Chapter 2, Problem 14P

The equivalent inductance L of three inductors connected in series-parallel as shown in Fig. P2.14 is given by

$L=125+\frac{L_1{L}_2}{L_1+L_2}$ (2.62)

1. Suppose $L_2=L_1+200\text{ mH}$, and that the equivalent inductance is $L=200$
2. mH. Substitute these values in equation (2.62) and obtain the following quadratic equation: $L_1^2+50L_1-15,000=0$
3. (2.63)
4. Solve the quadratic equation (2.63) for $L_1$
5. by each of the following methods: factoring, completing the square and the quadratic formula.