State and explain Kirchhoff's rules.

Explanation

Kirchhoff.s first rule states that the algebraic sum of the currents at any junction of a circuit is zero. It is a based on the conservation of electric charge. All charges that enter a given junction in a circuit must leave that junction since charge cannot build up or disappear at a junction.
Sign convention: Current entering the junction is taken as positive and current leaving the junction is taken as negative.

Applying this convention for first rule to the junction A in Figure.
`I_1 + I_2 - I_3 - I_4 - I_5 = 0`
(or)
`I_1 + I_2 = I_3 + I_4 + I_5`
Kirchhoff.s second rule states that in a closed circuit the algebraic sum of the products of the current and resistance of each part of the circuit is equal to the total emf included in the circuit. This rule follows from the law of conservation of energy for an isolated system.
Sign convention: The product of current and resistance is taken as positive when the direction of the current is followed. Suppose if the direction of current is opposite to the direction of the loop, then product of current and resistance across the resistor is negative. (Fig.(a) and (b)). The emf is considered positive when proceeding from the negative to the positive terminal of the cell. (Fig (c) and (d)).

Kirchhoff voltage rule has to be applied only when all currents in the circuit reach a steady state condition.