Let two resistors of resistance R₁ and R₂ be connected in parallel across a p.d. of V volts. According to ohm’s law current flowing through resistor  R₁ I₁ = V
                                                                    R₁
Current through resistor R₂, I₂ = V
                                             R₂
Dividing expression (i) by expression (ii) we get

              I₁= V/R1 = R2
              I₂   V/R₂    R₁

Hence current flowing through each resistor, when connected in parallel, is inversely proportional to their respective resistances.

Since conductance is reciprocal of resistance and if G₁ and G₂ are the respective conductance of resistors R₁ and R₂ then

            1 = R₁ and  1 = R₂
           G₁             G2

Substituting the above values of R₁ and R₂ in expression (iii) we get

            I₁ = 1/G₂ = G₁
            I₂    1/G₁    G₂

Adding one on both sides of the expression (iv) we get

           I₁ + 1 = G₁ + 1
           I₂          G₂

or        I₁ + I₂ = G₁ + G₂
              I₂           G₂

or        I₂ = I₁ + I₂ X G₂
                 G₁+ G₂
Since  I₁ + I₂ = I and  G₁ + G₂ = 1 + 1 = 1 = G
                                               R₁   R₂  R

             I₂ = I X G₂
                        G

and        I₁ = I X G₁
                        G

Hence current in any branch of parallel circuit is directly proportional to its respective conductance and is equal to the total current flowing through the circuit multiplied by the ratio of the conductance of the branch to that of the circuit.

For more help in Current Distribution in Parallel Circuits click the button below to submit your homework assignment