Current Division in Parallel Circuit of Resistors

Consider a parallel circuit of tow resistor and connected across a source of V volts.

       Current through R₁ is I₁ and R₂ is I₂  , while total current drawn from source is I_T.

.^..                                I_T = I₁  + I₂ 

But                             I₁  = V/R₁   , I₂  = V/R₂

i.e.                              V =I₁ R₁  = I₂  R₂

.^..                                 I₁  = I₂   (R₂/R₁)

       Substituting value of I₁ in I_T,

Key point : In general, the current in any branch is equal to the ratio of opposite branch resistance to the total resistance value, multiplied by the total current in the circuit.

Example : Find the magnitude of total current, current through and if , R₁ = 10 Ω , R₂= 20 Ω and V = 50V.

Solution :

      The equivalent resistance of tow is,

                            R_eq =(R₁ R₂ ) / ( R₁ + R₂ ) = (10 x 20)/ (10 + 20) = 6.67 .

                            I_T = V/R_eq = 50/6.67 = 7.5 A

       As per the current distribution in parallel circuit,

It can be verified that  :         I_T = I₁  + I₂ .