Tutorials: Electronics fundamentals (ELEFU)

Power and Energy

last updated: 2021-12-20

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Songs of this chapter:
The black eyed peas > The E.N.D. > Boom Boom Pow (full version).
The black eyed peas > The E.N.D. > Rock That Body.

On the album "The E.N.D." (Energy Never Dies) from the "The black eyed peas" we get interesting lyrics. In the full version of the song "Boom Boom Pow":

The Energy Never Dies
Energy cannot be destroyed
Or created
It always is
And it always will be

Such lyrics make the heart of a physics teacher pounding ;).

In another song ("Rock That Body") on the same album however we get:
"Electric shock, energy like a billion watts"
Don't remember this!!!! because the unit of the energy is surly not Watt. In more than 50 % of all newspaper articles units of energy and power are not correct. Hopefully we can get it right in this chapter :).

Power (to the people) (wiki)

Songs of this chapter:
John Lennon > Power to the people

As seen in the chapter about Ohm's law we can calculate the a constant electrical power in a DC circuit with the following formula:


By substituting Ohm's law we get two derived formulas:



Here a wheel with all the possible conversions of the formulas:

ohms law pie chart

As the power drawn from a circuit mostly changes over time we must difference between instantaneous power and average power. For the instantaneous power we use:


Power is the rate, per unit time, of doing work or transferring heat.

The symbol for the power is P. The SI unit is the J/s (joule per second) or Watt.

This gives us another formula for constant power:


Mostly power is not constant. We calculate the average power with:


For exact instantaneous power we use the limit from the time interval approaching zero:


Peak power is the maximum value the instantaneous power of a machine can have. If we name the power of a wind power plant or a photovoltaic power plant we speak of the peak power of the machine. Sometimes the peak is added to the unit (e.g. 4KWp).

Quantities of power

wrist watch 0.02 W
human (average power) 100 W
personal computer 500 W
average power of a cyclist during TDF 250 W
peak power of a cyclist during TDF 600 W
average power of a horse 500 W
unit horse power (lift 75 kg 1 m in 1 s) 735.5 W
power of the sun on a shiny day in Europe 1000 W
LAM solar car Râ-le-Sol (1992) 12 kW
Nissan Leaf 2020 (EV) 110 kW (147 hp)
electric locomotive 3 MW
biggest wind power plant 2020 12 MW
all Luxembourgian wind power plants 2020 153 MW
all Luxembourgian pv plants 2020 187 MW
one machine in Vianden (SEO) 100/200 MW
Luxembourgian peak power demand 2019 (CREOS) 0.829 GW
pumped storage hydro power plant Vianden (SEO) 1.3 GW
nuclear power plant Cattenom: 4x1.3GW 5.2 GW
Just do it Power 1

Electrical efficiency (wiki)

With climate change it is important to reduce our energy consumption. The electrical efficiency of all our electronic devices must be increased!

The efficiency of a device is defined as useful power output divided by the total electrical power input.

The symbol for the efficiency is the small Greek letter η. Efficiency is a dimensionless number and is often expressed in percent.


Just do it Power 2
Just do it Power 3

solar cell

Work (wiki)

Songs of this chapter:
The Bangles > Different Light > Manic Monday.

No pain, no gain :).
A force does work if acting on a body, there is a displacement of the point of application in the direction of the force. Work transfers energy from one place to another, or one form to another.

For mechanical work:
If a constant force F acts on an object while the object is displaced a distance s, (force and displacement are parallel to each other) the work done on the object is the product of F and s.

W = Fs

If the force and the displacement are in the same direction, the work is positive. If the force and the displacement are in opposite directions (e.g. braking a car) the work is negative.

The unit Joule is equivalent to the newton-meter and the watt-second.


The symbol for work is W. The SI unit of work is the joule (J) (work expended by a force of one newton through a displacement of one meter) or watt-second (W⋅s).

The newton-meter (N⋅m) is sometimes used for work, but this can be confused with the same unit newton-meter, which is the measurement unit of torque.To avoid confusion joule should be used. Non-SI units of work include the kilowatt-hour and the horsepower-hour.

And as already seen we can calculate the work by multiplying power and time:

W = Fs

If work is done, energy is transferred to an object. Energy and work have the same units!

Energy (wiki)

We can't live without energy, without food, without sun! Because energy in Europe is cheap and obtainable almost immediately and everywhere we often forget it's importance.

Energy is the ability to do work.
Energy is work that is stored.

W = E2-E1

If we lift a book from the floor (initial state, potential energy E1) to a table, the finite state is the potential energy on the table E2. Positive Work was done to the system by lifting the book. The system was energized (energy input). If we push the book from the table the system itself performs work (negative sign, energy output).

The symbol for energy is E. The SI unit is the joule (J) or watt-second (W⋅s)


For technical use it is important to be able to change the form of energy.

