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- Beispielaufgabe: Gleichstromschaltungen berechnen - Kirchhoff'sche Sätze und Ohm'sches Gesetz
Beispielaufgabe: Gleichstromschaltungen berechnen - Kirchhoff'sche Sätze und Ohm'sches Gesetz
Berechnung der Ströme und Spannungen in einem Widerstandsnetzwerk mit Hilfe der Kirchhoffschen Sätze und des Ohmschen Gesetzes. Mein GET-Skript, Trainingsaufgaben, Musterlösungen und eine Übersicht über alle Videos gibt es hier: https://www.hsu-hh.de/get/lehre/repetitorium
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Video Transcript
In this video, I will explain how to calculate the currents and voltages that occur within a circuit.
The circuit shown here is given.
The resistance values of the resistors R1 to R5 are known.
The current I5, which flows through the resistor R5, is also known.
To calculate such a circuit, we need the following laws.
On the one hand, the following laws are necessary.
Ohm's law, which indicates the relationship between current and voltage at the resistance.
It is important to remember that the Ohm's law states that
current and voltage are indicated in the consumer counter-system.
This means that current and voltage at the resistance point in the same direction.
If, by definition, the current points in the other direction than the voltage,
the Ohm's law must be used with a negative sign.
Secondly, we need the Kirchhoff's set of measures, which states that the sum
of the voltages in a measure is zero. In this example, the Kirchhoff's set of measures
is illustrated. Here we have the section of a network, there are three
resistors that are connected in a measure, and at these three resistors
three voltages drop. If we now draw a mass cycle here, here we have
drawn it in the clockwise direction, then the mass set means that I go through the mass in the
circulation direction and add up the voltage. With the first resistance, I see
my circulation direction goes from the bottom up here, but the voltage is drawn from the top to the bottom
Therefore, I have a negative sign in front of the voltage U1.
The same here. The mass set says minus U1 minus U2 plus U3,
because here the mass cycle and voltage are drawn in the same direction.
And the sum of these three voltages is zero.
Third, we need the Kirchhoff's knot set.
which says that the sum of all currents flowing into a node is zero.
However, the currents flowing into a node, such as I1 and I2,
are counted positively and a current flowing out of the node is counted negatively.
Therefore, the set of nodes I1 plus I2 minus I3 is equal to zero.
Now we turn these three laws on our network.
The current was given I5 and the resistance values are known.
The following is always the size that is to be calculated at the moment,
marked red, the sizes that are already known are marked blue.
The current I5 is known.
The Ohm's law can be used to calculate the voltage U5.
U5 is simply the product of R5 and I5.
Next, we want to calculate the voltage U4.
If we apply the Mach number here, we see that U4 plus U5 is equal to zero.
If we convert this, we get U4 is equal to minus U5.
If you think about it, the two resistors are parallel.
The voltage that is dropped on both resistors must therefore be the same.
But because the voltage U4 was defined in the opposite direction from the point of view of U5,
the voltage U4 is negative. Next, we can calculate the current I4.
We now know U4 and can apply the Ohm's law here.
But we must be careful that the current and voltage are shown in different directions.
We must therefore use the Ohm's law with a negative sign.
This means that we can convert the Ohm's law to the current I4 and also determine the current I4.
Next, we can calculate the current I3 using the Kirchhoff's knot set,
because the currents I4 and I5 are already known.
If we apply the knot set to the knot up here, we get
