====== Block 02 — Electric charge, current, voltage ======

===== Learning objectives =====
<callout>
After this 90-minute block, you can
  * 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).
  * Define electric current $I$ as rate of charge flow; relate $I$ to moving charge via $I = \frac{{\rm d}Q}{{\rm d}t}$.
  * 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**.
  * 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>

===== 90-minute plan =====
  - Warm-up (5–10 min): 
    - Recall of SI units from Block 01; estimate “How many electrons per second flow at $1~\rm A$?” 
    - Quick quiz – “What is larger: voltage of a lightning strike or mains outlet?” 
  - Core concepts & derivations (60–70 min):  
    - Electric charge: definition, elementary charge, Coulomb’s law (overview only).  
    - Charge carriers in metals vs. electrolytes.  
    - Electric current: definition, instantaneous and average values, unit check.  
    - Typical magnitudes; conventional vs. electron flow.  
  - Practice (10–20 min): Quick calculations and sim-based exercises.  
  - Wrap-up (5 min): Summary and pitfalls.

===== Conceptual overview =====
<callout icon="fa fa-lightbulb-o" color="blue">
  - **Charge $Q$** is the fundamental “substance” of electricity, always in multiples of the elementary charge.  
  - **Like charges repel, unlike charges attract**; forces are described by Coulomb’s law (detail in Block 09).  
  - **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.  
  - This block connects Block 01 (units) to Block 03 (voltage and resistance), and prepares for Kirchhoff’s laws in Block 04.
</callout>

~~PAGEBREAK~~ ~~CLEARFIX~~

===== Core content =====

==== Electric charge ====

<WRAP right>
<imgcaption AtomicModel | Atomic model according to Bohr / Sommerfeld>
</imgcaption>
{{drawio>Atommodell.svg}}
</WRAP>
  * 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 AtomicModel>
  * Due to the electrons and protons it is **quantized** in multiples of the elementary charge:

\begin{align*}
e &= 1.602 \cdot 10^{-19}~\rm C \\
Q &= n \cdot e
\end{align*}

with $n \in \mathbb{Z}$.

  * Positive charge: deficiency of electrons generates an excess of positive charges (e.g. ionized atoms).  
  * Negative charge: excess electrons overcompensates the positive charges.
  * charges with different signs attract each other. Charges with similar sign repell each other

\begin{align*}
[Q] = 1~\rm C = 1~A \cdot s
\end{align*}

<panel type="info" title="Example / micro-exercise">
How many electrons correspond to a charge of $1~\rm C$?  
\begin{align*}
n = \frac{Q}{e} = \frac{1~\rm C}{1.602\cdot 10^{-19}~\rm C} \approx 6.24 \cdot 10^{18}
\end{align*}
</panel>

==== Electric current ====
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*}
i(t) = \frac{{\rm d}Q}{{\rm d}t}
\end{align*}

Unit check:

\begin{align*}
[i] &= \frac{[Q]}{[t]} = \frac{1~\rm C}{1~\rm s} = 1~\rm A
\end{align*}

Charge transport can take place through
  * In metals: flow of electrons.  
  * In electrolytes: movement of ions.  
  * In semiconductors: electrons and holes.  

<callout icon="fa fa-exclamation" color="red" title="Convention">
In this course, we generally use the **conventional current direction**: positive from $+$ to $-$. The electron flow is opposite.
</callout>

<panel type="info" title="Typical current magnitudes">
  * $10~\rm pA$ — control current in a FET gate  
  * $10~\rm \mu A$ — sensitive sensor output  
  * $10~\rm mA$ — LED or small sensor supply  
  * $10~\rm A$ — heating device  
  * $10~\rm kA$ — large generator output
</panel>

==== Electrodes ====
An electrode is a connection (or pin) of an electrical component. \\
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). \\
The name of the electrode is given as follows: 
  * **A**node: Electrode at which the current enters the component.
  * Cathode: Electrode at which the current exits the component. (in German //**K**athode//)

As a mnemonic, you can remember the diode's structure, shape, and electrodes (see <imgref BildNr8>).


<WRAP>
<imgcaption BildNr8 | Electrodes on the diode>
</imgcaption>
{{drawio>Diode_Elektroden.svg}}
</WRAP>


==== 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 =====

{{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"> 
<WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
A flashlight bulb is supplied with $I=0.25~\rm A$.  
How many electrons pass through the filament in one second?

<button size="xs" type="link" collapse="Strategy">{{icon>eye}} Strategy</button><collapse id="Strategy" collapsed="true">
Use $n=\frac{I \cdot t}{e}$ with $t=1~\rm s$.
</collapse>
<button size="xs" type="link" collapse="Solution">{{icon>eye}} Solution</button><collapse id="Solution" collapsed="true">
\begin{align*}
n = \frac{0.25~\rm C}{1.602 \cdot 10^{-19}~\rm C} \approx 1.6 \cdot 10^{18}
\end{align*}
</collapse>
</WRAP></WRAP></panel>

{{tagtopic>chapter1_4&nodate&nouser&noheader&nofooter&order=custom}}

===== Embedded resources =====
\\ \\
<WRAP column half>
Charge in Matter
{{youtube>HY_ZJTREpfU}}
</WRAP>

<WRAP column half>
What is Electric Charge and How Electricity Works
{{youtube>iqVtGNQAC2E}}
</WRAP>

<WRAP column half>
Electric - Hydraulic Analogy: Charge, Voltage, and Current 
{{youtube>Lvp_a_JkD2o}}
</WRAP>