Alternating current

Alternating current (AC) is electric current which in a sine wave pattern changes polarity from negative to positive and back again.

The alternating current generator was invented by Nikola Tesla in 1882. The first long-distance transmissions of alternating current were in 1891 near Telluride, Colorado, followed a few months later in Germany. Thomas Edison advocated the use of direct current, having many patents in that technology, but eventually alternating current came into general use. Charles Proteus Steinmetz of General Electric solved many of the problems associated with generation and transmission of electricity by alternating current. Unlike DC, AC can be stepped up by a transformer to a higher voltage, then sent along a transmission line with little loss of power, then returned to a safer voltage near its point of application.

Three-phase electrical generation is very common and is a more efficient use of conductors. Three-phase power is common only in industrial premises and many industrial electric motors are designed for it.

Mathematics of AC voltages

Alternating currents are usually associated with alternating voltages. An AC voltage v can described mathematically as a function of time by the following equation:

v(t)=A\times \sin(\omega t),

where

A is the amplitude in volts (also called the peak voltage),

ω is the angular frequency in radian/second, and

t is the time in seconds.

Since angular frequency is of more interest to mathematicians than to engineers, this is commonly rewritten as:

v(t)=A\times \sin(2\pi ft),

where

f is the frequency in hertz.

The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak. Since the maximum value of sin(x) is +1 and the minimum value is -1, an AC voltage swings between +A and -A. The peak-to-peak voltage, written as V_P-P, is therefore (+A)-(-A) = 2×A.

The size of an AC voltage is also sometimes stated as a root mean square (rms) value, written V_rms. For a sinusoidal voltage:

V_{rms}={A \over {\sqrt {2}}}.

V_rms is useful in calculating the power consumed by a load. If a DC voltage of V_DC delivers a certain power P into a given load, then an AC voltage of V_rms will deliver the same power P into the same load if V_rms = V_DC.

To illustrate these concepts, consider the 240 V AC mains used in the UK. It is so called because its rms value is (at least nominally) 240 V. This means that it has the same heating effect as 240 V DC. To work out its peak voltage (amplitude), we can modify the above equation to:

A=V_{rms}\times {\sqrt {2}}.

For our 240 V AC, the peak voltage V_P-P or A is therefore 240 V × √2 = 339 V (approx.). The peak-to-peak value of the 240 V AC mains is even higher: 2 × 240 V × √2 = 679 V (approx.)