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  • Calculate the power dissipated by a resistor and power supplied by a power supply.
  • Calculate the cost of electricity under various circumstances.

Power in electric circuits

Power is associated by many people with electricity. Knowing that power is the rate of energy use or energy conversion, what is the expression for electric power    ? Power transmission lines might come to mind. We also think of lightbulbs in terms of their power ratings in watts. Let us compare a 25-W bulb with a 60-W bulb. (See [link] (a).) Since both operate on the same voltage, the 60-W bulb must draw more current to have a greater power rating. Thus the 60-W bulb’s resistance must be lower than that of a 25-W bulb. If we increase voltage, we also increase power. For example, when a 25-W bulb that is designed to operate on 120 V is connected to 240 V, it briefly glows very brightly and then burns out. Precisely how are voltage, current, and resistance related to electric power?

Part a has two images. The image on the left is a photograph of a twenty five watt incandescent bulb emitting a dim, yellowish white color. The image on the right is a photograph of a sixty watt incandescent bulb emitting a brighter white light. Part b is a single photograph of a compact fluorescent lightbulb glowing in bright pure white color.
(a) Which of these lightbulbs, the 25-W bulb (upper left) or the 60-W bulb (upper right), has the higher resistance? Which draws more current? Which uses the most energy? Can you tell from the color that the 25-W filament is cooler? Is the brighter bulb a different color and if so why? (credits: Dickbauch, Wikimedia Commons; Greg Westfall, Flickr) (b) This compact fluorescent light (CFL) puts out the same intensity of light as the 60-W bulb, but at 1/4 to 1/10 the input power. (credit: dbgg1979, Flickr)

Electric energy depends on both the voltage involved and the charge moved. This is expressed most simply as PE = qV size 12{"PE"= ital "qV"} {} , where q size 12{q} {} is the charge moved and V size 12{V} {} is the voltage (or more precisely, the potential difference the charge moves through). Power is the rate at which energy is moved, and so electric power is

P = PE t = qV t . size 12{P = { { ital "PE"} over {t} } = { { ital "qV"} over {t} } "."} {}

Recognizing that current is I = q / t size 12{I = q/t} {} (note that Δ t = t size 12{Δt=t} {} here), the expression for power becomes

P = IV. size 12{P = ital "IV."} {}

Electric power ( P size 12{P} {} ) is simply the product of current times voltage. Power has familiar units of watts. Since the SI unit for potential energy (PE) is the joule, power has units of joules per second, or watts. Thus, 1 A V = 1 W size 12{"1 A " cdot V=" 1 W"} {} . For example, cars often have one or more auxiliary power outlets with which you can charge a cell phone or other electronic devices. These outlets may be rated at 20 A, so that the circuit can deliver a maximum power P = IV = ( 20 A ) ( 12 V ) = 240 W . In some applications, electric power may be expressed as volt-amperes or even kilovolt-amperes ( 1 kA V = 1 kW size 12{"1 kA " cdot V=" 1 kW"} {} ).

To see the relationship of power to resistance, we combine Ohm’s law with P = IV size 12{P = ital "IV"} {} . Substituting I = V/R size 12{I = ital "V/R"} {} gives P = ( V / R ) V = V 2 / R size 12{P = \( V/R \) V=V rSup { size 8{2} } R} {} . Similarly, substituting V = IR size 12{V= ital "IR"} {} gives P = I ( IR ) = I 2 R size 12{P =I \( ital "IR" \) = I rSup { size 8{2} } R} {} . Three expressions for electric power are listed together here for convenience:

P = IV size 12{P = ital "IV"} {}
P = V 2 R size 12{P = { {V rSup { size 8{2} } } over {R} } } {}
P = I 2 R . size 12{P = I rSup { size 8{2} } R"."} {}

Note that the first equation is always valid, whereas the other two can be used only for resistors. In a simple circuit, with one voltage source and a single resistor, the power supplied by the voltage source and that dissipated by the resistor are identical. (In more complicated circuits, P size 12{P} {} can be the power dissipated by a single device and not the total power in the circuit.)

