Chapter 2, Problem 21P

Consider a capacitor C and an inductor L connected in parallel as shown in Fig. P2.21. The total reactance X in ohms is given by $X=\frac{\omega L}{1-{\omega }^{2}LC}$, where $\omega$ is the angular frequency in rad/s.

(a) Suppose $L=\text{1}.0$ mH and $C=1$ F. If the total reactance is $X=1.0\Omega$ ft show that the angular frequency $\omega$ satisfies the quadratic equation of ${\omega }^2+\omega -1000=0$.

(b) Sake the quadratic equation for $\omega$ by the methods of completing the square and the quadratic formula.