Electrical Engineering BMT & UFC › Physical Fundamentals

Energy

The state of a body is described, among other things, by its mass, its density, its position in space and its energy. The energy of a body describes the part of its state that can easily be changed and is therefore technically interesting, because the different forms of energy can be converted into each other. If, for example, a machine is to move something, it must convert some form of energy into kinetic energy. Energy is not created or destroyed; it is only ever converted from one form into another.

Whenever we want to achieve something with electric current, electrical energy is converted into another form. When you drive an electric car, for example, electrical energy is drawn from the battery and converted into kinetic energy in the motor.

Assume that the battery of the electric car is fully charged at the start of the journey. Now you sit behind the wheel and accelerate. The car accelerates and reaches a speed of, for example, v = 10 m/s. Your car has a mass of m = 2000 kg. It has a kinetic energy of

\[ \begin{gathered} W = \frac{1}{2} m v^2 = \frac{1}{2} \cdot 2000\,\mathrm{kg} \cdot \left(10\,\frac{\mathrm{m}}{\mathrm{s}}\right)^2 = 100\,\mathrm{kJ} \\[4pt] W\text{: symbol for energy} \\[4pt] [W] = \mathrm{J}\text{, "joule": unit of energy} \end{gathered} \]

This energy must have come from somewhere. It was stored in the battery. After you have reached this speed, the battery is therefore somewhat less charged. Usually, one form of energy decreases and another increases. The electrical energy in the battery decreases when the kinetic energy increases.

To illuminate, move, heat, cool, display or deform something technically, an input energy is always converted into another form of energy. In electrical engineering, one of the forms of energy involved is always electrical energy.

Examples

Motor: conversion of electrical energy into kinetic energy
Hotplate: conversion of electrical energy into heat (thermal energy)
Generator: conversion of kinetic energy into electrical energy
Torch: conversion of electrical energy into light

A change in energy is "transported" by power. A change in energy always occurs in the form of power.

Let us look at an analogy: you can imagine two forms of energy as two piles of sand. The amount of sand on the two piles indicates how much energy is present in each form. If you move sand from pile to pile with a shovel, the amount of sand per unit of time corresponds to the power. If you work fast and move a lot of sand per unit of time, the power is high. The energy changes quickly.

Power has the symbol P and the unit W ("watt"). Mathematically, we express this as follows:

\[ \begin{gathered} P(t) = \frac{dW(t)}{dt} \\[6pt] P(t) = \text{constant over time: } P(t) = \frac{W(t)}{t} \end{gathered} \]

The change in energy over time corresponds to the time derivative of the energy dW / dt. If you shovel sand with constant power, we can simplify the term to W / t. According to the formula, the power P thus also corresponds to the amount of sand (energy) that you shovel around within a time interval (t).

If you accelerate hard in the electric car, a lot of electrical energy per unit of time is converted from the battery into kinetic energy. Intuitively, the car becomes faster in a short time. Then the power is high. For cars, the maximum power is often used as a selling point. With a powerful car, you can quickly (in little time) convert a lot of electrical energy into kinetic energy.

If you press the accelerator gently, the car accelerates more slowly, so less power is available to convert electrical energy into kinetic energy. Here again is the summary of energy and power:

Physical quantity	Symbol	Unit name	Unit symbol
Energy	\(W\)	joule	\(1\,\mathrm{J} = 1\,\mathrm{W} \cdot \mathrm{s}\)
Power	\(P\)	watt	\(1\,\mathrm{W}\)

Note that the symbol for energy, "W as in WORK", uses the same letter as the unit of power, "W as in watt". This is somewhat unfortunate, but you will get used to it over time.

In order to use electrical energy technically, we have to understand it and be able to calculate it. Electrical energy is calculated from electric charge. That is why we look at electric charge in the next chapter. It is the elementary quantity of electrical engineering.