Processing math: 100%

Kelvinov most, izvodjenje

potenciometarski razdelnik

(%i1) vb: R2 / (R1 + R2) * E;
(%o1)ER2R2+R1

razdelnik na strani nepoznatog otpornika

(%i2) va: v2 + R2 / (R1 + R2) * (v1 - v2);
(%o2)(v1v2)R2R2+R1+v2
(%i3) va: ratsimp(va);
(%o3)v2R1+v1R2R2+R1

da nadjemo v1 i v2

(%i4) v2: R4 / (R4 + Rz + R3) * E;
(%o4)ER4R4+R3+Rz
(%i5) v1: (R4 + Rz) / (R4 + Rz + R3) * E;
(%o5)E(Rz+R4)R4+R3+Rz

da sredimo izraze, prljav posao za wxMaxima

(%i6) va;
(%o6)v2R1+v1R2R2+R1
(%i7) va: ev(va);
(%o7)ER1R4R4+R3+Rz+ER2(Rz+R4)R4+R3+RzR2+R1
(%i8) va: ratsimp(va);
(%o8)RzER2+(ER2+ER1)R4(R1+R2)R4+(R1+R2)R3+RzR2+RzR1
(%i9) va: factor(va);
(%o9)E(RzR2+R1R4+R2R4)(R2+R1)(R4+R3+Rz)

ravnoteza mosta

(%i10) e: va - vb;
(%o10)E(RzR2+R1R4+R2R4)(R2+R1)(R4+R3+Rz)ER2R2+R1
(%i11) e: ratsimp(e);
(%o11)ER1R4ER2R3(R1+R2)R4+(R1+R2)R3+RzR2+RzR1
(%i12) e: factor(e);
(%o12)E(R1R4R2R3)(R2+R1)(R4+R3+Rz)

imenilac me ne zanima, hocu nulu brojioca

(%i13) ne: num(e);
(%o13)E(R1R4R2R3)

i da resimo

(%i14) Rx: solve(ne, R4);
(%o14)[R4=R2R3R1]

to je sve, lakse nego rukom na tabli!


Created with wxMaxima.