Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

Link zu dieser Vergleichsansicht

Nächste Überarbeitung		 Vorhergehende Überarbeitung
electrical_engineering_and_electronics_1:block02 [2025/09/27 15:44] – angelegt mexleadminelectrical_engineering_and_electronics_1:block02 [2025/09/28 23:33] (aktuell) – mexleadmin
Zeile 1: Zeile 1:
-====== Block 02 — Electric charge and current ======+====== Block 02 — Electric charge, current, voltage ======
  
 ===== Learning objectives ===== ===== Learning objectives =====
 <callout> <callout>
 +After this 90-minute block, you can
   * Define electric charge $Q$ and explain its quantization in multiples of the elementary charge $e$.   * Define electric charge $Q$ and explain its quantization in multiples of the elementary charge $e$.
   * Distinguish positive and negative charges, their interactions, and typical carriers (electrons, ions).   * Distinguish positive and negative charges, their interactions, and typical carriers (electrons, ions).
Zeile 8: Zeile 9:
   * Apply the unit check for $1~\rm A = 1~C/s$ and recall typical current magnitudes (pA … kA).   * Apply the unit check for $1~\rm A = 1~C/s$ and recall typical current magnitudes (pA … kA).
   * Explain and consistently use the **conventional current direction**.   * Explain and consistently use the **conventional current direction**.
-  * Identify and sketch the symbols of the **ideal current and voltage source**.+  * Define electric voltage $U$ as potential difference and relate it to energy per unit charge: $U=W/Q$. 
 +  * Distinguish potential reference (ground) and explain why only voltage differences are measurable.
 </callout> </callout>
  
 ===== 90-minute plan ===== ===== 90-minute plan =====
-  - Warm-up (5–10 min): Recall of SI units from Block 01; estimate “How many electrons per second flow at $1~\rm A$?”+  - Warm-up (5–10 min):  
 +    - Recall of SI units from Block 01; estimate “How many electrons per second flow at $1~\rm A$?”  
 +    - Quick quiz – “What is larger: voltage of a lightning strike or mains outlet?” 
   - Core concepts & derivations (60–70 min):     - Core concepts & derivations (60–70 min):  
     - Electric charge: definition, elementary charge, Coulomb’s law (overview only).       - Electric charge: definition, elementary charge, Coulomb’s law (overview only).  
Zeile 18: Zeile 22:
     - Electric current: definition, instantaneous and average values, unit check.       - Electric current: definition, instantaneous and average values, unit check.  
     - Typical magnitudes; conventional vs. electron flow.       - Typical magnitudes; conventional vs. electron flow.  
-    - Ideal current source, symbol, and U–I diagram.   
   - Practice (10–20 min): Quick calculations and sim-based exercises.     - Practice (10–20 min): Quick calculations and sim-based exercises.  
   - Wrap-up (5 min): Summary and pitfalls.   - Wrap-up (5 min): Summary and pitfalls.
Zeile 28: Zeile 31:
   - **Current $I$** quantifies *how fast* charge moves: $1~\rm A$ = $1~C/s$.     - **Current $I$** quantifies *how fast* charge moves: $1~\rm A$ = $1~C/s$.  
   - Convention: we follow **conventional current direction** (positive charge motion, from $+$ to $-$), even though in metals electrons move oppositely.     - Convention: we follow **conventional current direction** (positive charge motion, from $+$ to $-$), even though in metals electrons move oppositely.  
-  - Ideal current sources deliver a fixed current regardless of load voltage — a useful abstraction for circuit analysis.   
   - This block connects Block 01 (units) to Block 03 (voltage and resistance), and prepares for Kirchhoff’s laws in Block 04.   - This block connects Block 01 (units) to Block 03 (voltage and resistance), and prepares for Kirchhoff’s laws in Block 04.
 </callout> </callout>
Zeile 39: Zeile 41:
  
