Kirchoff’s first Law or Junction Rule : In an electric circuit, the algebraic sum of currents at any junction is zero.

Or the sum of currents entering junction is equal to the sum of currents leaving the junction.

Mathematically, ΣI=0

Sing convention for applying junction rule :

1. The currents flowing towards the junction are taken as positive.
2. The currents flowing away from the junction are taken as negative.

Applying junction rule to junction j in fig., we get

Σ I = 0

I₁ + I₂ + I₃ + I₄ =0

I₁ + I₂ + I₄ = I₃

Incoming current = outgoing current.

This rule is based on the law of conservation of charge.

Kirchoff’s 2^nd law or loop rule : Around any closed loop of network , the algebraic sum of changes in potentials must be zero.

Or

The algebraic sum of the emfs in any loop of a circuit is equal to the sum of the products of currents and resistance in it mathematically, Σ ΔV = 0, or Σɛ = ΣlR

Sign convention for applying loop rule :

1. The emf of a cell is taken as positive if the direction of traversal is from its negative to positive terminal ( through the electrolyte ) otherwise negative.
2. The current resistance (lR) product is taken as +ve if the resistor is traversed in the same direction of assumed current otherwise negative.

Illustration :

Let us consider the circuit as shown in fig.

Applying Kirchhoff’s loop rule, to closed path ABCFA, we get

ɛ₁ - ɛ₂ = I₁R₁ - I₂R₂

similarly, applying KVL to mesh CDEFC, we get

ɛ₂ = I₂R₂ + (I₁ + I₂) R₃

this rule is based on the law of conservation of energy.