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#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~ Complex series circuit \\
<fs medium>(written test, approx. 8 % of a 120-minute written test, SS2021)</fs> #@TaskText_HTML@#

A series circuit of $C = 4.95~\rm nF$, $R = 200 ~\rm \Omega$ at $f = 40 ~\rm kHz$ shall be given.

a) Determine the complex impedance $\underline{Z}_C$. 

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The complex impedance $\underline{Z}_C$ is given as 
\begin{align*}
\underline{Z}_C &= {{1}\over{{\rm j} \cdot 2\pi \cdot f \cdot C }} \\
                &= {{-{\rm j}}\over{2\pi \cdot  40 \cdot 10^3 ~\rm Hz \cdot 4.95 \cdot 10^{-9} ~\rm F }} \\
                &= -{\rm j} \cdot 803.81... ~\rm \Omega \\
\end{align*}

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$\underline{Z}_C = -{\rm j} \cdot 804 ~\rm \Omega $
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b) Determine the absolute value of the resulting impedance of the series circuit using an impedance vector diagram. 
Pay attention to the correct dimensioning. 

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{{drawio>ee2:9Xy69AxG3GI3NR26_solution1.svg}}

Based on the diagram: $|\underline{Z}|= 828 ~\Omega$
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