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

First law: In any electrical circuit, the algebraic sum of all the currents meeting at a point is zero. i.e. Σi = 0. Consider the given circuit where we can suppose outward direction of current as positive and inward as negative then at the point O

According to Kirchhoff’s first law, at junction O

I₁ + I₂ = I₃

Second law: In any closed loop of electrical conductors, the algebraic sum of product of resistance and the respective current in the different branches is equal to the total e.m.f applied in the closed loop.

Justification: Kirchhoff’s rules are according to the law of conservation of charge as at any junction of circuit, the sum of currents entering the junction must equal the sum of currents leaving. Hence, it shows that currents are steady.

By analytic way we can find balance condition of Wheatstone bridge and same result is obtained when we use Kirchhoff’s second rule, this justifies second law.