[caption id="attachment_1739" align="alignright" width="200"] Gustav Robert Kirchhoff[/caption] Kirchhoff laws are essential for resistor network theory. They were formulated by the German scientist Gustav Kirchhoff in 1845. The laws describe the conservation of energy and charge in electrical networks. They are also called Kirchhoff’s circuit laws. Kirchhoff contributed also to other fields of science, therefore the generic term Kirchhoff law can have different meanings. Both circuit laws, the Kirchhoff Current Law (KCL) and the Kirchhoff Voltage Law (KVL), will be explained in detail. Kirchhoff Current Law (KCL) The Kirchhoff Current Law (KCL) states that the sum of all currents leaving a node in any electrical network is always equal to zero. It is based on the principle of conservation of electric charge. The law is also referred to as Kirchhoff’s first law. In formula form this is given by: The KCL is easier to understand with an example. Look at an arbitrary “node A” from a resistor network. Three branches are connected to this node. Two of the currents are known: I1 is 2 amperes and I2 is 4 amperes. The current law states that the sum of I1, I2 and I3 must be zero: Kirchhoff Voltage Law (KVL) The second law is also called Kirchhoff’s voltage law (KVL). It states that the sum of the voltage rises and voltage drops over all elements in a closed loop is equal to zero. In formula form: Let’s take an example to explain the second law. Consider a part of a resistor network with an internal closed loop, as shown in the picture below. We want to know the voltage drop between node B and C (VBC). The sum of voltage drops in the loop ABCD must be zero, so we can write: The two circuit laws are explained in the video below....
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