Theory on kirchhoff's law.

Kirchhoff's laws :-

Many electric circuits cannot be reduced to simple series-parallel combinations. However, it is always possible to analyze such circuits by applying two rules. These rules are known as kirchhoff's rule.

Rules are as follows:-

1. kirchhoff's junction rule:- The algebric sum of the current into any junction is zero.

That is:-

 The junction rule is based on "conservation of electric charge" 

This law also tell:-  "The sum of all the currents directed towards a point in a circuit is equal to the sum of all the currents directed away from the point."

 applying the kirchhoff's junction rule in above fig, we find

i 1 +i 2 = i 3 + i 4.

sign convention:-      * sign is +ve if current direction towards junction .

                                    * sign is -ve if current direction away from junction.

2. Kirchhoff's loop rule:- The algebric sum of potential differences in any loop including those associated emf's  and those of resistive elements, must equal zero.

That is:-

The loop rule is based on" electrostatic field is conservative in nature".

now we study how to apply it:-

In case of only emf is given in circuit.

sign convention:- * sign is +ve when the direction of emf is from low to higher  potential.

                            *sign is -ve when the dirction of emf is from higher to lower potential.

[here lower potential means negative polarity side & higher potential means higher polarity side. The samll line of emf shows -ve polarity & the larger line of emf shows +ve polarity.]

In case when resistance and current are given.

sign convention:- *sign is positive when current is forward in direction of resistance.

                              *sign is negative when current is reverse in direction of resistance.

Now we apply both resistance & emf in a circuit & find equation for this circuit.

 The equation will be,

+ i R2 +E2 + i R1 +E1 = 0.