Explanation of Direct Current DC and Alternating Current AC Voltages !
DC and AC voltages:
Definition Systematic research in the field of electricity began in the 19th century with experiments purely on DC (direct current) voltages. Separation of charge caused by friction between two materials was one source of DC voltage. Early machines generating (very low levels of) electric power such as electrostatic machines, inductance machines and belt generators as well as the batteries developed during this period produced DC voltages as well, i.e. they gave rise to direct current when resistive loads were connected. Today, DC voltages are mainly used to supply electronic circuits, e.g. in radios, pocket calculators and PCs. DC voltage and current are defined as follows:
A DC voltage is a voltage of constant magnitude and direction. For loads of constant resistance, this type of voltage gives rise to direct current (DC).
The following animation provides an example of a direct current characteristic.
Large amounts of electrical energy are commonly produced by converting mechanical (kinetic) energy into electrical energy by means of electromagnetic induction using generators. The same principle is employed on a smaller scale in bicycle dynamos, for instance. In this case, the generator's rotation produces an AC voltage, the magnitude and direction of which change over time. Applying this voltage to a load like a bicycle lamp causes an alternating current to flow through the lamp. AC voltage and current are defined in general as follows:
An electrical potential, the magnitude and direction of which change over time, is termed an AC voltage. The current produced by such a voltage in a load is termed alternating current (AC).
The animations below show two examples of alternating current. Whereas the current in the upper example has a somewhat irregular characteristic, the lower current has a periodic, rectangular characteristic. In this case, the current's amplitude remains constant but its direction (or sign) changes periodically. During this course, any current which changes over time (AC), will be represented in lower case, as opposed to DC which will be indicated using a capital I.
Sinusoidal alternating quantities: Whereas in communications engineering and information technology, various shapes of alternating voltage (such as the square wave considered earlier) can prove useful, electrical energy technology is dominated by sinusoidal alternating voltage and current, usually produced by generators and used for transmitting energy via hightension transmission lines. Such voltages and currents follow a sinewave curve as shown in the animation below.
Rootmeansquare value of voltage and current:
Applying a sinusoidal voltage u(t) to a resistive load R causes the following current to flow through the load according to Ohm's law:
Because the voltage and current are timedependent variables, so is the power produced in the resistor. It is defined by the following equation:
The diagrams below show the time characteristics of an AC voltage and current (upper diagram) along with the power (lower diagram).
The area enclosed between the power curve and time axis is a measure of the electrical energy converted by the resistor into heat. If a horizontal line is drawn parallel to the time axis at a height of p0/2, the areas above and below this line respectively (shaded in matching colours below) are equal in size. An average power p0/2 ascertained in this manner over several periods of oscillation would perform the same amount of work as the continuously changing instantaneous power p(t) does. This is illustrated by the diagram below.
The following animation demonstrates this relationship.
A DC voltage U that would be needed to develop the same power as the AC voltage in the resistor is determined as follows:
Resolving this equation in terms of the DC voltage U gives
This voltage U is termed the root mean square value of the alternating signal. Because it is a timeindependent variable, it is designated in uppercase just like a direct voltage. Root mean square values of alternating current are specified in the same manner. In other words:
The rms values U and I of AC voltage and current in a resistor R develop the same power P as a DC current I and voltage U of equal magnitude.
The relationship between the rms and peak values of current and voltage in the case of the sinusoidal variables considered here is given by the following equations:
Accordingly, the rms value of a voltage or current is about 70% of the peak value.
Example: a mains voltage with an rms value U = 220 V has a peak value
Naturally, the rms values of nonsinusoidal periodic signals like triangular and rectangular forms can also be defined. In such cases, however, the mathematical relationship (i.e. conversion ratio) between the rms and peak (amplitude) values varies in accordance with the signal shape under consideration.
Characteristic parameters of sinusoidal signals:
The instantaneous value u(t) of a sinusoidal alternating voltage is given by the equation
The diagram below shows the shape of such a signal.
u_{0} is termed the voltage's peak value; it represents the largest positive or negative voltage and is also called signal amplitude. The variable w is the angular frequency determined from the frequency of oscillation f using the equation
The product of the angular frequency and time w·t gives the instantaneous value of the phase angle.
The time T taken to complete one oscillation is termed the period of oscillation. Its inverse is equal to the frequency f, i.e. the number of oscillations per second:
The unit of frequency is named Hertz (abbreviated to Hz ) after the German physicist. 1 Hz corresponds to one oscillation per second. The period in the example above is T = 0.02 s, i.e. the frequency is f = 1/T = 50 Hz. This is the figure for the mains frequency usually used in Europe. The mains frequency in the US and most other countries in the Americas is 60 Hz.
If, unlike the example above, the alternating voltage does not start at the coordinate origins but is instead displaced along the time axis, this displacement can be represented by adding a phase angle j to the argument of the sine function. The instantaneous voltage value is then determined by the equation
All these equations apply in the same way to sinusoidal alternating current.
The following interactive animation can be used to visualise sinusoidal signals of different amplitudes, frequencies and phase angles. Use the slider controls to vary these characteristic parameters and observe the resulting display
Sample applications and advantages of alternating quantities: 
Alternating current and threephase current (a special form of alternating current) nowadays dominate most areas of electrical engineering, including energy technology, communications engineering and information technology. This is due, in particular, to the following advantages:
