Chapter 32, Problem 72EAP

Consider the parallel RLC circuit shown in FIGURE CP32.72.

a. Show that the current drawn from the emf is

$I={\epsilon }_0\sqrt{\frac{1}{R^2}+{\left(\frac{1}{\omega L}-\omega C\right)}^2}$

Hint: Start with a phasor that is common to all three circuit elements.

b. What is I in the 1imits $\omega \to 0$ and $\omega \to \infty$ ?

c. Find the frequency for which I is a minimum.

d. Sketch a graph of I versus $\omega$ .