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The image shows the diagram that explains, through an electrical circuit, the second law of the physicist Kirchhoff, that the algebraic sum of all the voltage drops around the network loop or the closed path in a circuit is equal to zero.

A loop must have at least two sides and be a closed shape, as shown in the figure, a rectangle through which the line passes once through each node.

The loop has four nodes, in the four corners of the horizontal rectangle, rendered by embossed circles.

The network branches between the electrical components is marked by bold lines.

This circuit has three resistors and a battery.

The resistors at the top, right and bottom, are components of the electrical circuit with the role of reducing the current voltage between two points and are highlighted by blank rectangles.

The electric battery in the center of the left side of the loop is represented by the specific symbol, respectively, two parallel lines, spaced between them, the longer line being up and the shorter down, denoted by the plus and minus charges.

For example, if the voltage at the battery terminals is 2.5 volts, at the terminals of the upper resistor one is 1.5 volts, at the second resistor on the right is 0.5 volts and at thethird  lower resistor is also 0.5 volts , then the equation would go as follows, starting from the battery:

2.5 volts minus 1.5 volts minus 0.5 volts minus 0.5 volts equals zero.

General information

Gustav Kirchhoff, a German physicist, has developed two laws related to the conservation of electrical current within the electrical circuits.

First of all, let’s summarize what an electrical circuit means: it is the path the electrical current has to travel between a power source and an electrical powered device. The circulation or travelling of electrical current between the source and the consumer is achieved using electric conductors, such as the connecting wires. In order to have a clearer image regarding the electrical circuit, we will describe a simple circuit, consisting of a battery, two connecting wires and an electric motor. We know that the battery has two terminals, meaning two ends through which it can be connected to a power source. In the case of direct current (DC), which is present in a battery, the movement of electrons, represented by the electrical current, always takes place from the positive terminal to the negative terminal. At the two ends of the motor the two connecting wires are attached. If we make the two wires from the motor touch the terminals of the battery, then the electrical circuit will be created. The current will enter through the positive end, go through the motor coil and exit through the negative end, returning to the battery. The electric current passing through the motor will determine the latter to function. At first, we could say it is an everlasting process, which is endless, unless we would disconnect the electric circuit. However, because a portion of the electrical current converts into rotation movement, therefore it does not return to where it originated, the current from the battery will be used up in time.

In order to understand Kirchhoff’s laws, we must know the main elements of an electric network. An electric network or power grid can consist of one or several power sources, as well as one or more consumers. The main elements are:

  • the network node or junction, meaning the point in which at least three connecting wires are linked to each other;
  • the network branch, meaning the area between two consecutive nodes;
  • the network loop, meaning the closed polygonal path, formed by a succession of several sources or consumers of electrical current.

The second law by Kirchhoff applies to network loops. We quote its text: “along the path of a network loop, the algebraic sum of the electromotor tensions is equal to the algebraic sum of the products between the current’s intensity and the total resistance on each branch” or
“the sum of electromotive forces in a loop equals the sum of potential drops in the loop” (1).

To conclude, knowing the text of Kirchhoff’s laws, we can state that these laws are useful while solving equations with one or more unknowns or variables regarding the tension and intensities of the electrical current in certain points within an electrical network, based on some already known data.


  4. for (1)

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