Chapter 31, Problem 18P

Two ideal inductors, L₁ and L₂, have zero internal resistance and are far apart, so their magnetic fields do not influence each other. (a) Assuming these inductors are connected in series, show that they are equivalent to a single ideal inductor having L_eq = L₁ + L₂. (b) Assuming these same two inductors are connected in parallel, show that they are equivalent to a single ideal inductor having 1/L_eq = 1/L₁ + 1/L₂. (c) What If? Now consider two inductors L₁ and L₂ that have nonzero internal resistances R₁ and R₂, respectively. Assume they are still far apart, so their mutual inductance is zero, and assume they are connected in series. Show that they are equivalent to a single inductor having L_eq = L₁ + L₂ and R_eq = R₁ + R₂. (d) If these same inductors are now connected in parallel, is it necessarily true that they are equivalent to a single ideal inductor having 1/L_eq = 1/L₁ + 1/L₂ and 1/R_eq = 1/R₁ + 1/R₂? Explain your answer.