Different forms of energy:

We distinguish different forms of energy:

Two special forms are the thermal energy (heat) and the electrical energy:

Quantities of energy

1 eV (electron-volt) 1.6·10-19 J 4.44·10-23 Wh
working person (8 h) 3 MJ 0.833 kWh
burning 1 kg of brown coal 8.5 MJ 2.4 kWh
burning 1 kg of dry wood 14.7 MJ 4.1 kWh
1 kg TNT 15.2 MJ 4.2 kWh
1 kg chocolate spread 22.3 MJ 6.2 kWh
1 kg 1 kg diesel fuel (1.2 l) 42.65 MJ 11.8 kWh
1 kg hydrogen (11.1 m³) 120 MJ 33.3 kWh
annual production PV Luxembourg 2020 576 TJ 160 GWh
annual production wind Luxembourg 2019 1.26 PJ 351 GWh
1 kg uraniumdioxid (3.2%) 2.46 PJ 683 GWh
annual consumption electricity Luxembourg 2020 23,6 PJ 6543 GWh
annual consumption Luxembourg 2018 186.6 PJ 51.8 TWh
annual consumption world 2019 622.8 EJ 173 PWh
annual solar energy on earth 5.6·1024 J 1555 EWh
daily radiation sun 3.3·1031 J 9.17·1024 kWh
annual radiation sun 1.2·1034 J 3.3·1027 kWh
total energy sun 1045 J 2.77·1038 kWh
Just do it Energy 1

Law of conservation of energy (wiki)

In a closed system, the amount of energy is fixed. You can't create any more energy inside the system or destroy any of the energy that's already in there. But you can convert the energy you have from one form to another (and sometimes back again).

It's important to be able to convert energy from one form to another. The law of conservation of energy says, that no energy is lost, which contradicts on first sight our everyday experience. If we use 1 kWh of electrical energy to lighten our house, we will get only about 0.15 kWh of radiant energy. 0.85 kWh thermal energy are losses in our eyes. This is true in summer as we can't use the resulting heat. In winter we will heat our home, and the thermal energy is not lost, as it has not to be produced by our heating installation.

If we speak of energy consumption, there is no consumption but a degradation of energy from a high order energy (e.g. electric energy) to a low order energy (heat at low temperature level).

Energy transformation is done by energy conversion machines. They convert one energy form to another. Often they need more than one step to reach the final form.

energy conversion

Just do it Energy 2
         ↗ mechanical electrical chemical thermal
    chemical battery

The efficiency (η) of energy conversion is the ratio between the useful output of an energy conversion machine and the input. It is the same as for the power because in a ratio the time can be eliminated.

sankey mini



Often the conversion from one form of energy to another will need more than one step. We get a chain of energy conversions.

sankey mini

The total efficiency can be calculated with:


Her are some examples of efficiencies of energy conversion machines. The values are approximately because the efficiency depends heavily on the operating point.

Examples of efficiencies of energy

Conversion process Energy efficiency
Electric heater 100 %
Big electric generator 95–99 %
Big electric motor 90–99 %
Switched-mode power supply 80-96 %
Lithium-ion battery 80–90 %
Solar collector 80 %
Little electric motor 58 %
Fuel cell 60 %
Electrolysis of water 60 %
Gas turbine plus steam turbine (combined cycle) 58 %
Gas turbine 40 %
Diesel engine 40 %
World Electricity generation (net) 33 %
Gasoline engine 30 %
Light-emitting diode (LED) 26 %
Solar cell 25 %
Muscle 20 %
Fluorescent lamp 14 %
Photosynthesis 1-6 %
Incandescent light bulb 1–2 %
Just do it Energy 3

Energy storage with batteries

For IoT devices we often use chemical batteries to get energy.

First we must distinguish between primary batteries which are used once and then discarded and secondary batteries that can be discharged and recharged multiple times.

In primary batteries like alkaline batteries the electrode materials are irreversibly changed during discharge. They can be used only once.

In secondary batteries the original composition of the electrodes can be restored by reverse current. They are also named rechargeable battery or accumulator. Today we often use lithium-ion batteries because of their high specific energy (energy by unit mass).

The capacity of a battery is the amount of electric charge it can deliver at the rated voltage. It is normally expressed in ampere-hour (A·h). The capacity marked on a cell is usually measured during 20 hours at 20 °C on a new battery. The current delivered during this 20 hours must be such that the cell remains above a specified terminal voltage per cell.

The voltage of the battery declines steadily during use, so the total usable capacity depends on the cut-off voltage of device. Devices using per example alkaline cells (1.5 V) can stop functioning at 1.4 V. Other devices still work at 1 V. So the capacity of a battery depends on multiple factors, including battery chemistry, the load (current), the required terminal voltage, the storage period, the age of the battery, ambient temperature e.t.c..

If batteries are not used for a long time they discharge themselves and lose capacity due to irreversible side reactions (internal self-discharge). Also when batteries are recharged, the capacity is reduced a little bit. After enough recharges, in essence all capacity is lost and the battery stops producing power. The number of recharges before a battery is useless is named load cycle or charge cycle.

Discharging the battery at a low rate (current) results in a higher capacity than at a higher current.A battery rated at 3.4 A·h for a 20-hour discharge will not deliver a current of 1.7 A for two hours, but less.

Just do it Energy 4

Equivalent circuit diagram for batteries

We can think of a battery as an ideal voltage source in series with an internal resistance.

battery equivalent circuit

When we measure the voltage of a battery without load (RL = ∞) we get the open circuit voltage U0.

With load a current is flowing in the circuit, generating a loss of voltage on the inner resistance of the battery. There is a drop of the battery voltage proportional to the current.

formula Ubatt

battery equivalent circuit w. load

For a short circuit (RL = 0) the battery voltage is zero (Ubatt = 0·I). The open circuit voltage equates the voltage on the internal resistance U0 = URi. We can calculate the internal resistance with:

formula Ri

or if we get two working points:

formula Ri 2

battery diagram

Just do it Energy 5
Just do it Energy 6
Just do it Energy 7

liio rover