The resultant inductance of two inductors L₁ and L₂ when they are connected in parallel in an A.C. circuit is .

Question

Accepted Answer

(4) (L₁L₂)/(L₁+L₂). Idea: in parallel both coils have the same voltage V across them, and the total current is the sum of the branch currents (coils apart, so no mutual inductance). For each coil V = L₁(dI₁)/(dt) = L₂(dI₂)/(dt), and (dI)/(dt) = (dI₁)/(dt)+(dI₂)/(dt). So V/L = V/(L₁)+V/(L₂), i.e. 1/L = 1/(L₁)+1/(L₂). Hence L = (L₁L₂)/(L₁+L₂): inductors combine like resistors. (In an a.c. circuit the reactances ω L combine the same way and give the same result.)

The resultant inductance of two inductors L₁ and L₂ when they are connected in parallel in an A.C. circuit is ______.

Step-by-step solution

Why the other options are wrong