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投稿者 スレッド
webadm
投稿日時: 2007-10-26 20:24
Webmaster
登録日: 2004-11-7
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投稿: 3082
Re: 問題59:漏洩抵抗のある架線を流れる電流
心配なのでn=1の時のI1も合成抵抗と分流則から計算すると

(%i5) (E/(r+R1+1/(1/R2+1/R1)))*(R2/(R1+R2));
(%o5) (E*R2)/((1/(1/R2+1/R1)+R1+r)*(R2+R1))
(%i6) factor(%);
(%o6) (E*R2)/(2*R1*R2+r*R2+R1^2+r*R1)

今度はn=1の時の漸化式の解からk=n,n=1としてMaximaで処理すると

(%i2)
subst(n, k, I[k]=(((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^k*(sqrt(4*R1*R2+R1^2)*(E*(-R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n+r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)
+E*R1*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+r*E*(2*R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n)+E*R1*(R2*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+3*R2*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+r*((-sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+E*R1^2*((-sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n))/(2^k*(R1*(r*(2*R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+12*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))-2*R2^2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*r^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n-2*R2^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+r^2*(2*R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+R1^2*(8*R2*((
-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+4*r*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+2*R1^3*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n))+(((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^k*(-sqrt(4*R1*R2+R1^2)*(E*(R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n-R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+E*R1*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)-r*E*(-2*R2*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n-2*R2*((-sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^(2*n))-E*R1*(-3*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n-r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n-R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+E*R1^2*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n))/(2^k*(R1*(r*(2*R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+12*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))-2*R2^2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*r^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n-2*R2^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+r^2*(2*R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+R1^2*(8*R2*((
-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+4*r*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+2*R1^3*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)));
(%o2) I[n]=(((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*(sqrt(4*R1*R2+R1^2)*(E*(-R2*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+R2*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+
E*R1*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+r*E*
(2*R2*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+E*R1*(R2*
((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+3*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+r*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+E*R1^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*
((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n))/(2^n*(R1*(r*(2*R2*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+12*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*
((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))-2*R2^2*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2^2*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+2*r^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n-
2*R2^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+r^2*(2*R2*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*
((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+R1^2*(8*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*
((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+4*r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+2*R1^3*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n))+(((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*(-sqrt(4*R1*R2+R1^2)*(E*(R2*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n-R2*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+E*R1*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)-r*E*
(-2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n-2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))-E*R1*(-3*R2*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n-r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n-R2*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+E*R1^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n))/(2^n*(R1*(r*(2*
R2*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+12*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+2*R2*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))-2*R2^2*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*
((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+2*r^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n-2*R2^2*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+r^2*(2*R2*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*
((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+R1^2*(8*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*
((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+4*r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+2*R1^3*
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n))
(%i3)
subst(1, n, I[n]=(((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*(sqrt(4*R1*R2+R1^2)*(E*(-R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n+r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)
+E*R1*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+r*E*(2*R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n)+E*R1*(R2*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n)+3*R2*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+r*((-sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+E*R1^2*((-sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n))/(2^n*(R1*(r*(2*R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+12*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))-2*R2^2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*r^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n-2*R2^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+r^2*(2*R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+R1^2*(8*R2*((
-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+4*r*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+2*R1^3*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n))+(((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n*(-sqrt(4*R1*R2+R1^2)*(E*(R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n-R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+E*R1*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)-r*E*(-2*R2*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n-2*R2*((-sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^(2*n))-E*R1*(-3*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n-r*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n-R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+E*R1^2*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n))/(2^n*(R1*(r*(2*R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+12*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))-2*R2^2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*r^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)
+2*R2+R1)/R2)^n-2*R2^2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+r^2*(2*R2*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^(2*n)+4*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n+2*R2*((-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^(2*n))+R1^2*(8*R2*((
-sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n+4*r*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)+2*R1^3*((-sqrt(4*R1*R2
+R1^2)+2*R2+R1)/R2)^n*((sqrt(4*R1*R2+R1^2)+2*R2+R1)/R2)^n)));
(%o3) I[1]=((-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)*(E*(-(sqrt(4*R1*R2+R1^2)+2*R2+R1)^2/R2+
((-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2+(r*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2)+
(E*R1*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2)+r*E*
((2*(sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)/R2+(2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2)+E*R1*(
(sqrt(4*R1*R2+R1^2)+2*R2+R1)^2/R2+(3*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2+
(r*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2)+(E*R1^2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2)
)/(2*R2*(R1*(r*
((2*(sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)/R2+(12*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2+(2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)/R2)
-2*(sqrt(4*R1*R2+R1^2)+2*R2+R1)^2+(2*r^2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2+4*
(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1)-2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)+r^2*
((2*(sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)/R2+(4*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2+(2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)/R2)
+R1^2*
((8*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2+(4*r*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2)+
(2*R1^3*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2))+((sqrt(4*R1*R2+R1^2)+2*R2+R1)*(-sqrt(4*R1*R2+R1^2)*(E*
(((-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2+(r*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2-
(-sqrt(4*R1*R2+R1^2)+2*R2+R1)^2/R2)+(E*R1*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2)-r*E*
(-(2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2-(2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)/R2)-E*R1*(-
(3*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2-(r*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2-
(-sqrt(4*R1*R2+R1^2)+2*R2+R1)^2/R2)+(E*R1^2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2))/(2*R2*(R1*(r*
((2*(sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)/R2+(12*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2+(2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)/R2)
-2*(sqrt(4*R1*R2+R1^2)+2*R2+R1)^2+(2*r^2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2+4*
(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1)-2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)+r^2*
((2*(sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)/R2+(4*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2+(2*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)^2)/R2)
+R1^2*
((8*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2+(4*r*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2)+
(2*R1^3*(-sqrt(4*R1*R2+R1^2)+2*R2+R1)*(sqrt(4*R1*R2+R1^2)+2*R2+R1))/R2^2))
(%i4) factor(%);
(%o4) I[1]=-(E*(sqrt(R1*(4*R2+R1))-2*R2-R1)*(sqrt(R1*(4*R2+R1))+2*R2+R1))/(4*R2*(2*R1*R2+r*R2+R1^2+r*R1))
(%i9) ratsimp(%);
(%o9) I[1]=(E*R2)/((2*R1+r)*R2+R1^2+r*R1)

