# 20.4 Electric power and energy  (Page 4/7)

 Page 4 / 7

## Making connections: take-home experiment—electrical energy use inventory

1) Make a list of the power ratings on a range of appliances in your home or room. Explain why something like a toaster has a higher rating than a digital clock. Estimate the energy consumed by these appliances in an average day (by estimating their time of use). Some appliances might only state the operating current. If the household voltage is 120 V, then use $P=\text{IV}$ . 2) Check out the total wattage used in the rest rooms of your school’s floor or building. (You might need to assume the long fluorescent lights in use are rated at 32 W.) Suppose that the building was closed all weekend and that these lights were left on from 6 p.m. Friday until 8 a.m. Monday. What would this oversight cost? How about for an entire year of weekends?

## Section summary

• Electric power $P$ is the rate (in watts) that energy is supplied by a source or dissipated by a device.
• Three expressions for electrical power are
$P=\text{IV,}$
$P=\frac{{V}^{2}}{R}\text{,}$

and

$P={I}^{2}R\text{.}$
• The energy used by a device with a power $P$ over a time $t$ is $E=\text{Pt}$ .

## Conceptual questions

Why do incandescent lightbulbs grow dim late in their lives, particularly just before their filaments break?

The power dissipated in a resistor is given by $P={V}^{2}/R$ , which means power decreases if resistance increases. Yet this power is also given by $P={I}^{2}R$ , which means power increases if resistance increases. Explain why there is no contradiction here.

## Problem exercises

What is the power of a $1.00×{\text{10}}^{\text{2}}\phantom{\rule{0.25em}{0ex}}\text{MV}$ lightning bolt having a current of ${2.00 × 10}^{\text{4}}\phantom{\rule{0.25em}{0ex}}\text{A}$ ?

$2\text{.}\text{00}×{\text{10}}^{\text{12}}\phantom{\rule{0.25em}{0ex}}\text{W}$

What power is supplied to the starter motor of a large truck that draws 250 A of current from a 24.0-V battery hookup?

A charge of 4.00 C of charge passes through a pocket calculator’s solar cells in 4.00 h. What is the power output, given the calculator’s voltage output is 3.00 V? (See [link] .)

How many watts does a flashlight that has $6.00×{\text{10}}^{\text{2}}\phantom{\rule{0.25em}{0ex}}\text{C}$ pass through it in 0.500 h use if its voltage is 3.00 V?

Find the power dissipated in each of these extension cords: (a) an extension cord having a $0\text{.}\text{0600}\phantom{\rule{0.25em}{0ex}}\text{-}\phantom{\rule{0.25em}{0ex}}\Omega$ resistance and through which 5.00 A is flowing; (b) a cheaper cord utilizing thinner wire and with a resistance of $0\text{.}\text{300}\phantom{\rule{0.25em}{0ex}}\Omega .$

(a) 1.50 W

(b) 7.50 W

Verify that the units of a volt-ampere are watts, as implied by the equation $P=\text{IV}$ .

Show that the units $1\phantom{\rule{0.25em}{0ex}}{\text{V}}^{2}/\Omega =1\text{W}$ , as implied by the equation $P={V}^{2}/R$ .

$\frac{{V}^{2}}{\Omega }=\frac{{V}^{2}}{\text{V/A}}=\text{AV}=\left(\frac{C}{s}\right)\left(\frac{J}{C}\right)=\frac{J}{s}=1\phantom{\rule{0.25em}{0ex}}\text{W}$

Show that the units $1\phantom{\rule{0.25em}{0ex}}{\text{A}}^{2}\cdot \Omega =1\phantom{\rule{0.25em}{0ex}}\text{W}$ , as implied by the equation $P={I}^{2}R$ .

Verify the energy unit equivalence that $1\phantom{\rule{0.25em}{0ex}}\text{kW}\cdot \text{h = 3}\text{.}\text{60}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{J}$ .

$1\phantom{\rule{0.25em}{0ex}}\text{kW}\cdot \text{h=}\left(\frac{1×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{J}}{\text{1 s}}\right)\left(1 h\right)\left(\frac{\text{3600 s}}{\text{1 h}}\right)=3\text{.}\text{60}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{J}$

Electrons in an X-ray tube are accelerated through $1.00×{\text{10}}^{\text{2}}\phantom{\rule{0.25em}{0ex}}\text{kV}$ and directed toward a target to produce X-rays. Calculate the power of the electron beam in this tube if it has a current of 15.0 mA.

