Question

State the two Kirchhoff’s rules used in electric networks. How are these rules justified?

Answer 1

The two Kirchhoff’s rules for electric circuits are related to the current and voltage respectively. The first law is related to the sum of current entering and leaving a point in an electric circuit while the second law is related to the sum of the voltages flowing through a closed loop of an electric circuit.

Complete step-by-step solution:
We have two Kirchhoff’s laws for electrical circuits which give relation for currents and voltages flowing through an electrical circuit.
The first Kirchhoff’s law is known as Kirchhoff’s current law. This law states that the sum of all the currents entering and leaving a point in an electrical circuit is always equal to zero. Consider the following figure in which we have four currents ${I_1}$, ${I_2}$, ${I_3}$, and ${I_4}$ which are flowing towards or away from the common point P where all of them meet.

Following the convention given in note, we get ${I_1} + \left( { - {I_2}} \right) + \left( { - {I_3}} \right) + {I_4} = 0$
The second Kirchhoff’s law is known as Kirchhoff’s voltage law which states that in a closed-loop in an electrical circuit, the sum of all voltages is always zero taken in either clockwise or anticlockwise direction. Consider the following diagram

Using the convention given in the note, we get the following expression:
$- V + IR = 0$
These two laws are justified by the fact that the first law of currents shows us the conservation of charge in the circuit while the second law of voltages shows the conservation of energy in the circuit.

Note: 1. We follow the following convention for the first law: All current entering a junction are taken to be positive while all currents leaving a junction are taken as negative.
2. The convention used for the second law is that when we go from a positive potential to negative potential then the potential difference is taken as positive and vice-versa.