[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....
What is Ohm’s law? Ohm’s law states that the electrical current through a conductor is proportional to the potential difference across it. Furthermore, the electrical resistance of the conductor is constant. This leads to the mathematical equation: where I is the current in amperes, V the voltage in volts and R the resistance in ohms. To illustrate: a resistor of one ohm subjected to a current of 1A has a voltage difference of 1V across its terminals. The equation is named after Georg Ohm. In 1827 he published his findings that form the basis of the formula that is used today. He performed a large series of experiments that showed the relation between applied voltage and current through a conductor. The law is therefore empirical. Although Ohm’s law is one of the fundamentals of electrical engineering, at the time of publication it was received with criticism. The ohm is adopted as the official SI unit for electrical resistance. Gustav Kirchhoff (known from Kirchhoff’s circuit laws) made a generalization that is more used in physics: where σ is the conductivity parameter (material specific), J is the current density in a location of that material, and E the electric field in that location. Ohm’s law and resistors Resistors are passive elements that introduce resistance to the flow of electric current in a circuit. A resistor that functions according to Ohm’s law is called an Ohmic resistor. When current passes through an Ohmic resistor, the voltage drop across the terminals is proportionally to the magnitude of resistance. Ohm’s formula stays also valid for circuits with varying voltage or current, so it can be used for AC circuits as well. For capacitors and inductors the law can of course not be used, since their I-V curve is inherently not linear (not Ohmic). Ohm’s formula...