1 Basic Electrical Quantities#
Electric engineering is based on a small number of fundamental quantities that describe the behavior of electric charges and fields.
In this section, we examine the most important ones: charge, current, voltage, resistance, and conductance.
1.1 Electric Charge#
1.1.1 Atomic Structure#
All matter consists of the smallest building blocks of matter — atoms.
An atom is made up of:
- a heavy nucleus (containing protons and neutrons)
- an electron shell, where electrons orbit the nucleus
In a neutral atom, the number of electrons equals the number of protons.
1.1.2 The Elementary Charge#
Within the atom, we encounter electric charge.
Both protons and electrons are electrically charged, while neutrons are neutral.
Types of charges and their effects:
- Proton (p⁺): positively charged
- Electron (e⁻): negatively charged
- Neutron (n): uncharged
Protons and electrons carry equal but opposite charges.
$$ e = 1.6 \times 10^{-19}\,\text{C} $$This is the smallest natural quantity of electric charge, also known as the elementary charge.
1.1.3 Electric Charge (Quantity of Electricity)#
The total amount of elementary charges in a system is called the electric charge \( Q \).
- Symbol: \( Q \)
- Unit: Coulomb (C) or Ampere-second (As)
Formula:
$$ Q = I \times t $$where
\( Q \) = charge [C],
\( I \) = current [A],
\( t \) = time [s]
1.1.4 The Ion — Charged Atom#
Ions are electrically charged atoms.
They are formed when an atom loses or gains electrons.
Ions are essential for the conduction of electric current in liquids and gases.
1.2 Electric Current#
1.2.1 Conductors#
In some materials—especially metals—certain electrons can move freely between atoms.
These are called free electrons.
Only materials with many free electrons can effectively conduct electricity.
Examples of conducting materials:
Copper, aluminum, iron, steel, silver, gold, carbon, brass.
1.2.2 Insulators#
Materials with very few free electrons are insulators.
Examples of insulating materials:
Plastic, ceramic, oil, air, glass, mica, dry wood.
1.2.3 Semiconductors#
Semiconductors are materials that conduct electricity only under certain conditions (e.g., under heat or light).
At low temperatures, they behave as insulators.
When energy is added (through heat or light), some bound electrons become free, allowing current flow.
Typical semiconductors: Silicon, germanium, selenium.
1.2.4 Electric Current and Current Strength#
The flow of charge carriers (electrons or ions) through a conductor is called electric current.
The current strength indicates how many charges pass through a cross-section of a conductor per second.
Definition:
When \( 6.24 \times 10^{18} \) electrons flow per second through a conductor, the current equals 1 Ampere (A).
Formula:
$$ I = \frac{Q}{t} $$- \( I \): current [A]
- \( Q \): charge [C]
- \( t \): time [s]
Example:
How many electrons flow per second if \( I = 1 A \)?
1.2.5 Electric Circuit#
A simple electrical circuit consists of:
- Voltage source (battery, generator)
- Load or consumer (resistor, lamp)
- Conducting wires
The voltage source drives the electrons through the closed circuit.
A switch allows the current to be turned on or off.
1.2.6 Current Direction#
Two conventions exist:
- Physical direction: from negative (−) to positive (+) pole (electron flow)
- Technical direction: from positive (+) to negative (−) pole
In electrical engineering, the technical current direction is commonly used.
1.2.7 Current Density#
The current density describes how much current flows per unit of cross-sectional area:
$$ J = \frac{I}{A} $$- \( J \): current density [A/mm²]
- \( I \): current [A]
- \( A \): cross-section [mm²]
Higher current density → higher heating effect.
1.2.8 Effects of Electric Current#
Electric current can be observed through its effects:
- Thermal Effect:
Collisions between electrons and atoms generate heat (Joule heating). - Light Effect:
In lamps, heating causes glowing or gas discharge illumination. - Magnetic Effect:
Every current produces a magnetic field — used in motors, relays, speakers, etc. - Chemical Effect:
Current can decompose substances (electrolysis) or deposit metals (electroplating).
Measuring Electric Current#
Electric current is measured using an ammeter, which must be connected in series with the circuit.
Symbol: ⊗A or (A).
Types of Current#
Direct Current (DC):
Current flows in one direction only.
Symbol:⎓orDCAlternating Current (AC):
Current periodically changes direction and magnitude.
Symbol:~orAC
1.3 Electric Voltage#
Electric voltage is the potential difference between two points in a circuit — it acts like the driving force pushing electrons through a conductor.
Symbol: \( U \)
Unit: Volt (V)
Formula Relationship:
1 V = 1 Joule / Coulomb
Common prefixes:
1 kV = 1000 V, 1 mV = 0.001 V, 1 µV = 0.000001 V
Measuring Voltage#
Voltage is measured with a voltmeter, which must be connected in parallel to the component.
Symbol: ⊗V or (V)
Electric Potential#
The electric potential \( \varphi \) describes the energy level of a charge at a given point.
The voltage between two points is the potential difference:
1.4 Electrical Resistance#
The motion of electrons in a conductor is hindered by collisions with atoms — this opposition is called electrical resistance.
Symbol: \( R \)
Unit: Ohm (Ω)
Definition:
$$ 1\,\Omega = \frac{1\,\text{V}}{1\,\text{A}} $$Multiples:
1 kΩ = 10³ Ω, 1 MΩ = 10⁶ Ω, 1 mΩ = 10⁻³ Ω
1.5 Conductance#
Conductance \( G \) indicates how easily current can pass through a material.
It is the reciprocal of resistance:
Unit: Siemens (S)
Examples:
| Resistance (Ω) | Conductance (S) |
|---|---|
| 2.2 kΩ | 0.000454 S |
| 150 Ω | 0.00667 S |
| 50 Ω | 0.02 S |
| 1 kΩ | 0.001 S |
1.6 Ohm’s Law#
The relationship between voltage, current, and resistance was established by Georg Simon Ohm.
$$ U = R \times I \\ I = \frac{U}{R} \\ R = \frac{U}{I} $$Mnemonic (Ohm’s Triangle):
U
-----
I | R
Plotting \( I \) against \( U \) gives a straight line through the origin — the resistance line.
A steeper line corresponds to a smaller resistance.
1.7 Resistance of Conductors#
The resistance of a conductor depends on:
- Material (specific resistivity \( \rho \))
- Length \( l \)
- Cross-section \( A \)
or using conductivity \( \gamma = 1 / \rho \):
$$ R_L = \frac{l}{\gamma \cdot A} $$Units:
\( \rho \) in Ω·mm²/m | \( \gamma \) in m/(Ω·mm²)
| Material | \( \rho\,[\Omega·mm²/m] \) | \( \gamma\,[m/(\Omega·mm²)] \) |
|---|---|---|
| Copper | 0.0178 | 56 |
| Aluminum | 0.028 | 35.7 |
| Silver | 0.016 | 62.5 |
1.8 Temperature Dependence of Resistance#
Resistance changes with temperature according to the temperature coefficient \( \alpha \):
$$ R_2 = R_1 \cdot [1 + \alpha \cdot (\vartheta_2 - \vartheta_1)] $$For copper: \( \alpha \approx 0.004\,\text{K}^{-1} \)
Example:
A copper wire has \( R_{20°C} = 4.8 Ω \).
At 61.75 °C:
💡 Summary:
Electric quantities form the foundation of all circuit analysis.
Understanding how charge, current, voltage, and resistance relate allows us to calculate and predict electrical behavior in any circuit.