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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

why static friction is greater than Kinetic friction
Ali Reply
draw magnetic field pattern for two wire carrying current in the same direction
Ven Reply
An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so that she can use some small appliances on her trip.
nkombo Reply
What is the ratio of turns in the primary and secondary coils of her transformer?
nkombo
How electric lines and equipotential surface are mutually perpendicular?
Abid Reply
The potential difference between any two points on the surface is zero that implies È.Ŕ=0, Where R is the distance between two different points &E= Electric field intensity. From which we have cos þ =0, where þ is the angle between the directions of field and distance line, as E andR are zero. Thus
MAHADEV
sorry..E and R are non zero...
MAHADEV
By how much leeway (both percentage and mass) would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?
Elene Reply
what Is linear momentum
Victoria Reply
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where
Fayyaz
Myanmar
Pyae
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Iroko
hello
Abdu
Describe an experiment to determine short half life
Tyson Reply
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Kenedy Reply
it's a natural phenomena
Hassan
sap
Emmanuel
please can someone help me with explanations of wave
Benedine
A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
Musa Reply
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Caya Reply
it is the science which we used in our daily life
Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
it is branch of science which deals with study of happening in the human life
AMIT
A 20MH coil has a resistance of 50 ohms and is connected in series with a capacitor to a 250MV supply if the circuit is to resonate at 100KHZ, Determine 1: the capacitance of the capacitor 2: the working voltage of the circuit, given that pie =3.142
Musa
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Kelly
Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Eden Reply
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
Yeah true ilwith d help of Adiabatic
Kelly
what are the fundamentals qualities
Magret Reply
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Kalilu
what is physic
Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
Moses
Physic... Is a purging medicine, which stimulates evacuation of the bowels.
Moses
are you asking for qualities or quantities?
Noman
give examples of three dimensional frame of reference
Ekwunazor Reply
Universe
Noman
Yes the Universe itself
Astronomy
Examine different types of shoes, including sports shoes and thongs. In terms of physics, why are the bottom surfaces designed as they are? What differences will dry and wet conditions make for these surfaces?
Lathan Reply
sports shoes are designed in such a way they are gripped well with your feet and their bases have and high friction surfaces, Thong shoes are for comfort, these are easily removed and light weight. these are usually low friction surfaces but in wet conditions they offer greater friction.
Noman
thong sleepers are usually used in restrooms.
Noman
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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