\( \DeclareMathOperator{\abs}{abs}
\)
Kelvinov most, izvodjenje
(%i1)
|
vb: R2 / (R1 + R2) * E; |
\[\mathrm{\tt (\%o1) }\quad \frac{E\cdot \mathit{R2}}{\mathit{R2}+\mathit{R1}}\]
(%i2)
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va: v2 + R2 / (R1 + R2) * (v1 - v2); |
\[\mathrm{\tt (\%o2) }\quad \frac{\left( \mathit{v1}-\mathit{v2}\right) \cdot \mathit{R2}}{\mathit{R2}+\mathit{R1}}+\mathit{v2}\]
\[\mathrm{\tt (\%o3) }\quad \frac{\mathit{v2}\cdot \mathit{R1}+\mathit{v1}\cdot \mathit{R2}}{\mathit{R2}+\mathit{R1}}\]
(%i4)
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v2: R4 / (R4 + Rz + R3) * E; |
\[\mathrm{\tt (\%o4) }\quad \frac{E\cdot \mathit{R4}}{\mathit{R4}+\mathit{R3}+\mathit{Rz}}\]
(%i5)
|
v1: (R4 + Rz) / (R4 + Rz + R3) * E; |
\[\mathrm{\tt (\%o5) }\quad \frac{E\cdot \left( \mathit{Rz}+\mathit{R4}\right) }{\mathit{R4}+\mathit{R3}+\mathit{Rz}}\]
\[\mathrm{\tt (\%o6) }\quad \frac{\mathit{v2}\cdot \mathit{R1}+\mathit{v1}\cdot \mathit{R2}}{\mathit{R2}+\mathit{R1}}\]
\[\mathrm{\tt (\%o7) }\quad \frac{\frac{E\cdot \mathit{R1}\cdot \mathit{R4}}{\mathit{R4}+\mathit{R3}+\mathit{Rz}}+\frac{E\cdot \mathit{R2}\cdot \left( \mathit{Rz}+\mathit{R4}\right) }{\mathit{R4}+\mathit{R3}+\mathit{Rz}}}{\mathit{R2}+\mathit{R1}}\]
\[\mathrm{\tt (\%o8) }\quad \frac{\mathit{Rz}\cdot E\cdot \mathit{R2}+\left( E\cdot \mathit{R2}+E\cdot \mathit{R1}\right) \cdot \mathit{R4}}{\left( \mathit{R1}+\mathit{R2}\right) \cdot \mathit{R4}+\left( \mathit{R1}+\mathit{R2}\right) \cdot \mathit{R3}+\mathit{Rz}\cdot \mathit{R2}+\mathit{Rz}\cdot \mathit{R1}}\]
\[\mathrm{\tt (\%o9) }\quad \frac{E\cdot \left( \mathit{Rz}\cdot \mathit{R2}+\mathit{R1}\cdot \mathit{R4}+\mathit{R2}\cdot \mathit{R4}\right) }{\left( \mathit{R2}+\mathit{R1}\right) \cdot \left( \mathit{R4}+\mathit{R3}+\mathit{Rz}\right) }\]
\[\mathrm{\tt (\%o10) }\quad \frac{E\cdot \left( \mathit{Rz}\cdot \mathit{R2}+\mathit{R1}\cdot \mathit{R4}+\mathit{R2}\cdot \mathit{R4}\right) }{\left( \mathit{R2}+\mathit{R1}\right) \cdot \left( \mathit{R4}+\mathit{R3}+\mathit{Rz}\right) }-\frac{E\cdot \mathit{R2}}{\mathit{R2}+\mathit{R1}}\]
\[\mathrm{\tt (\%o11) }\quad \frac{E\cdot \mathit{R1}\cdot \mathit{R4}-E\cdot \mathit{R2}\cdot \mathit{R3}}{\left( \mathit{R1}+\mathit{R2}\right) \cdot \mathit{R4}+\left( \mathit{R1}+\mathit{R2}\right) \cdot \mathit{R3}+\mathit{Rz}\cdot \mathit{R2}+\mathit{Rz}\cdot \mathit{R1}}\]
\[\mathrm{\tt (\%o12) }\quad \frac{E\cdot \left( \mathit{R1}\cdot \mathit{R4}-\mathit{R2}\cdot \mathit{R3}\right) }{\left( \mathit{R2}+\mathit{R1}\right) \cdot \left( \mathit{R4}+\mathit{R3}+\mathit{Rz}\right) }\]
\[\mathrm{\tt (\%o13) }\quad E\cdot \left( \mathit{R1}\cdot \mathit{R4}-\mathit{R2}\cdot \mathit{R3}\right) \]
(%i14)
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Rx: solve(ne, R4); |
\[\mathrm{\tt (\%o14) }\quad [\mathit{R4}=\frac{\mathit{R2}\cdot \mathit{R3}}{\mathit{R1}}]\]
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