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Kelvinov most, izvodjenje

potenciometarski razdelnik

(%i1) vb: R2 / (R1 + R2) * E;
(%o1)E⋅R2R2+R1

razdelnik na strani nepoznatog otpornika

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

da nadjemo v1 i v2

(%i4) v2: R4 / (R4 + Rz + R3) * E;
(%o4)E⋅R4R4+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)v2⋅R1+v1⋅R2R2+R1
(%i7) va: ev(va);
(%o7)E⋅R1⋅R4R4+R3+Rz+E⋅R2⋅(Rz+R4)R4+R3+RzR2+R1
(%i8) va: ratsimp(va);
(%o8)Rz⋅E⋅R2+(E⋅R2+E⋅R1)⋅R4(R1+R2)⋅R4+(R1+R2)⋅R3+Rz⋅R2+Rz⋅R1
(%i9) va: factor(va);
(%o9)E⋅(Rz⋅R2+R1⋅R4+R2⋅R4)(R2+R1)⋅(R4+R3+Rz)

ravnoteza mosta

(%i10) e: va - vb;
(%o10)E⋅(Rz⋅R2+R1⋅R4+R2⋅R4)(R2+R1)⋅(R4+R3+Rz)−E⋅R2R2+R1
(%i11) e: ratsimp(e);
(%o11)E⋅R1⋅R4−E⋅R2⋅R3(R1+R2)⋅R4+(R1+R2)⋅R3+Rz⋅R2+Rz⋅R1
(%i12) e: factor(e);
(%o12)E⋅(R1⋅R4−R2⋅R3)(R2+R1)⋅(R4+R3+Rz)

imenilac me ne zanima, hocu nulu brojioca

(%i13) ne: num(e);
(%o13)E⋅(R1⋅R4−R2⋅R3)

i da resimo

(%i14) Rx: solve(ne, R4);
(%o14)[R4=R2⋅R3R1]

to je sve, lakse nego rukom na tabli!

Created with wxMaxima.