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electrical_engineering_1:block01 [2025/09/27 12:21] – angelegt - Externe Bearbeitung 127.0.0.1electrical_engineering_1:block01 [2025/09/29 09:27] (aktuell) – mexleadmin
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 +===== Block 01 — Physical Quantities, Units, Charge & Current =====
 +
 +==== Learning objectives ====
 +  * Convert and compare values using SI base units and prefixes from atto (a) to exa (E).
 +  * Explain electric charge as multiples of the elementary charge and compute total charge from particle count.
 +  * Define electric current as time rate of charge flow, relate conventional current to electron flow, and use correct reference arrows.
 +  * Apply unit analysis to check formulas and results.
 +
 +==== 90-minute plan ====
 +  - Warm-up (10 min): SI prefixes speed-drill; unit sanity checks (▶ quick quiz).
 +  - Core concepts & derivations (60 min): SI system & prefixes → charge and the elementary charge → current as charge per time; conventional vs electron flow; reference arrows in circuits.
 +  - Practice (15 min): ✎ Conversions & short calculations (prefixes; Q–I–t triangle); direction questions with mixed charge carriers.
 +  - Wrap-up (5 min): Recap key formulas and common mistakes; preview: voltage & potential (next block).
 +
 +==== Conceptual overview ====
 +**What’s the game?** In circuits we count **how much charge** moves (**Q**, coulombs) and **how fast** it moves (**I**, amperes). SI units and prefixes let us express tiny sensor signals and huge lightning currents on one common scale. Current direction is a **convention** (positive-charge movement) and must not be confused with the motion of electrons, which are negatively charged and usually move the other way.
 +
 +==== Core definitions & formulas ====
 +**SI base & derived (used today)**
 +  * Charge $Q$ in coulomb (C); time $t$ in second (s); current $I$ in ampere (A).
 +
 +**Prefixes (selected)**
 +  * $1~\mathrm{mA}=10^{-3}~\mathrm{A}$, $1~\mathrm{\mu A}=10^{-6}~\mathrm{A}$, $1~\mathrm{nA}=10^{-9}~\mathrm{A}$, $1~\mathrm{kA}=10^{3}~\mathrm{A}$.
 +  * Tip: move powers of ten, not the decimal point “by feeling”.
 +
 +**Charge (discrete and continuous)**
 +  * $Q = n \cdot e$ with $e=1.602\times 10^{-19}~\mathrm{C}$ (elementary charge).
 +  * Typical values: single ion $e$; small capacitor on a sensor: $Q \sim \mathrm{pC}$–$\mathrm{nC}$.
 +
 +**Current (definition)**
 +  * $I = \dfrac{\mathrm{d}Q}{\mathrm{d}t}$ (or $I \approx \Delta Q / \Delta t$ for averages).
 +  * Unit check: $[I]=\mathrm{C/s}=\mathrm{A}$.
 +  * Typical values: biopotentials $\sim \mathrm{\mu A}$; GPIO pin $\sim \mathrm{mA}$; motor windings $\sim \mathrm{A}$.
 +
 +**Conventional vs electron flow**
 +  * **Conventional current** points in the direction **positive charges** would move.
 +  * Electron flow is opposite in direction to conventional current in metals.
 +  * Reference arrows for later circuit work: choose arbitrarily **before** calculation, then interpret sign after.
 +
 +<tabcaption core01_vars|Symbols, units, typical values>
 +^ Symbol ^ Meaning ^ SI unit ^ Typical values ^
 +| $Q$ | Electric charge | C | $\mathrm{pC}$ (sensors) … $\mathrm{mC}$ |
 +| $e$ | Elementary charge | C | $1.602\times 10^{-19}~\mathrm{C}$ |
 +| $n$ | Number of charges/particles | – | $10^3 \ldots 10^{20}$ (context dependent) |
 +| $t$ | Time | s | $\mathrm{ms}$ … $\mathrm{s}$ |
 +| $I$ | Electric current ($\mathrm{d}Q/\mathrm{d}t$) | A | $\mathrm{\mu A}$ … $\mathrm{A}$ |
 +</tabcaption>
 +
 +==== Worked example(s) ====
 +=== Example 1 — Prefix fluency & charge moved ===
 +A sensor draws $3.6~\mathrm{mA}$ continuously.  
 +a) Express this in $\mathrm{A}$ and in $\mathrm{\mu A}$.  
 +b) How much charge passes in $250~\mathrm{ms}$?
 +
 +**Solution.**  
 +a) $3.6~\mathrm{mA}=3.6\times 10^{-3}~\mathrm{A}=3600~\mathrm{\mu A}$.  
 +b) $Q = I \cdot t = 3.6\times 10^{-3}~\mathrm{A}\cdot 0.250~\mathrm{s}=9.0\times 10^{-4}~\mathrm{C}=0.90~\mathrm{mC}$.
 +
 +=== Example 2 — From particles to current ===
 +A current in a thin gold wire is due to electrons. In $20~\mathrm{ms}$, $n=7.5\times 10^{15}$ electrons pass a cross-section. What average current flows?
 +
 +**Solution.**  
 +Total charge $Q = n e = 7.5\times 10^{15}\cdot 1.602\times 10^{-19}~\mathrm{C}\approx 1.20\times 10^{-3}~\mathrm{C}$.  
 +$I \approx Q/t = (1.20\times 10^{-3})/0.020 \approx 0.060~\mathrm{A}=60~\mathrm{mA}$.  
 +**Direction:** electron motion right→left implies **conventional current** left→right.
 +
 +=== Example 3 — Mixed carriers & current direction ===
 +In an electrolyte between faces $A_1$ and $A_2$, during $\Delta t=1~\mathrm{s}$, $\Delta Q_p=+40~\mathrm{\mu C}$ moves from $A_1$ to $A_2$ and $\Delta Q_n=-25~\mathrm{\mu C}$ (negative) moves from $A_2$ to $A_1$. What is the algebraic current from $A_1$ to $A_2$?
 +
 +**Solution.**  
 +Total charge transfer $\Delta Q=\Delta Q_p-\Delta Q_n = 40~\mathrm{\mu C}-(-25~\mathrm{\mu C})=65~\mathrm{\mu C}$.  
 +$I=\Delta Q/\Delta t=65~\mathrm{\mu A}$ **from $A_1$ to $A_2$** (positive).
 +
 +==== Quick checks ====
 +  * What is the SI unit of charge? ++++ Answer|
 +Coulomb (C).
 +++++
 +  * Convert $47~\mathrm{k\Omega}$ to $\mathrm{\Omega}$. ++++ Answer|
 +$47~\mathrm{k\Omega}=47\,000~\mathrm{\Omega}$.
 +++++
 +  * State the definition of $1~\mathrm{A}$ using charge and time. ++++ Answer|
 +$1~\mathrm{A}$ flows if $1~\mathrm{C}$ passes a cross-section in $1~\mathrm{s}$.
 +++++
 +  * If electrons drift to the right, which way is conventional current? ++++ Answer|
 +To the **left** (opposite electron motion).
 +++++
 +  * Compute the number of electrons in $1.0~\mathrm{nC}$. ++++ Answer|
 +$n=Q/e \approx (1.0\times10^{-9})/(1.602\times10^{-19})\approx 6.24\times10^{9}$ electrons.
 +++++
 +
 +==== Embedded resources ====
 +  * {{youtube>jjvIy04PwYI}}
 +  * {{drawio>Atommodell.svg}}
 +  * {{youtube>HY_ZJTREpfU}}
 +  * {{drawio>pos_neg_Ladungen_im_Leiter.svg}}
 +
 +==== Common pitfalls & misconceptions ====
 +  * Mixing up **quantity vs unit** (e.g., writing “mA” when you mean “m” as a prefix on amperes) or stacking prefixes (No: “$\mu k$A”).
 +  * Confusing **charge** (C) with **current** (A) or **voltage** (V). Use unit analysis to catch errors early.
 +  * Forgetting that **conventional current** follows positive charge flow; electrons go the opposite way in metals.
 +  * Dropping sign information when interpreting reference arrows; always place arrows **before** calculation and read signs **after**.
 +
 +==== Mini-assignment / homework (optional) ====
 +  * Build a two-column “prefix ladder” from $10^{-18}$ to $10^{18}$ and place **five real-world examples** across it (e.g., biocurrent, USB device current, motor phase current). Bring it next time.
 +  * Compute: A wearable draws $220~\mathrm{\mu A}$ in standby for $18~\mathrm{h}$. How much charge (in mAh and in C) is used?
 +
 +==== References & links ====
 +  * Later: voltage & potential and ideal sources → [[:eee1:block-02-voltage-power|Block 02 — Voltage & Power]].
 +  * Later: resistance, conductance, and temperature dependence → [[:eee1:block-03-resistance|Block 03 — Resistance & Practical Resistors]].
 +  * Lab safety and measurement rules → [[lab_regulation|Laboratory regulations]].
 +
 +**⚠ Safety:** When measuring current, never put a multimeter in **voltage** mode across a source; use the **current** input and series connection to avoid a short circuit.