Energy

Prof. Dr. Thorsten Jungmann (last updated 2026-05-04)

Energy (German: Energie) can be neither created nor destroyed, but only converted from one form into another – colloquially ‘consumed’ (law of energy conservation according to Helmholtz).

In electrical engineering, energy is also referred to as work. This reflects the close connection between mechanical and electrical energy. Both are just as closely linked to thermal energy. In this script, I use the terms energy and work synonymously.

Water analogy: Imagine energy as the water in a reservoir. The water cannot disappear; it only flows from one place to another. In the same way, electrical energy is only converted – into heat, light, motion or other forms of energy.

1 Quantity symbol and unit

The quantity symbol of energy or work is the letter $W$. The unit of energy or work is the watt-second ($\mathrm{Ws}$) or the joule $\mathrm{J}$.

$$[W]=\mathrm{Ws}=\mathrm{J}$$

While the watt-second ($\mathrm{Ws}$) clearly denotes electrical energy, the joule ($\mathrm{J}$) can stand for any form of energy. In theory, the newton metre ($\mathrm{Nm}$), which is typically used in mechanics, also stands for energy.

This relationship reveals the connection between the engineering sciences:

$$[W_{\text{mech}}]=[W_{\text{therm}}]=[W_{\text{el}}]$$ $$1\mathrm{Nm}=1\mathrm{J}=1\mathrm{Ws}$$

The basic formula for electrical energy is:

$$W=P\cdot t$$

where:

• $W$ the energy
• $P$ the power
• $t$ the time

2 Forms of energy

Energy can exist in various forms:

Mechanical energy

Refers to macroscopic changes in motion and position and is the primary initial form for generators.

• Positional/potential energy (German: Lage-/Potenzielle Energie): Energy stored in an object because of its position in a force field.
  • Reservoirs in hydroelectric power stations.
• Motion/kinetic energy (German: Bewegungs-/Kinetische Energie): Energy of a moving object.
  • The rotational energy of wind turbines and water wheels.

Thermal energy

The energy stored in the disordered motion of atoms and molecules.

• Thermal energy (German: Wärmeenergie): In electrical engineering, it is often regarded as power loss or used as an intermediate step in electricity generation.
  • A generator produces heat through friction and electrical resistors.

Nuclear energy

The energy stored in atomic nuclei.

• Nuclear energy: Released during nuclear fission or nuclear fusion.
  • In nuclear power stations, nuclear energy is converted into heat to produce steam and drive turbines.

Electromagnetic energy

These forms are directly related to electric and magnetic fields and are at the heart of electrical engineering.

• Electrical energy: The energy that is stored in electric fields or transferred by the flow of charge carriers.
  • The energy in the capacitor or the current flow in the electric circuit.
• Magnetic energy (German: Magnetische Energie): The energy stored in a magnetic field.
  • The energy in the inductor or the energy in a transformer.
• Radiant energy (German: Strahlungsenergie): Energy transferred in the form of electromagnetic waves.
  • Solar energy that is converted into electrical energy by photovoltaics.

Chemical energy

The energy stored in chemical compounds.

• Chemical energy: Released or stored through chemical reactions.
  • The energy in batteries and rechargeable batteries that is converted into electrical energy.

Example of energy conversion

To illustrate this, consider the following thought experiment, in which, for simplicity, I disregard the losses:

If I fill up my car with 70 litres of diesel (fuel with an energy content of approx. $36MJ/L$ (megajoules per litre), the tank holds the chemical energy of $36MJ/L\cdot 70\mathrm{L}=2520\mathrm{MJ}=2.5\mathrm{GJ}$, which can be converted into kinetic energy by combustion in the engine. With this, the 2-litre turbodiesel with its 103 kW (140 hp) takes me roughly 870 km.

Alternatively, with this amount of energy I could supply a detached house that ‘consumes’ $W=3000kWh/a$ of electrical energy per year with electrical energy for a good 84 days, i.e. just under a quarter of a year:

$$t=\frac{2.5\cdot 10^9\mathrm{J}}{3000kWh/a}=\frac{694\mathrm{kWh}}{3000\mathrm{kWh}}\cdot \mathrm{a}=0.22\mathrm{a}\cdot \frac{365\mathrm{d}}{\mathrm{a}}=\underline{84.5\mathrm{d}}$$

On the units

Here it makes sense to calculate with the kilowatt-hour ($1\mathrm{kWh}=1000\cdot 3600\mathrm{Ws}=3.6\mathrm{MJ}$) as the more common unit of electrical energy. Incidentally, we can also speak of electrical work, which is why the ‘electricity’ meter is actually called an energy meter or work meter.

