NCERT · Class 12 · Physics · Current ElectricityState Kirchhoff's rules for electrical networks. Write down the underlying conservation law on which each of these two rules is based.

Kirchhoff's rules are essential for analyzing complex electrical circuits where Ohm's law alone is insufficient. There are two primary rules:

1. Kirchhoff's Current Law (KCL or Junction Rule): This rule states that the algebraic sum of all electric currents meeting at any junction in a closed electrical circuit is always zero. Mathematically, it is expressed as $\sum I = 0$. Currents flowing towards the junction are conventionally taken as positive, while currents flowing away from the junction are taken as negative. This rule is fundamentally based on the law of conservation of charge, meaning that charge cannot accumulate at a junction.

2. Kirchhoff's Voltage Law (KVL or Loop Rule): This rule states that in any closed loop of a network, the algebraic sum of the products of currents and resistances in various branches of the loop is equal to the algebraic sum of the electromotive forces (EMFs) in that loop. Mathematically, it is expressed as $\sum IR = \sum E$. Alternatively, the algebraic sum of changes in potential around any closed loop is zero ($\sum \Delta V = 0$). This rule is fundamentally based on the law of conservation of energy, signifying that the total energy supplied to a unit charge by the sources is equal to the total energy dissipated across the circuit components.