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Learning objectives

By the end of this section, you will be able to:

  • Explain the differences and similarities between AC and DC current.
  • Calculate rms voltage, current, and average power.
  • Explain why AC current is used for power transmission.

Alternating current

Most of the examples dealt with so far, and particularly those utilizing batteries, have constant voltage sources. Once the current is established, it is thus also a constant. Direct current (DC) is the flow of electric charge in only one direction. It is the steady state of a constant-voltage circuit. Most well-known applications, however, use a time-varying voltage source. Alternating current (AC) is the flow of electric charge that periodically reverses direction. If the source varies periodically, particularly sinusoidally, the circuit is known as an alternating current circuit. Examples include the commercial and residential power that serves so many of our needs. [link] shows graphs of voltage and current versus time for typical DC and AC power. The AC voltages and frequencies commonly used in homes and businesses vary around the world.

Part a shows a graph of voltage V and current I versus time for a D C source. The time is along the x axis and V and I are along the y axis. The graph shows that the voltage V sub D C and the current I sub D C do not vary with time. Part b shows the variation of voltage V and current I with time for an A C source. The time is along the horizontal axis and V and I are along the vertical axis. The graph for I is a progressing sine wave with a peak value I sub zero on the positive y axis and negative I sub zero on the negative y axis. The graph for V is a progressing sine wave with a higher amplitude than the current curve with a peak value V sub zero on the positive y axis and negative V sub zero on the negative y axis. The peak values of the voltage and current sine waves occur at the same time because they are in phase.
(a) DC voltage and current are constant in time, once the current is established. (b) A graph of voltage and current versus time for 60-Hz AC power. The voltage and current are sinusoidal and are in phase for a simple resistance circuit. The frequencies and peak voltages of AC sources differ greatly.
The potential difference variation of an alternating current voltage source with time is shown as a progressing sine wave. The voltage is shown along the vertical axis and the time is along the horizontal axis. Circuit diagrams show that current flowing in one direction corresponds to positive values of the voltage sine wave. Current flowing in the opposite direction in the circuit corresponds to negative values of the voltage sine wave. The maximum value of the voltage sine wave is plus V sub zero. The minimum value of the voltage sine wave is minus V sub zero.
The potential difference V between the terminals of an AC voltage source fluctuates as shown. The mathematical expression for V is given by V = V 0 sin 2 π ft size 12{V = V rSub { size 8{0} } "sin"" 2"π ital "ft"} {} .

[link] shows a schematic of a simple circuit with an AC voltage source. The voltage between the terminals fluctuates as shown, with the AC voltage    given by

V = V 0 sin 2 π ft, size 12{V = V rSub { size 8{0} } "sin"" 2"π ital "ft"} {}

where V size 12{V} {} is the voltage at time t size 12{t} {} , V 0 size 12{V rSub { size 8{0} } } {} is the peak voltage, and f size 12{f} {} is the frequency in hertz. For this simple resistance circuit, I = V/R size 12{I = ital "V/R"} {} , and so the AC current    is

I = I 0 sin 2 π ft, size 12{I = I rSub { size 8{0} } " sin 2"π ital "ft"} {}

where I size 12{I} {} is the current at time t size 12{t} {} , and I 0 = V 0 /R size 12{I rSub { size 8{0} } = V rSub { size 8{0} } ital "/R"} {} is the peak current. For this example, the voltage and current are said to be in phase, as seen in [link] (b).

Current in the resistor alternates back and forth just like the driving voltage, since I = V/R size 12{I = ital "V/R"} {} . If the resistor is a fluorescent light bulb, for example, it brightens and dims 120 times per second as the current repeatedly goes through zero. A 120-Hz flicker is too rapid for your eyes to detect, but if you wave your hand back and forth between your face and a fluorescent light, you will see a stroboscopic effect evidencing AC. The fact that the light output fluctuates means that the power is fluctuating. The power supplied is P = IV size 12{P = ital "IV"} {} . Using the expressions for I size 12{I} {} and V size 12{V} {} above, we see that the time dependence of power is P = I 0 V 0 sin 2 2 π ft size 12{P= I rSub { size 8{0} } V rSub { size 8{0} } "sin" rSup { size 8{2} } " 2"π ital "ft"} {} , as shown in [link] .

Making connections: take-home experiment—ac/dc lights

Wave your hand back and forth between your face and a fluorescent light bulb. Do you observe the same thing with the headlights on your car? Explain what you observe. Warning: Do not look directly at very bright light .

A graph showing the variation of power P with time t. The power is along the vertical axis and time is along the horizontal axis. The curve is a sine wave starting at the origin on the horizontal axis and having the crests and troughs both above the positive horizontal axis. The maximum value of power is given by the peak value, which is the product of I sub zero and V sub zero. The average power is indicated by a dotted line through the center of the wave parallel to the horizontal axis with a value half of the product of I sub zero and V sub zero.
AC power as a function of time. Since the voltage and current are in phase here, their product is non-negative and fluctuates between zero and I 0 V 0 size 12{I rSub { size 8{0} } V rSub { size 8{0} } } {} . Average power is ( 1 / 2 ) I 0 V 0 size 12{ \( 1/2 \) I rSub { size 8{0} } V rSub { size 8{0} } } {} .

Questions & Answers

What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
Ali Reply
displacement in easy way.
Mubashir Reply
binding energy per nucleon
Poonam Reply
why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
why god made humenity
Ali
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
Abrar
when we face electric shock these elements work as a conductor that's why we got this shock
Abrar
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
why electromagnetic induction is not used in room heater ?
Gopi Reply
room?
Abrar
What is position?
Amoah Reply
What is law of gravition
sushil Reply
what is magnetism
Sandeep Reply
Practice Key Terms 6

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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