{4}{3}{i_1}^{'}+3{i_2}^{'}i3′=−34i1′+3i2′
−43i1+3i2=3Ci2′−3C(−43i1′+3i2′)-\frac{4}{3}i_1+3i_2=3C{i_2}^{'}-3C(-\frac{4}{3}{i_1}^{'}+3{i_2}^{'}) −34i1+3i2=3Ci2′−3C(−34i1′+3i2′)无脑化简
−43i1+3i2=3Ci2′+4Ci1′−9Ci2′-\frac{4}{3}i_1+3i_2=3C{i_2}^{'}+4C{i_1}^{'} -9C{i_2}^{'}−34i1+3i2=3Ci2′+4Ci1′−9Ci2′
−43i1+3i2=4Ci1′−6Ci2′-\frac{4}{3}i_1+3i_2=4C{i_1}^{'} -6C{i_2}^{'}−34i1+3i2=4Ci1′−6Ci2′第二个式子和第三个式子已经用完了,磨刀霍霍向第一个式子
i1=316ei+34i2i_1=\frac{3}{16}e_i+\frac{3}{4}i_2i1=163ei+43i2
−43i1+3i2=4Ci1′−6Ci2′-\frac{4}{3}i_1+3i_2=4C{i_1}^{'} -6C{i_2}^{'}−34i1+3i2=4Ci1′−6Ci2′
−43(316ei+34i2)+3i2=4Ci1′−6Ci2′-\frac{4}{3}(\frac{3}{16}e_i+\frac{3}{4}i_2)+3i_2=4C{i_1}^{'} -6C{i_2}^{'} −34(163ei+43i2)+3i2=4Ci1′−6Ci2′
−14ei+2i2=4Ci1′−6Ci2′-\frac{1}{4}e_i+2i_2=4C{i_1}^{'} -6C{i_2}^{'} −41ei+2i2=4Ci1′−6Ci2′我再代入
i1′=316ei′+34i2′{i_1}^{'}=\frac{3}{16}{e_i}^{'}+\frac{3}{4}{i_2}^{'}i1′=163ei′+43i2′
−14ei+2i2=4C(316ei′+34i2′)−6Ci2′-\frac{1}{4}e_i+2i_2=4C(\frac{3}{16}{e_i}^{'}+\frac{3}{4}{i_2}^{'})-6C{i_2}^{'} −41ei+2i2=4C(163ei′+43i2′)−6Ci2′
−14ei+2i2=34Cei′−3Ci2′-\frac{1}{4}e_i+2i_2=\frac{3}{4}C{e_i}^{'}-3C{i_2}^{'} −41ei+2i2=43Cei′−3Ci2′结合显然的等式
eo=2i2e_o=2i_2eo=2i2
eo′=2i2′{e_o}^{'}=2{i_2}^{'}eo′=2i2′万事大吉
eo+32Ceo′=14ei+34Cei′e_o+\frac{3}{2}C{e_o}^{'}=\frac{1}{4}e_i+\frac{3}{4}C{e_i}^{'} eo+23Ceo′=41ei+43Cei′