Question

The telecommunication circuit shown in FIGURE CP$32.71$ 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

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

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

c. What is the resonance frequency ${\omega }_0$? What is I at this frequency?

Short answer

(a) It is proved that $I=\frac{{\epsilon }_0}{\sqrt{R^2+{({\displaystyle \frac{1}{X_{{}_L}}}-{\displaystyle \frac{1}{X_C}})}^{-2}}}$.

(b) The I will be $\frac{V_0}{R}$at both $\omega \to 0$and $\omega \to \infty$.

(c) The angular frequency is ${\omega }_0=\frac{1}{\sqrt{LC}}$and $I=\frac{V_0}{R}$.

Step-by-step solution

Part (a) Step 1: Given Information

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Explanation

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