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We are most often concerned with average power rather than its fluctuations—that 60-W light bulb in your desk lamp has an average power consumption of 60 W, for example. As illustrated in [link] , the average power P ave size 12{P rSub { size 8{"ave"} } } {} is

P ave = 1 2 I 0 V 0 . size 12{P rSub { size 8{"ave"} } = { {1} over {2} } I rSub { size 8{0} } V rSub { size 8{0} } } {}

This is evident from the graph, since the areas above and below the ( 1 / 2 ) I 0 V 0 size 12{ \( 1/2 \) I rSub { size 8{0} } V rSub { size 8{0} } } {} line are equal, but it can also be proven using trigonometric identities. Similarly, we define an average or rms current     I rms size 12{I rSub { size 8{"rms"} } } {} and average or rms voltage     V rms size 12{V rSub { size 8{"rms"} } } {} to be, respectively,

I rms = I 0 2 size 12{I rSub { size 8{"rms "} } = { {I rSub { size 8{0} } } over { sqrt {2} } } } {}

and

V rms = V 0 2 . size 12{V rSub { size 8{"rms "} } = { {V rSub { size 8{0} } } over { sqrt {2} } } } {}

where rms stands for root mean square, a particular kind of average. In general, to obtain a root mean square, the particular quantity is squared, its mean (or average) is found, and the square root is taken. This is useful for AC, since the average value is zero. Now,

P ave = I rms V rms , size 12{P rSub { size 8{"ave"} } = I rSub { size 8{"rms"} } V rSub { size 8{"rms"} } } {}

which gives

P ave = I 0 2 V 0 2 = 1 2 I 0 V 0 , size 12{P rSub { size 8{"ave"} } = { {I rSub { size 8{0} } } over { sqrt {2} } } cdot { {V rSub { size 8{0} } } over { sqrt {2} } } = { {1} over {2} } I rSub { size 8{0} } V rSub { size 8{0} } } {}

as stated above. It is standard practice to quote I rms size 12{I rSub { size 8{"rms"} } } {} , V rms size 12{V rSub { size 8{"rms"} } } {} , and P ave size 12{P rSub { size 8{"ave"} } } {} rather than the peak values. For example, most household electricity is 120 V AC, which means that V rms size 12{V rSub { size 8{"rms"} } } {} is 120 V. The common 10-A circuit breaker will interrupt a sustained I rms size 12{I rSub { size 8{"rms"} } } {} greater than 10 A. Your 1.0-kW microwave oven consumes P ave = 1.0 kW size 12{P rSub { size 8{"ave"} } =1 "." 0`"kW"} {} , and so on. You can think of these rms and average values as the equivalent DC values for a simple resistive circuit.

To summarize, when dealing with AC, Ohm’s law and the equations for power are completely analogous to those for DC, but rms and average values are used for AC. Thus, for AC, Ohm’s law is written

I rms = V rms R . size 12{I rSub { size 8{"rms"} } = { {V rSub { size 8{"rms"} } } over {R} } } {}

The various expressions for AC power P ave size 12{P rSub { size 8{"ave"} } } {} are

P ave = I rms V rms , size 12{P rSub { size 8{"ave"} } = I rSub { size 8{"rms"} } V rSub { size 8{"rms"} } } {}
P ave = V rms 2 R , size 12{P rSub { size 8{"ave"} } = { {V rSub { size 8{"rms"} } rSup { size 8{2} } } over {R} } } {}

and

P ave = I rms 2 R . size 12{P rSub { size 8{"ave"} } = I rSub { size 8{"rms"} } rSup { size 8{2} } R} {}

Peak voltage and power for ac

(a) What is the value of the peak voltage for 120-V AC power? (b) What is the peak power consumption rate of a 60.0-W AC light bulb?

Strategy

We are told that V rms size 12{V rSub { size 8{"rms"} } } {} is 120 V and P ave size 12{P rSub { size 8{"ave"} } } {} is 60.0 W. We can use V rms = V 0 2 size 12{V rSub { size 8{"rms "} } = { {V rSub { size 8{0} } } over { sqrt {2} } } } {} to find the peak voltage, and we can manipulate the definition of power to find the peak power from the given average power.

Solution for (a)

Solving the equation V rms = V 0 2 size 12{V rSub { size 8{"rms "} } = { {V rSub { size 8{0} } } over { sqrt {2} } } } {} for the peak voltage V 0 size 12{V rSub { size 8{0} } } {} and substituting the known value for V rms size 12{V rSub { size 8{"rms"} } } {} gives

V 0 = 2 V rms = 1 . 414 ( 120 V ) = 170 V . size 12{V rSub { size 8{0} } = sqrt {2} V rSub { size 8{"rms"} } =" 1" "." "414" \( "120"" V" \) =" 170 V"} {}

Discussion for (a)

This means that the AC voltage swings from 170 V to –170 V and back 60 times every second. An equivalent DC voltage is a constant 120 V.

Solution for (b)

Peak power is peak current times peak voltage. Thus,

P 0 = I 0 V 0 = 2 1 2 I 0 V 0 = 2 P ave . size 12{P rSub { size 8{0} } = I rSub { size 8{0} } V rSub { size 8{0} } =" 2" left ( { {1} over {2} } I rSub { size 8{0} } V rSub { size 8{0} } right ) =" 2"P rSub { size 8{"ave"} } } {}

We know the average power is 60.0 W, and so

P 0 = 2 ( 60 . 0 W ) = 120 W . size 12{P rSub { size 8{0} } =" 2" \( "60" "." "0 W" \) =" 120 W"} {}

Discussion

So the power swings from zero to 120 W one hundred twenty times per second (twice each cycle), and the power averages 60 W.

Why use ac for power distribution?

Most large power-distribution systems are AC. Moreover, the power is transmitted at much higher voltages than the 120-V AC (240 V in most parts of the world) we use in homes and on the job. Economies of scale make it cheaper to build a few very large electric power-generation plants than to build numerous small ones. This necessitates sending power long distances, and it is obviously important that energy losses en route be minimized. High voltages can be transmitted with much smaller power losses than low voltages, as we shall see. (See [link] .) For safety reasons, the voltage at the user is reduced to familiar values. The crucial factor is that it is much easier to increase and decrease AC voltages than DC, so AC is used in most large power distribution systems.

Questions & Answers

are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, College physics ii. OpenStax CNX. Nov 29, 2012 Download for free at http://legacy.cnx.org/content/col11458/1.2
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