Basics of Electromagnetism

1

Electric Current: The Most Basic Explanation From a Physics Point of View

In this lesson you will learn the basics of the electric current, i.e. the definition, its physical meaning and unit.

Related formulas

Voltage: How it is created by charge separation!

Here you will learn what voltage is, how it is generated by charge separation, how a voltage source can be created, and what voltage has to do with current.

Related formulas

Electrical Energy (Work, Voltage, Charge)

$$ W ~=~ q \, U $$

3

Ohm's law: Formula, Graph and 3 Easy Examples

Here you learn Ohm's law, how it is expressed as a formula and as a graph. We also look at three examples.

Questions & Answers

What is the Difference Between an Ohmic and Non-Ohmic Conductor?

Related formulas

Ohm's Law (Resistance, Voltage, Current)

$$ U ~=~ R \, I $$

4

Simple (Series and Parallel) Circuits. The Basics.

Here you will learn how an electrical circuit works and how to apply Ohm's Law to it. You will also learn about parallel and series circuits and their difference.

Questions & Answers

What is the Difference between a Series and Parallel Connection of Resistors? What is the Difference Between an Ideal and Practical Voltage Source?

Related formulas

Series circuit (total resistance, equivalent resistance)

$$ R ~=~ R_1 ~+~ R_2 ~+~ R_3 ~+~ ... $$

Series Circuit of Resistors (Total Current)

$$ \class{red}{I} ~=~ \class{red}{I_1} ~=~ \class{red}{I_2} ~=~ \class{red}{I_3} ~=~ ... ~=~ \class{red}{I_n} $$

Series Circuit of Resistors (Voltage)

$$ U ~=~ U_1 ~+~ U_2 ~+~ U_3 ~+~ ... ~+~ U_n $$

Parallel connection (total resistance, equivalent resistance)

$$ \frac{1}{R} ~=~ \frac{1}{R_1} ~+~ \frac{1}{R_2} ~+~ \frac{1}{R_3} ~+~ ... $$

Parallel Circuit of Resistors (Total Current)

$$ \class{red}{I} ~=~ \class{red}{I_1} ~+~ \class{red}{I_2} ~+~ \class{red}{I_3} ~+~ ... ~+~ \class{red}{I_n} $$

Parallel Circuit of Resistors (Total Voltage)

$$ U ~=~ U_1 ~=~ U_2 ~=~ U_3 ~=~ ... $$

Voltage Divider (Output and Input Voltage, Resistors)

$$ U_{\text{out}} = \frac{R_2}{R_1 + R_2} \, U_{\text{in}} $$

Practical Voltage Source (Ideal Voltage, Internal Resistance)

$$ U = \frac{\class{blue}{U_0}}{1 + \frac{R_{\text i}}{R}} $$

5

Ideal and Real Voltage Source

Difference between an ideal and real voltmeter and what effect they have on voltage measurement.

6

Ideal and real Current Source

What is an ideal and what is a real ammeter? What is the difference between them and what influence they have on current measurement.

7

Electric Power

Simple derivation of the electric power P, which we express with voltage U and current I and then rewrite using the URI formula.

Related formulas

Electric power (voltage, current)

$$ P ~=~ U \, I $$

Electric Power (Current, Resistance)

$$ P ~=~ R \, I^2 $$

Electric Power (Voltage, Resistance)

$$ P ~=~ \frac{U^2}{R} $$

Ohm's Law (Resistance, Voltage, Current)

$$ U ~=~ R \, I $$

Electrical Energy (Voltage, Current, Time)

$$ W ~=~ U \, I \, t $$

8

What is the Vacuum Permittivity?

What does the electric constant (permittivity of the vacuum) describe and how can I determine it experimentally?

9

What is the Elementary Charge?

What is the elementary charge e of the electron and proton, what unit does it have and how can I determine it experimentally?

10

Plate Capacitor: Voltage, Capacitance and Eletric Force

Here the plate capacitor is simply explained. With the help of the capacitor you will learn about the electric voltage, electric field and electric capacitance and how to calculate them for a plate capacitor.

Exercises with solutions

Create a Plate Capacitor with a Certain Capacitance Charge in a thundercloud Capacitor with and without dielectric in comparison

Derivations & Experiments

Plate Capacitor: Potential, E-field, Charge and Capacitance

Here, the electrostatic potential, electric field and the capacitance of a plate capacitor are derived using Laplace's equation.

