# 8.7 Electric potential energy: potential difference  (Page 2/9)

 Page 2 / 9
$V=\frac{\text{PE}}{q}\text{.}$

## Electric potential

This is the electric potential energy per unit charge.

$V=\frac{\text{PE}}{q}$

Since PE is proportional to $q$ , the dependence on $q$ cancels. Thus $V$ does not depend on $q$ . The change in potential energy $\text{ΔPE}$ is crucial, and so we are concerned with the difference in potential or potential difference $\Delta V$ between two points, where

$\Delta V={V}_{\text{B}}-{V}_{\text{A}}=\frac{\Delta \text{PE}}{q}\text{.}$

The potential difference between points A and B, ${V}_{\text{B}}\phantom{\rule{0.25em}{0ex}}–\phantom{\rule{0.25em}{0ex}}{V}_{\text{A}}$ , is thus defined to be the change in potential energy of a charge $q$ moved from A to B, divided by the charge. Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta.

$\text{1 V = 1}\phantom{\rule{0.25em}{0ex}}\frac{J}{C}$

## Potential difference

The potential difference between points A and B, ${V}_{B}-{V}_{A}$ , is defined to be the change in potential energy of a charge $q$ moved from A to B, divided by the charge. Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta.

$\text{1 V = 1}\phantom{\rule{0.25em}{0ex}}\frac{J}{C}$

The familiar term voltage is the common name for potential difference. Keep in mind that whenever a voltage is quoted, it is understood to be the potential difference between two points. For example, every battery has two terminals, and its voltage is the potential difference between them. More fundamentally, the point you choose to be zero volts is arbitrary. This is analogous to the fact that gravitational potential energy has an arbitrary zero, such as sea level or perhaps a lecture hall floor.

In summary, the relationship between potential difference (or voltage) and electrical potential energy is given by

$\Delta V=\frac{\text{ΔPE}}{q}\phantom{\rule{0.25em}{0ex}}\text{and ΔPE =}\phantom{\rule{0.25em}{0ex}}q\Delta V\text{.}$

## Potential difference and electrical potential energy

The relationship between potential difference (or voltage) and electrical potential energy is given by

$\Delta V=\frac{\text{ΔPE}}{q}\phantom{\rule{0.25em}{0ex}}\text{and ΔPE =}\phantom{\rule{0.25em}{0ex}}q\Delta V\text{.}$

The second equation is equivalent to the first.

Voltage is not the same as energy. Voltage is the energy per unit charge. Thus a motorcycle battery and a car battery can both have the same voltage (more precisely, the same potential difference between battery terminals), yet one stores much more energy than the other since $\text{ΔPE =}\phantom{\rule{0.25em}{0ex}}q\Delta V$ . The car battery can move more charge than the motorcycle battery, although both are 12 V batteries.

## Calculating energy

Suppose you have a 12.0 V motorcycle battery that can move 5000 C of charge, and a 12.0 V car battery that can move 60,000 C of charge. How much energy does each deliver? (Assume that the numerical value of each charge is accurate to three significant figures.)

Strategy

To say we have a 12.0 V battery means that its terminals have a 12.0 V potential difference. When such a battery moves charge, it puts the charge through a potential difference of 12.0 V, and the charge is given a change in potential energy equal to $\text{ΔPE =}\phantom{\rule{0.25em}{0ex}}q\Delta V$ .

So to find the energy output, we multiply the charge moved by the potential difference.

Solution

For the motorcycle battery, $q=\text{5000 C}$ and $\Delta V=\text{12.0 V}$ . The total energy delivered by the motorcycle battery is

$\begin{array}{lll}{\text{ΔPE}}_{\text{cycle}}& =& \left(\text{5000 C}\right)\left(\text{12.0 V}\right)\\ & =& \left(\text{5000 C}\right)\left(\text{12.0 J/C}\right)\\ & =& 6.00×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{J.}\end{array}$

Similarly, for the car battery, $q=\text{60},\text{000}\phantom{\rule{0.25em}{0ex}}\text{C}$ and

$\begin{array}{lll}{\text{ΔPE}}_{\text{car}}& =& \left(\text{60,000 C}\right)\left(\text{12.0 V}\right)\\ & =& 7.20×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{J.}\end{array}$

Discussion

While voltage and energy are related, they are not the same thing. The voltages of the batteries are identical, but the energy supplied by each is quite different. Note also that as a battery is discharged, some of its energy is used internally and its terminal voltage drops, such as when headlights dim because of a low car battery. The energy supplied by the battery is still calculated as in this example, but not all of the energy is available for external use.

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
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
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
Got questions? Join the online conversation and get instant answers!