Chapter 31, Problem 18P

(a)

To determine

To show: The equivalent inductance is $L_{\text{eq}}=L_1+L_2$.

(b)

To determine

To show: The equivalent inductance in parallel combination is $\frac{1}{L_{\text{eq}}}=\frac{1}{L_1}+\frac{1}{L_2}$.

(c)

To determine

To show: The equivalent inductance and resistance when their internal resistance is non zero in series combination is $L_{\text{eq}}=L_1+L_2$ and $R_{\text{eq}}=R_1+R_2$ respectively.

(d)

To determine

Whether it is necessarily true that they are equivalent to a single ideal inductor having $\frac{1}{L_{\text{eq}}}=\frac{1}{L_1}+\frac{1}{L_2}$ and $\frac{1}{R_{\text{eq}}}=\frac{1}{R_1}+\frac{1}{R_2}$.