Ham radio exam preparation: Kirchhoff’s current and voltage laws and applications

 Kirchhoff's circuit laws are two equalities that deal with the current and potential difference or voltage in electrical circuits, described in 1845 by German physicist Gustav Kirchhoff. Interestingly, this year corresponds to the two-hundredth birth anniversary of Kirchhoff!

According to Kirchhoff's Current Law, total current entering a junction in an electrical circuit is equal to the total current leaving the junction. Kirchhoff's Current Law is also known as Kirchhoff's first law or junction rule. It is based on the conservation of charge principle which states that electricity is neither created nor destroyed as it flows through a circuit. Kirchhoff's Current Law is considered while designing and analyzing circuits, troubleshooting and repairing circuits. If currents entering a node is assigned positive values and that exiting it negative values, according to Kirchhoff's Current Law, the algebraic sum of all currents entering and exiting the node will be zero. It is the basis of most circuit simulation softwares and is used along with Ohm's law to perform nodal analysis. Nodal analysis, also known as node-voltage analysis or branch current method, is a method of determining the potential difference between nodes, which are points where elements or branches connect in an electrical circuit. An important limitation is that it is not applicable in high frequency alternating current circuits. Capacitive coupling of electric field can occur between the wires of a transmission line.


Kirchhoff's voltage law, also known as Kirchhoff's second law or Kirchhoff's loop rule, mentions that the sum of all voltages or potential differences around a closed loop is equal to zero. This means that sum of all individual voltage drops in a closed circuit will be equal to the voltage applied or supply voltage. In such a loop, the current path does not encounter a node more than once. Circuits having multiple loops can be analysed by applying Kirchhoff's voltage law to each of the loops. Kirchhoff's voltage law follows the the principle of conservation of energy. The loops can be traced in clockwise or counterclockwise direction. As the induced electric field produced by an inductor may not be confined to an inductor, leaked fields can cause error in calculation with high frequency alternating current circuits. 

Now we will use a simple circuit with three resistors and a battery to check the Kirchhoff's voltage law.

 

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