Consider two ideal inductors L1 and L2 that have zero internal resistance and are far apart, so that 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 Leq= L1 + L2.
(b) Assuming these same two inductors are connected in parallel, show that they are equivalent to a single ideal inductor having 1/Leq = 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 that their mutual inductance is zero. Assuming these inductors are connected in series, show that they are equivalent to a single inductor having Leq = L1 + L2 and Req = 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/Leq = 1/L1 + 1/L2 and 1/Req = 1/R1, 1/R2? Explain your answer.