An electric water heater consumes 5.00 kW for 2.00 h per day. What is the cost of running it for one year if electricity costs $\text{12.0 cents}\text{/kW}\cdot \text{h}$ ? See [link] .

\$438/y

How do you convert 0.0045kgcmÂ³ to the si unit?
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
I only know 5: •Solids •Liquids •Gases •Plasma •Bose-Einstein condensate
Thapelo
Alright Thank you
Falana
Which one is the Bose-Einstein
James
can you explain what plasma and the I her one you mentioned
Olatunde
u can say sun or stars are just the state of plasma
Mohit
but the are more than seven
Issa
what the meaning of continuum
What state of matter is fire
fire is not in any state of matter...fire is rather a form of energy produced from an oxidising reaction.
Xenda
Isn`t fire the plasma state of matter?
Walter
How can you define time?
Time can be defined as a continuous , dynamic , irreversible , unpredictable quantity .
Tanaya
what is the relativity of physics
How do you convert 0.0045kgcm³ to the si unit?
flint
What is the formula for motion
V=u+at V²=u²-2as
flint
S=ut+½at
flint
they are eqns of linear motion
King
S=Vt
Thapelo
v=u+at s=ut+at^\2 v^=u^+2as where ^=2
King
hi
hello
King
Explain dopplers effect
Not yet learnt
Bob
Explain motion with types
Bob
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
Scalar quantity Because acceleration has only magnitude
Bob
acleration is vectr quatity it is found in a spefied direction and it is product of displcemnt
bhat
its a scalar quantity
Paul
velocity is speed and direction. since velocity is a part of acceleration that makes acceleration a vector quantity. an example of this is centripetal acceleration. when you're moving in a circular patter at a constant speed, you are still accelerating because your direction is constantly changing.
Josh
acceleration is a vector quantity. As explained by Josh Thompson, even in circular motion, bodies undergoing circular motion only accelerate because on the constantly changing direction of their constant speed. also retardation and acceleration are differentiated by virtue of their direction in
fitzgerald
respect to prevailing force
fitzgerald
What is the difference between impulse and momentum?
Manyo
Momentum is the product of the mass of a body and the change in velocity of its motion. ie P=m(v-u)/t (SI unit is kgm/s). it is literally the impact of collision from a moving body. While Impulse is the product of momentum and time. I = Pt (SI unit is kgm) or it is literally the change in momentum
fitzgerald
Or I = m(v-u)
fitzgerald
Calculation of kinetic and potential energy
K.e=mv² P.e=mgh
Malia
K is actually 1/2 mv^2
Josh
what impulse is given to an a-particle of mass 6.7*10^-27 kg if it is ejected from a stationary nucleus at a speed of 3.2*10^-6ms²? what average force is needed if it is ejected in approximately 10^-8 s?
John
speed=velocity÷time velocity=speed×time=3.2×10^-6×10^-8=32×10^-14m/s impulse [I]=∆momentum[P]=mass×velocity=6.7×10^-27×32×10^-14=214.4×10^-41kg/ms force=impulse÷time=214.4×10^-41÷10^-8=214.4×10^-33N. dats how I solved it.if wrong pls correct me.
Melody
what is sound wave
sound wave is a mechanical longitudinal wave that transfers energy from one point to another
Ogor
its a longitudnal wave which is associted wth compresion nad rearfractions
bhat
what is power
it's also a capability to do something or act in a particular way.
Kayode
Newton laws of motion
Mike
power also known as the rate of ability to do work
Slim
power means capabilty to do work p=w/t its unit is watt or j/s it also represents how much work is done fr evry second
bhat
what does fluorine do?
strengthen and whiten teeth.
Gia
a simple pendulum make 50 oscillation in 1minute, what is it period of oscillation?
length of pendulm?
bhat
what is the difference between temperature and heat transfer?
temperature is the measurement of hotness or coldness of a body... heat transfer is the movement of heat from one body to another
Doc
U get it right
Titilayo
correct
PROMISE
heat is an energy possesed by any substance due to random kinetic energy possesed by molecules while temperature is driving force which gives direction of flow heat
bhat