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Different insights can be gained from the three different expressions for electric power. For example, P = V 2 / R size 12{P = V rSup { size 8{2} } /R} {} implies that the lower the resistance connected to a given voltage source, the greater the power delivered. Furthermore, since voltage is squared in P = V 2 / R size 12{P = V rSup { size 8{2} } /R} {} , the effect of applying a higher voltage is perhaps greater than expected. Thus, when the voltage is doubled to a 25-W bulb, its power nearly quadruples to about 100 W, burning it out. If the bulb’s resistance remained constant, its power would be exactly 100 W, but at the higher temperature its resistance is higher, too.

Calculating power dissipation and current: hot and cold power

(a) Consider the examples given in Ohm’s Law: Resistance and Simple Circuits and Resistance and Resistivity . Then find the power dissipated by the car headlight in these examples, both when it is hot and when it is cold. (b) What current does it draw when cold?

Strategy for (a)

For the hot headlight, we know voltage and current, so we can use P = IV size 12{P = ital "IV"} {} to find the power. For the cold headlight, we know the voltage and resistance, so we can use P = V 2 / R size 12{P = V rSup { size 8{2} } /R} {} to find the power.

Solution for (a)

Entering the known values of current and voltage for the hot headlight, we obtain

P = IV = ( 2 . 50 A ) ( 12 . 0 V ) = 30 . 0 W. size 12{P = ital "IV" = \( 2 "." "50 A" \) \( "12" "." "0 V" \) =" 30" "." "0 W."} {}

The cold resistance was 0 . 350 Ω size 12{0 "." "350" %OMEGA } {} , and so the power it uses when first switched on is

P = V 2 R = ( 12 . 0 V ) 2 0 . 350 Ω = 411 W. size 12{P = { {V rSup { size 8{2} } } over {R} } = { { \( "12" "." "0 V" \) rSup { size 8{2} } } over {0 "." "350" %OMEGA } } =" 411 W."} {}

Discussion for (a)

The 30 W dissipated by the hot headlight is typical. But the 411 W when cold is surprisingly higher. The initial power quickly decreases as the bulb’s temperature increases and its resistance increases.

Strategy and Solution for (b)

The current when the bulb is cold can be found several different ways. We rearrange one of the power equations, P = I 2 R size 12{P = I rSup { size 8{2} } R} {} , and enter known values, obtaining

I = P R = 411 W 0 . 350 Ω = 34 . 3 A. size 12{I = sqrt { { {P} over {R} } } = sqrt { { {"411 W"} over {0 "." "350 " %OMEGA } } } =" 34" "." "3 A."} {}

Discussion for (b)

The cold current is remarkably higher than the steady-state value of 2.50 A, but the current will quickly decline to that value as the bulb’s temperature increases. Most fuses and circuit breakers (used to limit the current in a circuit) are designed to tolerate very high currents briefly as a device comes on. In some cases, such as with electric motors, the current remains high for several seconds, necessitating special “slow blow” fuses.

The cost of electricity

The more electric appliances you use and the longer they are left on, the higher your electric bill. This familiar fact is based on the relationship between energy and power. You pay for the energy used. Since P = E / t size 12{P=E/t} {} , we see that

E = Pt size 12{E = ital "Pt"} {}

is the energy used by a device using power P size 12{P} {} for a time interval t size 12{t} {} . For example, the more lightbulbs burning, the greater P size 12{P} {} used; the longer they are on, the greater t size 12{t} {} is. The energy unit on electric bills is the kilowatt-hour ( kW h size 12{"kw" cdot h} {} ), consistent with the relationship E = Pt size 12{E = ital "Pt"} {} . It is easy to estimate the cost of operating electric appliances if you have some idea of their power consumption rate in watts or kilowatts, the time they are on in hours, and the cost per kilowatt-hour for your electric utility. Kilowatt-hours, like all other specialized energy units such as food calories, can be converted to joules. You can prove to yourself that 1 kW h = 3 . 6 × 10 6 J size 12{1"kW" cdot "h = 3" "." 6´"10" rSup { size 8{6} } " J"} {} .

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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How we can toraidal magnetic field
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How we can create polaidal magnetic field
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Mykayuh Reply
Because I'm writing a report and I would like to be really precise for the references
Gre Reply
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!
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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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