となり同じ結果が得られるので正しそうである。

n=2の時のI[1],I[2]は手計算が難しくなるので割愛。

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題名 投稿者 日時
   直流回路の演習と実験 webadm 2007-2-2 6:14
     分流回路の実験 webadm 2007-2-2 11:20
       分圧回路の実験 webadm 2007-2-3 1:35
         別の測定器でやってみた webadm 2007-2-3 13:47
           さらなる考察 webadm 2007-2-3 22:41
             そのほか考慮すべき点 webadm 2007-2-15 5:09
     直流回路の演習問題を見て webadm 2007-2-4 5:12
       初等の数学をすっかり忘れている webadm 2007-2-4 11:43
         なんとか出来た webadm 2007-2-4 12:33
     格子状抵抗ネットワークの意味 webadm 2007-2-4 21:13
       インピーダンスの思い出 webadm 2007-2-11 23:25
         dBとか webadm 2007-2-12 5:14
           Re: dBとか webadm 2007-4-2 5:29
             Boonton Radio CorpのThe Notebook webadm 2007-4-10 12:53
       早くも躓く webadm 2007-2-13 11:02
         まだ11ページしか進んでいない webadm 2007-2-15 3:51
           実学と理論 webadm 2007-2-22 6:56
             網目電流法の演習 webadm 2007-2-24 22:47
               やっと解けた webadm 2007-2-28 21:21
                 黒板かホワイトボードが欲しい webadm 2007-3-2 0:13
                   やっとp12問題9 webadm 2007-3-3 3:53
                     問題9完了 webadm 2007-3-4 3:44
                       問題10:正三角錐型ワイヤーフレーム webadm 2007-3-4 13:05
                         問題11:3x3格子状ワイヤーネットワーク webadm 2007-3-6 19:36
                           問題12:正立方体格子ワイヤー網 webadm 2007-3-8 10:37
                             問題14:3つのΔ接続ワイヤー網 webadm 2007-3-9 5:54
                               問題15:アッテネーターぽい回路 webadm 2007-3-23 11:59
                                 問題16:Δ接続・Y接続 webadm 2007-3-24 12:40
                                   問題17、18、19 webadm 2007-3-24 22:55
                                     問題20,21:枝電流法と網目電流法を誤解していた疑い webadm 2007-3-25 12:57
                                       問題22:電流計 webadm 2007-3-26 11:39
                                         問題23:電流計と電圧計 webadm 2007-3-26 12:03
                                           問題24:T型アッテネーター webadm 2007-3-27 11:19
                                             問題25:パイ型アッテネーター webadm 2007-3-30 19:49
                                               Re: 問題25:パイ型アッテネーター webadm 2007-4-12 11:16
                                                 Re: 問題25:パイ型アッテネーター webadm 2007-4-12 21:44
                                               問題26:検流計の内部抵抗を求める webadm 2007-5-4 13:34
                                                 問題27:抵抗計 webadm 2007-5-4 15:28
                                                   問題28:アッテネーター webadm 2007-8-18 9:57
                                                     問題29:ボリューム(アッテネーター) webadm 2007-8-22 18:26
                                                       問題30:ブリッジ回路解析 webadm 2007-8-26 12:05
                                                         Re: 問題30:ブリッジ回路解析 webadm 2007-8-26 22:25
                                                           Maxima超便利 webadm 2007-8-27 1:16
                                                             数式処理システムの問題点 webadm 2007-8-28 10:19
                                                               問題31:ブリッジの逆接続 webadm 2007-8-30 20:03
                                                                 問題32:剣流計の内部抵抗が0のブリッジ回路 webadm 2007-8-30 20:21
                                                                   問題33:平衡ブリッジによる抵抗測定 webadm 2007-9-1 11:16
                                                                     問題34:ひねったブリッジ回路 webadm 2007-9-5 14:27
                                                                       問題35:内部抵抗がない剣流計を流れる電流 webadm 2007-9-6 8:42
                                                                         問題36:バイパスされたT型アッテネーター webadm 2007-9-15 3:54
                                                                           問題37:Kelvinのダブルブリッジ webadm 2007-9-15 18:10
                                                                             問題38:地絡距離測定 webadm 2007-9-15 19:36
                                                                               問題39:キャパシタの並列接続 webadm 2007-9-21 19:33
                                                                                 問題40:キャパシタの直列接続 webadm 2007-9-21 19:53
                                                                                   問題41:コンデンサの直列接続計算 webadm 2007-9-22 3:54
                                                                                     問題42:コンデンサの直・並列組み合わせ回路計算 webadm 2007-9-22 19:26
                                                                                       問題43:コンデンサのY接続 webadm 2007-9-23 3:31
                                                                                         問題44:コンデンサーのラダー回路 webadm 2007-9-23 4:42
                                                                                           問題45:充電済みコンデンサの並列接続 webadm 2007-9-23 5:21
                                                                                             問題46:充電済みコンデンサの並列接続(その2) webadm 2007-9-24 8:27
                                                                                               問題47:充電済みコンデンサの並列接続(その3) webadm 2007-9-24 9:41
                                                                                                 問題48:変わり種ブリッジ回路 webadm 2007-9-24 10:18
                                                                                                   問題49:電圧を殺す webadm 2007-9-25 5:26
                                                                                                     問題50:偏微分を使った回路解析 webadm 2007-9-27 21:39
                                                                                                       Re: 問題50:偏微分を使った回路解析 webadm 2007-9-28 5:47
                                                                                                       問題51:偏微分を使った回路解析(その2) webadm 2007-9-28 9:45
