Inductors in parallel Two inductors L1 123 H and l2 2 23 H

Inductors in parallel. Two inductors L_1 = 1.23 H and l_2 - 2 23 H are connected m parallel and separated by a large distance to that the magnetic field of one cannot affect the other, (a) Calculate the equivalent inductance. (Review the derivations for resistors in parallel and capacitors in parallel. Whtch Is similar here?) What is the generalization of (a) for N = 36 similar inductors L = 3.17 h in parallel?

Solution

a)

Voltage is proportional to inductance .Now, the (independent) voltages for parallel elements are equal (V1 = V2), and the currents (which are generally functions of time) add (i1 (t) + i2 (t) = i(t))

di₁(t)/dt + di2(t)/dt=di(t)/dt

the conditions that led to the parallel resistor formula also apply to inductors. Therefore

1/L1+1/L2 = 1/L_eq

So Equivlenet inductance Leq = L1*L2/(L1+L2) =1.23*2.23/3.46 = .7927 H

b) Leqv for N parallel inductance , 1/Leqv = N/L

so leqv = L/N = 3.17/36 =.0880 H