Inductors in parallel Two inductors L1 134 H and L2 225 H

Inductors in parallel. Two inductors L_1 = 1.34 H and L_2 = 2.25 H are connected in parallel and separated by a large distance so that the magnetic field of one cannot affect the other. (a) Calculate the equivalent inductance. (b) What is the generalization of (a) for N = 39 similar inductors L = 3.19 H in parallel? Number units Number Units

Solution

(a). L1 = 1.34 H

     L2 = 2.25 H

Let the equivalent capacitance be L .

In parallel combination ,(1/L) =(1/L1)+(1/L2)

(1/L) =(1/1.34)+(1/2.25)

         = ( 2.25 +1.34)/(2.25x1.34)

     L = (2.25 x1.34)/(2.25+1.34)

       = 0.8398 H

(b).L= 3.19 H

N = 39

Let the equivalent inductance be L \'.

In parallel combination ,(1/L\') =(1/L)+(1/L) +......(1/L) (total 39 terms)

                                          = 39/L

From this L \' = L / 39

                    = 3.19 H / 39

                    = 81.79 x10 ^-3 H

                    = 81.79 mH