                                                                                                         問題52:偏微分を使った回路解析(その3) webadm 2007-9-28 11:56
                                                                                                           問題53:ちょっとひねった回路解析 webadm 2007-9-29 6:01
                                                                                                             問題54:ちょっとひねった回路解析(その2) webadm 2007-9-29 19:30
                                                                                                               問題55:ちょっとひねった回路解析(その3) webadm 2007-9-30 2:12
                                                                                                                 問題56:ちょっとひねった回路解析(その4) webadm 2007-9-30 22:24
                                                                                                                   問題57:無限に続く抵抗ラダー回路の解析 webadm 2007-10-3 12:16
                                                                                                                     Re: 問題57:無限に続く抵抗ラダー回路の解析 webadm 2007-10-5 8:30
                                                                                                                       Re: 問題57:無限に続く抵抗ラダー回路の解析 webadm 2007-10-7 3:17
                                                                                                                         Re: 問題57:無限に続く抵抗ラダー回路の解析 webadm 2007-10-7 3:30
                                                                                                                           Re: 問題57:無限に続く抵抗ラダー回路の解析 webadm 2007-10-7 22:30
                                                                                                                             Re: 問題57:無限に続く抵抗ラダー回路の解析 webadm 2007-10-8 5:26
                                                                                                                               問題58:n箇所つながった銅線回路 webadm 2007-10-8 11:12
                                                                                                                                 Re: 問題58:n箇所つながった銅線回路 webadm 2007-10-8 22:24
                                                                                                                                   Re: 問題58:n箇所つながった銅線回路 webadm 2007-10-9 10:27
                                                                                                                                     Re: 問題58:n箇所つながった銅線回路 webadm 2007-10-9 22:18
                                                                                                                                       Re: 問題58:n箇所つながった銅線回路 webadm 2007-10-10 4:19
                                                                                                                                         問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-10 5:33
                                                                                                                                           Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-11 3:06
                                                                                                                                             Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-11 4:12
                                                                                                                                               Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-11 5:02
                                                                                                                                                 Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-16 18:24
                                                                                                                                                 Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-17 9:39
                                                                                                                                                   Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-22 0:12
                                                                                                                                                     Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-25 22:12
                                                                                                                                                       Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-26 4:13
                                                                                                                                                         Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-26 4:28
                                                                                                                                                         » Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-26 20:24
                                                                                                                                                             Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-26 20:49
                                                                                                                                                               Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-27 11:05
                                                                                                                                                                 Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-27 20:53
