A voltage can be direct or indirect.

 DC voltage This is a voltage that does not change with time. DC voltage sources are e.g. batteries, accumulators, etc. AC voltage This is a voltage that changes with time. An example of a source is a household outlet for electrical appliances.

Several forms of alternating voltage are used. In computing, it has the shape of rectangular pulses, in video technology, it has a sawtooth shape, and in energy networks, it has a sinusoidal shape. Various forms of AC voltages for circuit testing can be generated using a function generator. We observe them with the help of an oscilloscope. The oscilloscope shows us a graph of voltage (y-axis) against time (x-axis) - see the image below.

In the following, we will limit ourselves to a sinusoidal voltage. In this case, the voltage varies according to a sine curve. It is determined by the maximum value or amplitude and frequency.

## Obtaining sinusoidal alternating voltage

Obtaining sinusoidal alternating voltage for energy purposes is most often done with the help of alternating voltage generators. These convert mechanical energy into electrical energy.

Let's imagine that a coil with windings rotates in a homogeneous field, as shown in the figure.

The magnetic flux through the loop is given as: We note that as the coil rotates, the change in angle with time is given as:  Due to the change in the magnetic flux, according to Faraday's law of induction, a voltage is induced in the coil which is given as: We insert equation 1 and note that only the cosine of the angle changes with time: Let's differentiate with respect to : The equation for sinusoidal alternating voltage is given as: where is the maximum value or amplitude and is given as: ## Average power and effective voltage

If we connect an AC voltage to a load resistor of resistance , it has an electrical power which is given as: We note from equation 2 above that:  We note that: (Maximum power) The electrical power therefore changes with time between zero and maximum power, as shown in the figure below:

The average power , with the help of which we also calculate the electrical work, is obtained by equating the area under the AC power graph (gray hatched) to the area under the average power graph (green lines). We get: We express the powers in terms of voltage and resistance: We multiply both sides of the equation by and take the square roots: The root-mean-square (rms) or effective voltage is the direct voltage that would give the consumer the same power as the alternating voltage with a maximum value of and for a sinusoidal alternating voltage, it is given as: If it is written in the data that the mains voltage is 230 V, this means its effective (and not maximum) value.

With the help of effective voltage, we can directly (without conversion) calculate electrical power and work.

The effective voltage is often written without an index, that is, only . The same applies to the average power, it is written only with .

The mains voltage in the household is e.g. 230 V (this is the rms/effective value) and a frequency of 50 Hz.