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Block 02 — Electric charge and current

Learning objectives

  • 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.
  • Identify and sketch the symbols of the ideal current and voltage source.

90-minute plan

  1. Warm-up (5–10 min): Recall of SI units from Block 01; estimate “How many electrons per second flow at $1~\rm A$?”
  2. Core concepts & derivations (60–70 min):
    1. Electric charge: definition, elementary charge, Coulomb’s law (overview only).
    2. Charge carriers in metals vs. electrolytes.
    3. Electric current: definition, instantaneous and average values, unit check.
    4. Typical magnitudes; conventional vs. electron flow.
    5. Ideal current source, symbol, and U–I diagram.
  3. Practice (10–20 min): Quick calculations and sim-based exercises.
  4. Wrap-up (5 min): Summary and pitfalls.

Conceptual overview

  1. Charge $Q$ is the fundamental “substance” of electricity, always in multiples of the elementary charge.
  2. Like charges repel, unlike charges attract; forces are described by Coulomb’s law (detail in Block 09).
  3. Current $I$ quantifies *how fast* charge moves: $1~\rm A$ = $1~C/s$.
  4. Convention: we follow conventional current direction (positive charge motion, from $+$ to $-$), even though in metals electrons move oppositely.
  5. Ideal current sources deliver a fixed current regardless of load voltage — a useful abstraction for circuit analysis.
  6. This block connects Block 01 (units) to Block 03 (voltage and resistance), and prepares for Kirchhoff’s laws in Block 04.

Core content

Electric charge

Abb. ##: Atomic model according to Bohr / Sommerfeld electrical_engineering_and_electronics_1:atommodell.svg

  • 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 Abbildung ##
  • 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*}

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*}

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*}

* In metals: flow of electrons. * In electrolytes: movement of ions. * In semiconductors: electrons and holes.

Convention

In this course, we generally use the conventional current direction: positive from $+$ to $-$. The electron flow is opposite.

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

Ideal current source

From circuit theory, we abstract the ideal current source:

  • Delivers a fixed current $I_s$, independent of load voltage.
  • Symbol: circle with arrow.
  • U–I characteristic: vertical line at $I = I_s$.

Abb. ##: ideal current source electrical_engineering_and_electronics_1:idealestromquelle.svg

Common pitfalls

  • Mixing electron flow vs. conventional current.
  • Misinterpreting current as “speed” rather than rate of charge flow.

Exercises

Exercise E7 Charges on a Ballon

A balloon has a charge of $Q=7~{\rm nC}$ on its surface.
How many additional electrons are on the balloon?

Solution

\begin{align*} Q &= 7~{\rm nC} = 7\cdot 10^{-9}~{\rm C} \\ n_{\rm e} &= {{7*10^{-9}~{\rm C}}\over{1.6022*10^{-19}~{\rm C/electron}}} = 43.7*10^{9}~{\rm electrons} \end{align*}

Result

\begin{align*} 43.7*10^{9}~{\rm electrons} \end{align*}

Exercise E8 Charges in Electroplating

To get a different metal coating onto a surface, often Electroplating is used. In this process, the surface is located in a liquid, which contains metal ions of the coating.
In the following, a copper coating (e.g. for corrosion resistance) shall be looked on. The charge of one copper ion is around $1.6022 \cdot 10^{-19}~{\rm C}$, what is the charge on the surface if there are $8 \cdot 10^{22}~{\rm ions}$ added?

Solution

\begin{align*} 8 * 10^{22} \cdot 1.6022 *10^{-19}~{\rm C} = 12'817.6~{\rm C} \end{align*}

Result

\begin{align*} 12'818~{\rm C} \end{align*}

Task 2.1: Counting charges in a current

A flashlight bulb is supplied with $I=0.25~\rm A$. How many electrons pass through the filament in one second?

Strategy

Use $n=\frac{I \cdot t}{e}$ with $t=1~\rm s$.

Solution

\begin{align*} n = \frac{0.25~\rm C}{1.602 \cdot 10^{-19}~\rm C} \approx 1.6 \cdot 10^{18} \end{align*}

Embedded resources



Charge in Matter

What is Electric Charge and How Electricity Works