                                                                                                                                                                   Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-29 1:45
                                                                                                                                                                     Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-29 10:07
                                                                                                                                                                       Re: 問題59:漏洩抵抗のある架線を流れる電流 webadm 2007-10-30 4:48
                                                                                                                                                                         問題60:短くした電熱線の消費電力 webadm 2007-10-30 9:38
                                                                                                                                                                           問題61:細く短くした電熱線の消費電力 webadm 2007-10-30 10:18
                                                                                                                                                                             問題62:2つの異なる電球を直列につなぐ webadm 2007-10-31 10:39
                                                                                                                                                                               問題63:電力伝送と整合 webadm 2007-10-31 11:07
                                                                                                                                                                                 問題64:電力伝送と整合(その2) webadm 2007-11-1 10:26
                                                                                                                                                                                   問題65:電力伝送と整合(その3) webadm 2007-11-1 10:56
                                                                                                                                                                                     問題66:電池の起電力と内部抵抗を求める webadm 2007-11-1 11:25
                                                                                                                                                                                       問題67:配線抵抗のある電力伝送回路 webadm 2007-11-7 9:49
                                                                                                                                                                                         問題68:電力伝送とマッチング(電源側) webadm 2007-11-7 10:17
                                                                                                                                                                                           問題69:カロリーと電力 webadm 2007-11-7 10:49
                                                                                                                                                                                             問題70:電力量と比熱と融点の応用(フューズ) webadm 2007-11-8 10:54
                                                                                                                                                                                               問題71:電力量と比熱と融点の応用(フューズ)の続き webadm 2007-11-8 11:02
                                                                                                                                                                                                 問題72:合成温度係数 webadm 2007-11-8 11:20
                                                                                                                                                                                                   問題73:抵抗値による温度測定 webadm 2007-11-8 11:40
                                                                                                                                                                                                     問題74:温度係数 webadm 2007-11-8 12:45
                                                                                                                                                                                                       Re: 問題74:温度係数 webadm 2007-11-8 14:07
                                                                                                                                                                                                         Re: 問題74:温度係数 webadm 2007-11-8 14:38
                                                                                                                                                                                                           問題75:膨張係数と温度係数 webadm 2007-11-10 11:29
                                                                                                                                                                                                             問題76:導線の温度上昇 webadm 2007-11-11 13:15
                                                                                                                                                                                                               問題77:温度補償抵抗回路 webadm 2007-11-11 23:25
                                                                             Re: 問題37:Kelvinのダブルブリッジ webadm 2007-9-26 7:48
                                                 Re: 問題26:検流計の内部抵抗を求める Anonymous 2007-5-26 2:32
                                                   Re: 問題26:検流計の内部抵抗を求める webadm 2007-5-26 21:00
                                     誤植発見 webadm 2007-3-25 13:07

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