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electrical_engineering_1:task_kricv9fh7haauo6q_with_calculation [2023/03/10 17:21] – mexleadminelectrical_engineering_1:task_kricv9fh7haauo6q_with_calculation [Unbekanntes Datum] (aktuell) – gelöscht - Externe Bearbeitung (Unbekanntes Datum) 127.0.0.1
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-{{tag>complex_impedance exam_ee1_WS2022}} 
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-<panel type="info" > <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> 
-<fs x-large>**Exercise ~~#@ee1_taskctr.#~~ : Complex Impedance Circuit  ** \\ (written test, approx. 15% of a 60-minute written test, WS2022) \\ \\ </fs> 
- 
-A circuit designed to filter the noise from a signal shall be analysed. \\  
-The input is given by a voltage source $u(t) = 3.0 ~\rm{V} \cdot sin⁡(2\pi \cdot 15 ~\rm{kHz} \cdot t)$ with an internal resistance of $10 ~\Omega$. \\ 
-This linear source is connected with an inductor of $330 ~ \rm{µH}$ and a capacitor of $0.22 ~\rm{µF}$, all in series.  
- 
-1. Draw the circuit diagram of the given circuit. \\ Label all components, voltages and currents. 
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-<button size="xs" type="link" collapse="kricv9fh7haauo6q_1_Solution">{{icon>eye}} Result</button><collapse id="kricv9fh7haauo6q_1_Solution" collapsed="true"> 
-<callout type="tip" icon="true"> 
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-{{drawio>electrical_engineering_1:kricv9fh7haauo6qCircuit.svg}} 
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-</callout></collapse> 
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-2. Calculate the single impedance $|\underline{Z}_C|$, $|\underline{Z}_L|$ such as $|\underline{Z}|$ of the overall circuit.  
- 
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-<callout type="tip" icon="true"> 
- 
-\begin{align*} 
-Z_C  &= {{1}\over{2\pi \cdot f \cdot C}}\\ 
-     &= {{1}\over{2\pi \cdot 15 ~\rm{kHz} \cdot 0.22 ~\rm{µF}}}\\ 
-\end{align*} 
-\\ 
-\begin{align*} 
-Z_L  &= 2\pi \cdot f \cdot L\\ 
-     &= 2\pi \cdot 15 ~\rm{kHz} \cdot 0.22 ~\rm{µF}\\ 
-\end{align*} 
-\\ 
-\begin{align*} 
-Z_C  &= {{1}\over{2\pi \cdot f \cdot C}}\\ 
-     &= {{1}\over{2\pi \cdot 15 ~\rm{kHz} \cdot 330 ~\rm{µH}}}\\ 
-\end{align*} 
-\\ 
-\begin{align*} 
- \underline{Z}  &= R + \underline{Z}_L + \underline{Z}_C \\  
-                &= R + j \cdot {Z}_L   - j \cdot {Z}_C \\  
-                &= R + j \cdot ({Z}_L - {Z}_C) \\  
-|\underline{Z}| &= \sqrt{R^2 + (\underline{Z}_L - \underline{Z}_C)^2 }\\ 
-\end{align*} 
-\\ 
- 
-</callout></collapse> 
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-\begin{align*} 
-Z_L &= 31.1 ~\Omega \\ 
-Z_C &= 48.2 ~\Omega \\ 
-Z   &= 19.8 ~\Omega 
-\end{align*}</callout> 
- \\ 
-</collapse> 
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-3. Draw the three impedance phasors $|\underline{Z}_C|$, $|\underline{Z}_L|$ and $|\underline{Z}_R|$ in a diagram. \\ Choose and appropriate scaling factor and write it down. 
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-<callout type="tip" icon="true"> 
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-{{drawio>electrical_engineering_1:kricv9fh7haauo6qCircuit3.svg}} 
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-</callout></collapse> 
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-4. Calculate the current $|\underline{I}|$. 
- 
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-<callout type="tip" icon="true"> 
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-\begin{align*} 
-Z       &= {{\hat{U}}\over{\hat{I}}} \\ 
-\hat{I} &= {{\hat{U}}\over{Z}} \\ 
-\end{align*} 
- 
-With $I = {{1}\over{\sqrt{2}}}\cdot \hat{I}$: 
-\begin{align*} 
-I  &= {{1}\over{\sqrt{2}}}\cdot {{\hat{U}}\over{Z}} \\ 
-   &= {{1}\over{\sqrt{2}}}\cdot {{3.0 ~\rm{V}}\over{19.28 ~\Omega}} \\ 
-\end{align*} 
- 
-</callout></collapse> 
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-<button size="xs" type="link" collapse="kricv9fh7haauo6q_4_solution">{{icon>eye}} Final result</button><collapse id="kricv9fh7haauo6q_4_solution" collapsed="true"><callout type="tip" icon="true"> 
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-\begin{align*} 
-I = 107 ~\rm{mA} 
-\end{align*}</callout> 
- \\ 
-</collapse> 
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