Related formulas

Plate Capacitor (Force, Voltage, Charge, Distance)

$$ F ~=~ \class{red}{q} \, \frac{U}{d} $$

Plate Capacitor (Capacitance)

$$ C ~=~ \varepsilon_0 \, \varepsilon_{\text r} \, \frac{A}{d} $$

Plate Capacitor (Energy, Electric Field)

$$ W_{\text{e}} ~=~ \frac{1}{2} \, \varepsilon_0 \, \varepsilon_{\text r} \, V \, \class{purple}{E}^2 $$

Plate Capacitor (Electric Field, Voltage, Distance)

$$ \class{purple}{E} ~=~ \frac{U}{d} $$

Capacitor (Energy, Capacitance, Charge)

$$ W_{\text{e}} ~=~ \frac{1}{2} \, \frac{Q^2}{C} $$

Capacitor (Energy, Voltage, Capacitance)

$$ W_{\text e} ~=~ \frac{1}{2} \, C \, U^2 $$

Plate capacitor (potential, voltage, distance)

$$ \varphi_x = - \frac{U}{d} \, x ~+~ \varphi_1 $$

Plate Capacitor (Attraction Force, Voltage)

$$ F ~=~ \frac{\varepsilon_0 \, \varepsilon_{\text r} \, A}{2d^2}\, U^2 $$

Plate Capacitor (Attraction Force, Charge)

$$ F ~=~ \frac{Q^2}{2\varepsilon_0 \, \varepsilon_{\text r} A} $$

11

What are Equipotential Lines?

What are equipotential lines and equipotential surfaces and what happens to a charge that moves on an equipotential.

12

RC Circuit: Charging and Discharging a Capacitor

Here you will learn about the RC circuit. This is a resistor and capacitor connected in series. The capacitor can be charged and discharged via the resistor.

Exercises with solutions

Charge, Capacitance and Half-Life of a Capacitor When Discharging From 50V to 15V.

Related formulas

Charging Capacitor (Current, Capacitance, Resistance, Time)

$$ I(t) ~=~ I_0 \, \mathrm{e}^{-\frac{t}{R\,C}} $$

Charging Capacitor (Voltage, Capacitance, Resistance, Time)

$$ U_{\text C}(t) ~=~ U_0 \, \left(1 - \mathrm{e}^{-\frac{t}{\class{brown}{R}\,C}}\right) $$

Charging a Capacitor (Voltage at the Resistor)

$$ U_{\text R}(t) ~=~ U_0 \, \mathrm{e}^{-\frac{t}{R\,C}} $$

Discharging Capacitor (Voltage, Capacitance, Resistance, Time)

$$ U_{\text C}(t) ~=~ U_0 \, \mathrm{e}^{-\frac{t}{R\,C} } $$

Discharging Capacitor (Discharge Current, Capacitance, Resistance, Time)

$$ I(t) ~=~ -I_0 \, \mathrm{e}^{-\frac{t}{R\,C}} $$

RC Circuit (Half-Life)

$$ t_{\text h} ~=~ R\,C \, \ln(2) $$

RC Circuit (Time Constant)

$$ \tau ~=~ R \, C $$

13

Capacitive reactance of a capacitor

Learn what capacitive reactance is and how to determine it for a capacitor in an AC circuit. We also make a simple example!

Related formulas

Capacitive Reactance (Capacitance, Frequency)

$$ \class{purple}{X_{\text C}} ~=~ -\frac{1}{2\pi \, f \, \class{purple}{C}} $$

14

Inductive Reactance of a Coil

Learn what inductive reactance is and how to determine it for a coil in an AC circuit.

Related formulas

Inductive Reactance (Inductance, Frequency)

$$ \class{brown}{X_{\text L}} ~=~ 2 \pi \, f \, \class{brown}{L} $$

15

What is the Vacuum Permeability?

What does the magnetic constant (magnetic permeability of the vacuum) describe and how can I determine it experimentally?

16

Left / Right-Hand Rule: How to Determine Lorentz Force Direction

You learn how to use the hand rule to determine the direction of the Lorentz force and whether you have to use your right or left hand.

17

Lorentz Force: How to Determine its Direction and Understand Formula

Learn how Lorentz force (magnetic force) deflects a moving charge (electron) in the magnetic field and how you can determine the direction of the deflection.

Exercises with solutions

An Ion Orbiting Around The Equator in The Magnetic Field

Derivations & Experiments