This article covers the nature of the voltage provided by the electrical outlets in your home. The first part of this article will be a brief review of Ohm’s Law. The second part of the article will be about the nature of Alternating Current.
Review of Ohm’s Law
Ohm’s Law states that electrical pressure is equal to the product of the flow of electricity and the resistance to that flow. Electrical pressure is measured in volts. The flow of electricity is known as current and is measured in amperes. Resistance to the flow of electricity is measured in ohms.
Ohm’s Law states that:
volts = amperes * ohms
The Nature of Alternating Current
The voltage output from a battery connected to a switch and a light bulb always flows in the same direction and is relatively constant as long as the battery is strong. The battery voltage is know as a DC voltage. The abbreviation DC stands for Direct Current. The current in a circuit with a battery is always flowing in the same direction.
However, the voltage from your AC outlet is very different. The voltage from your household outlet is typically around 110 volts AC. The letters AC stand for “Alternating Current.” In Alternating Current, the voltage and current are constantly changing. A detailed explanation is provided in the following paragraph.
If you plotted AC voltage vs time of a graph, you would end up with the wave shown in figure one. This waveform is called a sine wave. The vertical axis represents voltage and the horizontal axis represents time. The part of the sine wave that is above the horizontal axis represents a positive voltage. The part of the sine wave that is below the horizontal axis represents a negative voltage. When the voltage switches from positive to negative, the current also switches direction. Note that the part of the wave form below the horizontal axis is the mirror image of the part of the wave form above the horizontal line. If you plotted the amplitude of current vs time on a graph, you would have the sine wave shown in figure two. In figure two, I assumed the peak current to be 1 ampere.
Frequency and Period
Each figure shows one cycle of a sine wave. The frequency of the sine wave is the number of cycles in one second. For example: If one cycle takes 0.1 seconds to complete, then the frequency is:
Frequency = cycles/second = 1/(seconds/cycle)
cycles per second = 1/(0.1 seconds/cycle) = 10 cycles per second
The time required to complete a single cycle is known as the period. In this case, the period is 0.1 seconds.
The period of a waveform = 1/frequency.
period = 1/frequency = 1/(10 cycles per second) = 0.1 seconds
Instantaneous Voltage and Peak Voltage
The reason the wave is called a sine wave is that the waveform is defined by the trigonometric sine function.
The algebraic equation that describes the waveform contains the following variables.
v = The instantaneous voltage at a given moment in time.
V =The peak value that the voltage reaches. In figure one, the peak voltage is 1 volt.
The formula for the instantaneous voltage is
v = V * sin (2*pi*frequency*time)
where the expression (2*pi*frequency*time) is measured in radians.
One radian = 57.3 degrees
and pi is a constant.
pi = 3.14
Instantaneous Current and Peak Current
Lets assume that the circuit contains one resistor and no other components.
Then the formula for instantaneous current is
i = I * sin (2*pi*frequency*time)
i = instantaneous current at a given moment in time.
I = peak current.
In figure two, the peak current is one ampere.
Root Mean Square Voltage
Returning to figure one, the peak voltage is one volt.
The RMS (root mean square) voltage is equal to 0.707 times the peak voltage.
Therefore the RMS voltage for figure one is .707 * 1 volts = .707 volts.
RMS Voltage and Peak Voltage In Your Home
When we state that the AC voltage at your outlet is 110 volts, we are talking about the RMS voltage.
In your home outlet, the RMS voltage is 110 Volts AC.
The peak voltage equals the RMS voltage divided by 0.707
peak voltage = (110 volts RMS)/0.707 = 155.59 volts
The peak voltage in your home outlets is 155.59 volts.
This concludes the introduction of Alternating Current. Future articles will cover capacitors and inductors in AC circuits.
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Introductory Circuit Analysis Third Edition