 <WRAP right> <WRAP right>
-<imgcaption BildNr0 | Atomic model according to Bohr / Sommerfeld>+<imgcaption AtomicModel | Atomic model according to Bohr / Sommerfeld>
 </imgcaption> </imgcaption>
 {{drawio>Atommodell.svg}} {{drawio>Atommodell.svg}}
 </WRAP> </WRAP>
   * Electric charge $Q$ is a physical quantity indicating the amount of excess or deficit of electrons or ions.    * Electric charge $Q$ is a physical quantity indicating the amount of excess or deficit of electrons or ions. 
-  * the charge is based on the electron shell and the atomic nucleus, see the atomic model of Bohr and Sommerfeld in <imgref BildNr0>+  * the charge is based on the electron shell and the atomic nucleus, see the atomic model of Bohr and Sommerfeld in <imgref AtomicModel>
   * Due to the electrons and protons it is **quantized** in multiples of the elementary charge:   * Due to the electrons and protons it is **quantized** in multiples of the elementary charge:
  
Zeile 54: Zeile 56:
 with $n \in \mathbb{Z}$. with $n \in \mathbb{Z}$.
  
-* Positive charge: deficiency of electrons (e.g. ionized atoms).   +  * Positive charge: deficiency of electrons generates an excess of positive charges (e.g. ionized atoms).   
-* Negative charge: excess electrons.  +  * Negative charge: excess electrons overcompensates the positive charges. 
 +  * charges with different signs attract each other. Charges with similar sign repell each other
  
 \begin{align*} \begin{align*}
Zeile 69: Zeile 72:
  
 ==== Electric current ==== ==== Electric current ====
-An **electric current** arises when charges move in a preferred direction. The instantaneous current is defined as+An **electric current** arises when charges move in a preferred direction, e.g. by attraction and repulsion.  
 +The current is defined as  
 + 
 +\begin{align*} 
 +I = \frac{Q}{t} 
 +\end{align*} 
 + 
 +The instantaneous current is defined as
  
 \begin{align*} \begin{align*}
Zeile 81: Zeile 91:
 \end{align*} \end{align*}
  
-* In metals: flow of electrons.   +Charge transport can take place through 
-* In electrolytes: movement of ions.   +  * In metals: flow of electrons.   
-* In semiconductors: electrons and holes.  +  * In electrolytes: movement of ions.   
 +  * In semiconductors: electrons and holes.  
  
 <callout icon="fa fa-exclamation" color="red" title="Convention"> <callout icon="fa fa-exclamation" color="red" title="Convention">
-In this course, we always use the **conventional current direction**: positive from $+$ to $-$. Electron flow is opposite.+In this course, we generally use the **conventional current direction**: positive from $+$ to $-$. The electron flow is opposite.
 </callout> </callout>
  
Zeile 97: Zeile 108:
 </panel> </panel>
  
-==== Ideal current source ==== +==== Electrodes ==== 
-From circuit theory, we abstract the **ideal current source**:   +An electrode is a connection (or pin) of an electrical component. \\ 
-  * Delivers a fixed current $I_s$, independent of load voltage.   +Looking at a component, the electrode is characterized as the homogenous part of the component, where the charges come in / move out (usually made out of metal). \\ 
-  * Symbol: circle with arrow.   +The name of the electrode is given as follows:  
-  * U–I characteristic: vertical line at $I = I_s$.+  * **A**node: Electrode at which the current enters the component. 
 +  * Cathode: Electrode at which the current exits the component. (in German //**K**athode//)
  
-<WRAP group><WRAP column 45%> +As a mnemonic, you can remember the diode's structure, shape, and electrodes (see <imgref BildNr8>). 
-<imgcaption | ideal current source>+ 
 + 
 +<WRAP> 
 +<imgcaption BildNr8 | Electrodes on the diode>
 </imgcaption> </imgcaption>
-{{drawio>IdealeStromquelle.svg}} +{{drawio>Diode_Elektroden.svg}} 
-</WRAP><WRAP column 45%> +</WRAP>
-{{youtube>8_AWiueI4Qg}} +
-</WRAP></WRAP>+
  
