KIRCHOFF’S LAWS

Kirchoff’s laws are useful in complex network. That is circuits containing two or more than two batteries can be treated easily with the help of Kirchoff’s laws, which are two in numbers.

KIRCHOFF’S CURRENT LAW (KCL): - According to this law, “The algebraic sum of current meeting at a point in a conductor is zero”.

            Mathematically this law can be represented by

                                                Sum of I = 0

EXPLANATION: - It should be noted that all currents entering the junction should be taken as positive, while currents leaving the junction should be taken as negative.  I₁ + I₂ + (−I₃) = 0

                                    I₁ + I₂ = I₃

                                    I_in = I _out

KIRCHOFF’S VOLTAGE LAW (KVL): - According to this law, “The algebraic sum of all voltage changes around a closed circuit is zero”

            Mathematically this law can be represented by

                                                Sum of  V = 0

In other words “In any closed circuit the voltage drops is equal to the voltage rise”.

Using the above law a rise in potential will be taken as positive, while fall in potential will be taken as negative. This rule is applicable in battery emf and IR drops across resistors.

BATTERY emf’s: -  While going from positive to negative terminal of battery there is fall in potential, so it is taken as negative. Where as going from negative to positive terminal there is rise in potential, so it is taken as positive.                                                         

IR DROPS IN RESISTORS: -   If we go through a resistor in the same direction as its current there is a fall in potential, hence IR should be taken negative. However if we go in opposite direction, there is rise in voltage and hence IR should be taken positive.   

Applying the above laws to opposite circuit, we can write               

                        ε₁ – IR₁ – ε₂ – IR₂ = 0                                                         

                        ε₁ – ε₂ = IR₁ + IR₂

                        Σ ε = Σ IR                                                                                 ε₁ – IR₁ – ε₂ – IR₂ = 0      

ELECTROMOTIVE FORCE (emf): -

            Electromotive force can be defined as, “the power supplied by the source of electric current per unit electric current”.

                        Mathematically it can be represented as,

                                                ε = P / I

                                                   = W / q  or P = W / t and q = It

Its unit is joule per coulomb which is equal to volt.

SOURCE OF emf: - “A device which can maintain a constant potential difference across two points to which it is connected is called source of emf”.

Example: - Dry cell, automobile battery and electric generator are the common examples of source of emf.