Question

The \( L-R-C \) series circuit shown in (Figure 1) has an ac voltage source \( v_{\text {in }}(t)=V_{\text {in }} \cos (\omega t) \), where \( V_{\text {in }} \) is the input voltage amplitude and \( \omega \) is its angular frequency. The values of the resistance, inductance, and capacitance of the components are \( R, L \), and \( C \). The capacitance is variable. The output voltage is \( v_{\text {out }}=V_{\text {out }} \cos (\omega t+\theta) \). What is the output voltage amplitude \( V_{\text {out }} \) ? Express your answer in terms of some or all of the variables \( V_{\mathrm{in}}, R, L, C \), and \( \omega \). \[ V_{\text {out }}= \] \( \square \) Submit Previous Answers Request Answer Incorrect; Try Again; 4 attempts remaining Part B What is the phase angle \( \theta \) of the output voltage? Express your answer in terms of some or all of the variables \( V_{\text {in }}, R, L, C \), and \( \omega \). \[ \begin{array}{l} \square \sqrt[\square]{\square} A \Sigma \phi+C O \text { ? } \rightarrow ? \\ \theta=\square \end{array} \] Submit Previous Answers Request Answer Incorrect; Try Again; 5 attempts remaining Part C What is the value of \( \theta \) at resonance? 1 of 1 Figure Figure Submit Previous Answers Request Answer

          The \( L-R-C \) series circuit shown in (Figure 1) has an ac voltage source \( v_{\text {in }}(t)=V_{\text {in }} \cos (\omega t) \), where \( V_{\text {in }} \) is the input voltage amplitude and \( \omega \) is its angular frequency. The values of the resistance, inductance, and capacitance of the components are \( R, L \), and \( C \). The capacitance is variable. The output voltage is \( v_{\text {out }}=V_{\text {out }} \cos (\omega t+\theta) \).

What is the output voltage amplitude \( V_{\text {out }} \) ?
Express your answer in terms of some or all of the variables \( V_{\mathrm{in}}, R, L, C \), and \( \omega \).
\[
V_{\text {out }}=
\]
\( \square \)
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Part B

What is the phase angle \( \theta \) of the output voltage?
Express your answer in terms of some or all of the variables \( V_{\text {in }}, R, L, C \), and \( \omega \).
\[
\begin{array}{l}
\square \sqrt[\square]{\square} A \Sigma \phi+C O \text { ? } \rightarrow ? \\
\theta=\square
\end{array}
\]

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Part C

What is the value of \( \theta \) at resonance?
1 of 1

Figure
Figure
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The L-R-C series circuit shown in (Figure 1) has an ac voltage source vin (t)=Vin cos (ω t), where Vin is the input voltage amplitude and ω is its angular frequency. The values of the resistance, inductance, and capacitance of the components are R, L, and C. The capacitance is variable. The output voltage is vout =Vout cos (ω t+θ).

What is the output voltage amplitude Vout ?
Express your answer in terms of some or all of the variables Vin, R, L, C, and ω.

Vout =

□
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Part B

What is the phase angle θ of the output voltage?
Express your answer in terms of some or all of the variables Vin , R, L, C, and ω.

□√(□) A Σϕ+C O ? → ?
θ=□

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Part C

What is the value of θ at resonance?
1 of 1

Figure
Figure
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