-~~PAGEBREAK~~ ~~CLEARFIX~~+ 
 +==== Electric voltage ==== 
 + 
 +Every rock on a mountain has a higher energy potential than a rock in the valley. As higher up and as more mass the rock has, as more energy is stored. The energy difference $\Delta W_{1,2}$ is given by the height difference $\Delta h_{1,2}$ 
 + 
 +\begin{align*} 
 +\Delta W_{1,2} = m \cdot g \cdot \Delta h_{1,2} 
 +\end{align*} 
 + 
 +Similarily, charges on the positive pin of a battery has a higher energy potential than charges on the negative pin.  
 +Similar to the transport of a mass in the gravitational field, energy is needed/released when charge is moved in an electric field. We will look at the specific electric field starting from [[block09]]. 
 + 
 +For the energy in an electric field, as higher the object is charged ($Q$), as more energy $\Delta W_{1,2}$ can be released / is needed for movements. The equivalent to the height $h$ in the mechanic picture is the potential $\varphi$ in the electric case: 
 + 
 +\begin{align*} 
 +\Delta W_{1,2} = Q \cdot \Delta \varphi_{1,2} 
 +\end{align*} 
 + 
 +It follows that: \\ 
 +\begin{align*} 
 +\boxed{{\Delta W_{1,2} \over {Q}} = \varphi_1 - \varphi_2  = U_{1,2}} 
 +\end{align*} 
 + 
 +voltage $U_{1,2}$ is the energy $W_{1,2}$ per charge $Q$ between two points $1$ and $2$.  
 + 
 +  * **Units:** $[U]=[W]/[Q]=1~{\rm J}/1~{\rm C}=1~{\rm V}$. 
 +  * **Reference:** We choose one node as potential zero (“ground”); only differences are meaningful. 
 + 
 +<panel type="info" title="Typical voltage magnitudes"> 
 +  * Thermal noise: $\sim \mu{\rm V}$ 
 +  * Microcontroller: supply $1.8~{\rm V}$ to  $5.0~{\rm V}$ (often given as ''1V8'' and ''5V0'' or in general as ''VCC'' or ''VDD'') 
 +  * Mains: $230~{\rm V}$ 
 +  * Lightning: $>10^6~{\rm V}$ 
 +</panel> 
 + 
 +<panel type="info" title="Example / micro-exercise"> 
 +A charge $Q=2.0~{\rm mC}$ moves through a potential difference of $5.0~{\rm V}$. Energy transferred: \\ 
 +$W=U \cdot Q=5.0~{\rm V} \cdot 2.0~{\rm mC}=10.0~{\rm mJ}$. 
 +</panel> 
 + 
 + 
 +==== Comparison: Mechanics vs Electrics ==== 
 + 
 +<WRAP group><WRAP half column> 
 +<callout color="grey"> 
 +<WRAP> 
 +<imgcaption BildNr5 | Mechanical potential> 
 +</imgcaption> 
 +{{drawio>mechanisches_Potential.svg}} 
 +</WRAP> 
 + 
 +=== Mechanical System === 
 + 
 +**Potential Energy** 
 + 
 +Potential energy is always related to a reference level (reference height). 
 +The energy required to move $m$ from $h_1$ to $h_2$ is independent of the reference level. 
 + 
 +$\Delta W_{1,2} = W_1 - W_2 = m \cdot g \cdot h_1 - m \cdot g \cdot h_2 = m \cdot g \cdot (h_1 - h_2)$ 
 +</callout> 
 +</WRAP><WRAP half column> 
 +<callout color="grey"> 
 +<WRAP> 
 +<imgcaption BildNr6 | Electrical Potential> 
 +</imgcaption> 
 +{{drawio>elektrisches_Potential.svg}} 
 +</WRAP> 
 + 
 +=== Electrical System === 
 + 
 +**Potential** 
 + 
 +The potential $\varphi$ is always specified relative to a reference point. 
 + 
 +Common used are: 
 +  * Earth potential (ground, earth, ground). 
 +  * infinitely distant point 
 + 
 +To shift the charge, the potential difference must be overcome. The potential difference is independent of the reference potential. 
 +$\boxed{\Delta W_{1,2} = W_1 - W_2 = Q \cdot \varphi_1 - Q \cdot \varphi_2  = Q \cdot (\varphi_1 - \varphi_2)}$ 
 +</callout> 
 +</WRAP> 
 + 
 +===== Common pitfalls ===== 
 +  * Mixing electron flow vs. conventional current.   
 +  * Misinterpreting current as “speed” rather than rate of charge flow. 
 +  * Given the definition, rechargeable batteries not have a fixed cathode / anode. Here, usually discharging the battery is considered.
  
