Widerstand eines Kupferdrahtes
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The following quantities appear in the problem:
Länge \(\ell\) / Masse \(m\) / Kraft \(F\) / elektrischer Widerstand \(R\) / Volumen \(V\) / Fläche \(A\) / Ortsfaktor \(g\) / Radius \(r\) / Dichte \(\varrho\) / spezifischer elektrischer Widerstand \(\rho\) /
The following formulas must be used to solve the exercise:
\(\varrho = \dfrac{m}{V} \quad \) \(F = mg \quad \) \(A = \pi r^2 \quad \) \(R = \varrho \dfrac{\ell}{A} \quad \)
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Exercise:
DuSieBerechneBerechnen Sie den Widerstand eines Kupferdrahtes rO reO der Masse mO mit RO Radius.
Solution:
Der Kupferdraht hat A pi r^ pi qtyR^ A kreisförmige Querschnittsfläche und V fracmrho fracmr V Volumen womit seine Länge ell fracVA fracfracmrhopi r^ fracmpirho r^ fracVA l ist. Der Draht hat also R sscrhoel fracellA sscrhoel fracellpi r^ sscrhoel frac fracmpirho r^pi r^ sscrhoel fracmpi^rho r^ re fraclA Re elektrischen Widerstand. R sscrhoel fracmpi^rho r^ Re
DuSieBerechneBerechnen Sie den Widerstand eines Kupferdrahtes rO reO der Masse mO mit RO Radius.
Solution:
Der Kupferdraht hat A pi r^ pi qtyR^ A kreisförmige Querschnittsfläche und V fracmrho fracmr V Volumen womit seine Länge ell fracVA fracfracmrhopi r^ fracmpirho r^ fracVA l ist. Der Draht hat also R sscrhoel fracellA sscrhoel fracellpi r^ sscrhoel frac fracmpirho r^pi r^ sscrhoel fracmpi^rho r^ re fraclA Re elektrischen Widerstand. R sscrhoel fracmpi^rho r^ Re