The telecommunication circuit shown in $FIGURECP32.71$has a parallel inductor and capacitor in series with a resistor.

a. Use a phasor diagram to show that the peak current through the resistor is

$I=\frac{{\epsilon }_0}{\sqrt{R^2+{\left({\displaystyle \frac{1}{X_L}}-{\displaystyle \frac{1}{X_C}}\right)}^{-2}}}$

Hint: Start with the inductor phasor ${\nu }_L$.

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

c. What is the resonance frequency ${\omega }_o$? What is $I$at this frequency?

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