Lesson 38 Alternating Current

Alternating current (AC) is an oscillating current. It is created by a voltage that rises and falls.

Direct current (DC) is a steady flow of electricity where, idealy, its voltage is constant and equal to the current, that is also constant, multiplied by effective resistance of the circuit.

Consider a circuit that consists of an alternating voltage source, a capacitor, and an inductor. According to the mathematical rules of Gustav Kircchoff, the rises in voltage at the source is never greater than E(o) which is equivalent to the sum of voltage drops around the circuit.

E(o)sinwt = LdI/dt + q/c

The result is a differential equation that can be written in terms of charge q on the capacitor.

= Ld^2/dt^2 + q/c

E(o)sinwt = m(Ld^2/dt^2) + kx this same equation describes the displacement x of a harmonic oscillator.

Both equations lead to resonance, which, in a circuit can cause the flow of a great amount of charge.

Radio and television signals are transfered through electric resonance.

A capacitor opposes change in positive or negative charge, while an inductor opposes change in current in the same manner the intertial mass on a spring opposes change in velocity.

In an AC, if the frequency is low enough the charging and discharging of the capacitor can keep up with the oscillating applied voltage. At higher frequency, the capacitor cannot charge and discharge fast enough. Therefore, no voltage difference develops across it and nearly all voltage is across the resistor.

If an inductor is in the circuit at low frequency there is time for voltage to build within it and not across. In high frequency the voltage cannot change fast enough so most of the voltage is across the inductor.

When all elements are in the same circuit at low frequency, most voltage charges and discharges the capacitor. At higher frequency, most of the voltage is used changing the current in the inductor. If the frequency is at the resonant frequency, quite a large current flows.

Power = current x voltage

P = IV

Heating = P^2R/V^2

Therefore, the higher the voltage the less power is lst in transit over long distances along electric wires.

If AC passes through a loop of coil, a constantly changing magnetic flux is produced. If a set of coils of wires are wrapped around an iron loop, the flux is completely contained. This flux produces voltage.

Voltage can be increased or decreased safely with this method due to the fact that voltage is proportional to the number of coils of wire around the iron loop.

This is the reason AC won over DC in the modern world.