Explain Kirchhoff’s laws with examples.

Hint: Kirchhoff’s laws, better known as Kirchhoff’s circuit laws and comprising of Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL), are two equalities that deal with the current flowing through a node and the voltage across mesh elements respectively.

Complete step by step answer:
$\implies$ Kirchhoff’s Current Law (KCL) states that the algebraic sum of currents flowing through a node is zero, that is, for a given node \[\sum{i=0}\]. Think of the situation like this. There are a given number of friends who have to visit a park. Now, the park has two entrances and three exits. Given that no friend stays behind in the park after closing time and no one jumps over the fence of the park, the number of friends entering the park will be equal to the number of friends leaving the park. The friends here symbolise current and the park represents a particular node. With the help of this example, we can understand that the current flowing in the node will be equal to the current flowing out of the node, that is, there is no residual current at the node or the algebraic sum of the currents at the node is 0.

$\implies$ Kirchhoff’s Voltage Law (KVL) states that in a closed mesh or loop, the total voltage around the loop is equal to the sum of all the voltage drops within the same loop or \[\sum{V=\sum{iR\Rightarrow \sum{V-iR=0}}}\]. To visualize this, consider this example. Suppose you are taking a walk along a path and you meet several friends on your way; now each friend talks to you for a certain time interval making you lose that much amount of time from your walk. Similarly, in a loop, when current flows there’s a voltage drop across each resistor which is equal to the product of the current in a loop and the resistor value. In a closed-loop, the sum of voltage drops is equal to the voltage or the emf across the loop.

Note: The principle of KCL (also known as junction rule) is the conservation of electric charge whereas the principle of KVL (or loop law) is the conservation of energy. Kirchhoff’s Laws help us to analyse complex circuits that can’t be reduced to one equivalent resistance using what we generally know about series and parallel connections.