help whats the value of electricity that is flowing through each resistor?

könnt es auch auf deutsch erklären

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2 Antworten

poseidon42

Nutzer, der sehr aktiv auf gutefrage ist

im Thema Mathematik

23.06.2020, 02:32

Definiere zunächst:

R1 = 2 Ohm

R2 = 4 Ohm

R3 = 5 Ohm

V1 = 20 V

V2 = 14 V

V3 = 36 V

Ansatz mittels des Maschenstrom-Verfahrens:

1.) Definierender Maschen und der Maschenströme

Im1 = Maschstrom mit Masche R2 -> V1 -> R1 -> V2 -> R2

Im2 = Maschenstrom mit Masche R3 -> V3 -> R2 -> R3

2.) Anwenden der Kirchoffschen Maschenregel (hier schon mit Anwendung der Bauteilgleichungen ... )

M1)

R2*(Im1 - Im2) - V1 + R1*Im1 + V2 = 0

M2)

R3*Im2 - V3 + R2*(Im2 - Im1) = 0

3.) Lösen des linearen Gleichungssystems nach den Maschenströmen Im1 und Im2

i) (R1 + R2)*Im1 - R2*Im2 = V1 - V2

ii) (R3 + R2)*Im2 - R2*Im1 = V3

ii) * (R1 + R2) + i) * R2 ---> iii):

iii) (R3 + R2)*(R1 + R2)*im2 - (R2)^2 * Im2 = (R1 + R2)*(V1 - V2) + R2*V3

Umstellen liefert somit:

Im2 = [ (R1 + R2)*(V1 - V2) + R2*V3 ]/[ (R3 + R2)*(R1 + R2) - (R2)^2 ]

Und da nun Im2 bekannt ist folgt somit durch Einsetzen in i) und Umstellen

Im1 = [ V1 - V2 + R2*Im2 ]/[ (R1 + R2) ]

Somit sind also alle Maschenströme bekannt.

Die Ströme durch die einzelnen Widerstände bestimmen sich schließlich aus der Superposition der einzelnen Maschenströme durch die entsprechenden Widerstände.

Für mehr Infos zu dem Verfahren siehe:

https://de.wikipedia.org/wiki/Maschenstromverfahren

https://studyflix.de/elektrotechnik/maschenstromverfahren-329

...

Alternative Verfahren sind:

Superpositionsverfahren
Modifizierte Knotenpotential-Analyse

und hätten hier ebenfalls verwendet werden können.

Woher ich das weiß:Studium / Ausbildung – Studium der Elektrotechnik (Energie, Automatisierung)

Firato2

Beitragsersteller

23.06.2020, 02:42

wäre die antwort dann = Beim ersten = 5,21 A, Zweiten = 1,11 A, Dritten 6,32A ?

wenn ich herausfinden möchte Wie viel Ampere durch Jedem Einzelnen R fließt?

Hyperino

23.06.2020, 02:07

Wie viel Volt fließen durch, durch das System

Hyperino

23.06.2020, 02:08

Ups sorry hab die Frage falsch gelesen.

MatthiasHerz

23.06.2020, 02:13

Volt fließen nicht, Ampère fließen.

Es ist nach der jeweiligen Höhe des Stromes gefragt, der die Widerstände durchfließt, nicht nach der Spannung.

Firato2

Beitragsersteller

23.06.2020, 02:44

@MatthiasHerz

ah ye es ist gefragt wie viel Ampere durch jedem R fließt

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