Questions & Answers

is there a summary for this whole physics book
Fortune Reply
what the difference between laws and principles
Mary Reply
Hello want to study physics but it seems so difficult
Joshua Reply
Yes
Aifuwa
I read it but when I try to solve questions it seems difficult
Aifuwa
Jerry where are you from
Joshua
can i study some problem on motion and projection motion
Weamie
hello pls am new here so i want someone to highlight me on this "application of expansion/contraction
Awoke
want 2 do is just dat u rest for some minute,then u go back to the simple one nd one u understand and then go back to d difficult one,u will now understand it better.
rebecca
yess
rebecca
what of mine
Awoke
yess
rebecca
ok
Awoke
iam new here
Mohamed
u are welcome
Awoke
hello am new. am I welcome
Miracle
yes you are😁
clifford
we can all learn and help each other
Osei
yeah you are right
Neyaz
so we can all share our ideas on a certain topic
Osei
sure
clifford
in beginning all subjects are difficult need to work hard
Mohammed
hi guyz
Lamin
How can I understand physics
Thankgod
Where will I start from
Thankgod
(fundamentals of physics) start there
clifford
OK thanks
Thankgod
Hello, im college now, engineering, 1 years, what book of physics i must use, to be understand easily?
Megryan
try physics for scientist and engineers/ cutnell and Johnson
clifford
Okey po!
Megryan
Is not difficult if u really want to learn
Gabriel
explanations on harmonic motion
Tumwiine Reply
example ofchange of state of the body in the effectof heat
Abiodun Reply
solid ice = liquid water due to radical changes in temperature which are controlled by the capacity of heat an object can withstand.
Shii
what is the upper fix point of the temperature scale
Mohamed
why is the thermal expansion of thermometric liquid in glass increased in volume
Mohamed
what's heat?
sununu
heat is energy, it called heat energy. Energy moves from a hot body to a cool body. Fire transfers energy to a pot of water and the more energy the water has the hotter it becomes.
clifford
Heat is the transfer of energy from one place to another
Gabriel
what is normal force?
Neyaz Reply
the force that pushes upward on us. the force that opposes gravity
clifford
upthrust of air
Abdikadir
Newton's 3rd law. the force of the ground (earth) that pushes back on gravity, keeping us on the ground instead of sinking into it.
clifford
I really need lots of questions on frictional force
Ogboru Reply
Questions or answers?
Shii
I can help answering what I can
Shii
does friction also need some force to perform?
Mohit
no friction is a force just like the gravitational force
clifford
yeah but u can't apply friction anywhere else like other forces
Mohit
I don't understand that question. friction does work alongside other forces based on the situation.
clifford
eg. when walking there are two forces acting on us gravitational and frictional force. friction helps us move forward and gravity keeps us on the ground
clifford
friction is a contact force. Two surfaces are necessary for the force to work.
clifford
hope this helped
clifford
the friction force which oppose while it contact with surrounding. there are two kind of friction. slidding and rolling friction.
Neyaz
Two unequal masses M1 and M2 are connected by a string of tension T on a plane,find the acceleration and tension in the string
Ogboru
derive the equation
Ogboru
Hi
Olamide
What is physics?
Jeuloriz Reply
physics is a branch of science in which we are dealing with the knowledge of our physical things. macroscopic as well as microscopic. we are going look inside the univers with the help of physics. you can learn nature with the help of physics. so many branches of physics you have to learn physics.
vijay
What are quarks?
Breanna Reply
6 type of quarks
Neyaz
what is candela
Akani Reply
Candela is the unit for the measurement of light intensity.
Osei
any one can prove that 1hrpower= 746 watt
Neyaz Reply
Newton second is the unit of ...............?
Neyaz
Impulse and momentum
Fauzia
force×time and mass× velocity
vijay
Good
Neyaz
What is the simple harmonic motion?
Fauzia Reply
oscillatory motion under a retarding force proportional to the amount of displacement from an equilibrium position
Yuri
Straight out of google, you could do that to, I suppose.
Yuri
*too
Yuri
ok
Fauzia
Oscillatory motion under a regarding force proportional to the amount of displacement from an equilibrium position
Neyaz
examples of work done by load of gravity
Maureen Reply
What is ehrenfest theorem?
Fauzia Reply
You can look it up, faster and more reliable answer.
Yuri
That isn't a question to ask on a forum and I also have no idea what that is.
Yuri
what is the work done by gravity on the load 87kj,11.684m,mass xkg[g=19m/s
Maureen
What is law of mass action?
Fauzia Reply
rate of chemical reactions is proportional to concentration of reactants ...
muhammad
ok thanks
Fauzia
what the difference between laws and principles
Mary
Practice Key Terms 1

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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