Question

A series $R L C$ circuit has components with the following values: $L=20.0 \mathrm{mH}, C=100 \mathrm{nF}, R=20.0 \Omega,$ and $\Delta V_{\max }=$ $100 \mathrm{~V},$ with $\Delta v=\Delta V_{\max } \sin \omega t .$ Find (a) the resonant fre- quency of the circuit, (b) the amplitude of the current at the resonant frequency, (c) the $Q$ of the circuit, and (d) the amplitude of the voltage across the inductor at resonance.

          A series $R L C$ circuit has components with the following values: $L=20.0 \mathrm{mH}, C=100 \mathrm{nF}, R=20.0 \Omega,$ and $\Delta V_{\max }=$
$100 \mathrm{~V},$ with $\Delta v=\Delta V_{\max } \sin \omega t .$ Find (a) the resonant fre-
quency of the circuit, (b) the amplitude of the current at the resonant frequency, (c) the $Q$ of the circuit, and (d) the amplitude of the voltage across the inductor at resonance.

Added by Debra H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Eduard Sanchez

06/28/2022

Step 1

Step 1: Calculate the resonant frequency of the circuit using the formula: \[f_{\text{res}} = \frac{1}{2\pi\sqrt{LC}}\] Substitute the given values: $L = 20 \times 10^{-3} \, \text{H}$ and $C = 100 \times 10^{-9} \, \text{F}$ \[f_{\text{res}} = Show more…

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A series $R L C$ circuit has components with the following values: $L=20.0 \mathrm{mH}, C=100 \mathrm{nF}, R=20.0 \Omega,$ and $\Delta V_{\max }=$ $100 \mathrm{~V},$ with $\Delta v=\Delta V_{\max } \sin \omega t .$ Find (a) the resonant fre- quency of the circuit, (b) the amplitude of the current at the resonant frequency, (c) the $Q$ of the circuit, and (d) the amplitude of the voltage across the inductor at resonance.