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webadm | 投稿日時: 2007-10-26 20:24 |
Webmaster 登録日: 2004-11-7 居住地: 投稿: 3107 |
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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