Alternatively, I could also use the energy for heating and, for example, bring a small garden pool (approx. 3.5 m in diameter, 80 cm high) with 7 500 L of water to the boil. With an industrial 30 kW heater, this would take a good 23 hours and ‘consume’ an amount of energy of $30\mathrm{kW}\cdot 23.14\mathrm{h}=694\mathrm{kWh}=2.5\mathrm{GJ}$.

So energy is energy. In electrical engineering in particular and in the engineering sciences in general, the aim is always to convert energy with as little loss as possible in order to store or use it. In this sense, both the ‘generation’ of energy and the ‘consumption’ of energy are actually conversion processes.

3 Practical and worked examples

3.1 Energy in the capacitor

The energy stored in the electric field of a capacitor is calculated as follows:

$$W_C=\frac{1}{2}\cdot C\cdot U^2$$

where:

• $W_C$ the energy stored in the capacitor
• $C$ the capacitance
• $U$ the voltage

This formula shows: the energy increases with the square of the voltage applied to the capacitor.

3.2 Energy in the inductor

The energy stored in the magnetic field of an inductor is calculated as follows:

$$W_L=\frac{1}{2}\cdot L\cdot I^2$$

where:

• $W_L$ the energy stored in the inductor
• $L$ the inductance
• $I$ the current

3.3 Energy in the resistor

The energy converted into heat in a resistor is calculated as follows:

$$W_R=P\cdot t=U\cdot I\cdot t=I^2\cdot R\cdot t$$

where:

• $W_R$ the energy converted in the resistor
• $P$ the power
• $U$ the voltage
• $I$ the current
• $R$ the resistance
• $t$ the time

3.4 Energy content of a battery

The energy content of a battery or a rechargeable battery is often stated in watt-hours ($\mathrm{Wh}$) or ampere-hours ($\mathrm{Ah}$):

$$W=U_0\cdot Q=U_0\cdot I\cdot t$$

where:

• $U_0$ the rated voltage of the battery
• $Q$ the electric charge in ampere-hours
• $I$ the current
• $t$ the time

4 Typical orders of magnitude

Energy values in electrical engineering span many orders of magnitude:

• Microjoules ($\mu \mathrm{J}=10^{-6}\mathrm{J}$): energy in small capacitors
• Joules ($\mathrm{J}$): A defibrillator discharges a few hundred joules per shock.
• Kilojoules ($\mathrm{kJ}$): energy content of an AA cell
• Kilowatt-hours ($\mathrm{kWh}=3.6\cdot 10^6\mathrm{J}$): household and industrial electricity consumption

Example: A standard AA battery contains about 10 kJ of energy, while a household consumes about 10–20 kWh per day.

5 Example phrasings

• ‘The capacitor stores 2.5 mJ of energy.’
• ‘The device consumes 50 Wh per day.’
• ‘The battery has a capacity of 2 500 mAh at 3.7 V.’
• ‘The energy loss in the resistor is 0.8 J per second.’
• ‘The inductor releases 15 µJ of energy when switched off.’
• ‘The annual electricity consumption (more precisely: the electrical work) is 4 500 kWh.’
• ‘The air-to-water heat pump consumes 144 kWh of electrical energy per day and delivers 432 kWh of thermal energy.’

6 Related quantities

• Power is the energy converted per unit of time:

$$P=\frac{W}{t}$$

• The energy in the electric field (capacitor) depends on the capacitance and the voltage:

$$W_C=\frac{1}{2}\cdot C\cdot U^2=\frac{Q^2}{2C}$$

• The energy in the magnetic field (inductor) depends on the inductance and the current:

$$W_L=\frac{1}{2}\cdot L\cdot I^2$$

• The energy loss in the resistor depends on the resistance, the current and the time:

$$W_R=I^2\cdot R\cdot t=\frac{U^2}{R}\cdot t$$

7 Relevant components

Energy plays a role in all electrical components and devices.
In this script, capacitors, inductors and rechargeable batteries are particularly relevant.