 ===== Exercises ===== ===== Exercises =====
 +
 +{{tagtopic>chapter1_2&nodate&nouser&noheader&nofooter&order=custom}}
 +
 +
 +#@TaskTitle_HTML@#1.5.1 Direction of the voltage 
 +#@TaskText_HTML@#
 +
 +<WRAP>
 +<imgcaption BildNr21 | Example of conventional voltage specification>
 +</imgcaption>
 +{{drawio>BeispKonventionelleSpannungsangabe.svg}}
 +</WRAP>
 +
 +Explain whether the voltages $U_{\rm Batt}$, $U_{12}$ and $U_{21}$ in <imgref BildNr21> are positive or negative according to the voltage definition.
 +
 +#@HiddenBegin_HTML~1,Hints~@#
 +  * Which terminal has the higher potential? 
 +  * From where to where does the arrow point? 
 +#@HiddenEnd_HTML~1,Hints~@#
 +
 +
 +#@HiddenBegin_HTML~2,Result~@#
 +  * ''+'' is the higher potential. Terminal 1 has the higher potential. $\varphi_1 > \varphi_2$
 +  * For $U_{\rm Batt}$: The arrow starts at terminal 1 and ends at terminal 2. So $U_{\rm Batt}=U_{12}>0$
 +  * $U_{21}<0$
 +#@HiddenEnd_HTML~1l2,Result~@#
 +
 +#@TaskEnd_HTML@#
 +
  
 <panel type="info" title="Task 2.1: Counting charges in a current">  <panel type="info" title="Task 2.1: Counting charges in a current"> 
Zeile 130: Zeile 258:
 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-<panel type="info" title="Task 2.2: Simulation — observe current direction">  +{{tagtopic>chapter1_4&nodate&nouser&noheader&nofooter&order=custom}}
-<WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> +
-Open the circuit sim and flip the battery polarity. Observe current arrow and electron movement.   +
-{{url>https://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjCAMB0l3BWcMBMcUHYMGZIA4UA2ATmIxEJRCQBZsAoAJxDqsJvA0JGO8hBRpITTt14hsacMSr9Mw5pP5gZEwnnA0OyhHBGsKHGuJQI+LDHubHup7kumyQBKxKkqqNMPfVRwQhRYTMxZvNQ1+dUCUGmVVbzlYvzAAkQcPASTsbHMzVxj+bO4vHwiLEQKJHP8NTCcweHoANxqBDCowLh5zfiT+JH4YMARiYeM6SBl6AGUBPFr8TLlF5RAAMwBDABsAZwBTPxR6AHc5hY101WikwQ4EtqdsYmFT+8qU2vaoE-BCOS+Pg9vgAPAQjaQQTBIFRGTIgab0UHYGjkFIQbAIDQpWFSI5Ip7gFISFGE2gSfgASXo2Es4U0HGweDuKCxfheEiZrQM7BBbTuxFqeCQaAgHHc9CAA noborder}} +
-</WRAP></WRAP></panel> +
- +
-<panel type="info" title="Task 2.3: Identify source symbols">  +
-<WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> +
-Sketch and label the symbols for an ideal voltage source and an ideal current source.   +
-Which one enforces a fixed $U$, which one enforces a fixed $I$? +
-</WRAP></WRAP></panel>+
  
 ===== Embedded resources ===== ===== Embedded resources =====
Zeile 149: Zeile 267:
 </WRAP> </WRAP>
  
 +<WRAP column half>
 +What is Electric Charge and How Electricity Works
 +{{youtube>iqVtGNQAC2E}}
 +</WRAP>
  
-===== Summary & checklist ===== +<WRAP column half> 
-<callout> +Electric - Hydraulic Analogy: Charge, Voltage, and Current  
-  - Electric charge $Q$ is quantized in multiples of $e=1.602\cdot 10^{-19}~\rm C$.   +{{youtube>Lvp_a_JkD2o}} 
-  - Current $I = \frac{{\rm d}Q}{{\rm d}t}$; $1~\rm A = 1~C/s$.   +</WRAP>
-  - **Conventional current direction** runs from $+$ to $-$. Electron flow is opposite.   +
-  - Typical currents range from pA (sensors) to kA (power generators).   +
-  - Ideal current sources supply fixed current independent of load.   +
-  - Pitfalls:   +
-    * Mixing electron flow vs. conventional current.   +
-    * Forgetting unit checks ($\rm A = C/s$).   +
-    * Misinterpreting current as “speed” rather than rate of charge flow. +
-</callout>+