State the two Kirchhoff's laws. Explain briefly how these rules are justified.

Kirchhoff’s First Law or Junction Rule states that “The sum of the currents flowing towards a junction is equal to the sum of currents leaving the junction.”

This is in accordance with the conservation of charge which is the basis of Kirchhoff’s current rule. 

Here, I₁, I₂ I₃, and I₄ are the currents flowing through the respective wires.

Convention: The current flowing towards the junction is taken as positive and the current flowing away from the junction is taken as negative. 

I₃ + (− I₁) + (− I₂) + (− I₄) = 0 

Kirchhoff’s Second Law or Loop Rule states that In a closed loop, the algebraic sum of the emf is equal to the algebraic sum of the products of the resistances and the currents flowing through them. 

 OR

“The algebraic sum of all the potential drops and EMFs along any closed path in a network is zero.”

For the closed loop BACB:

E₁ − E₂ = I₁R₁ + I₂R₂ − I₃R₃

For the closed loop CADC:

E₂ = I₃R₃ + I₄R₄ + I₅R₅
This law is based on the law of conservation of energy.