# 7.2 Electric potential and potential difference  (Page 2/12)

 Page 2 / 12

## Calculating energy

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 $\text{Δ}U=q\text{Δ}V.$ To find the energy output, we multiply the charge moved by the potential difference.

## Solution

For the motorcycle battery, $q=5000\phantom{\rule{0.2em}{0ex}}\text{C}$ and $\text{Δ}V=12.0\phantom{\rule{0.2em}{0ex}}\text{V}$ . The total energy delivered by the motorcycle battery is

$\text{Δ}{U}_{\text{cycle}}=\left(5000\phantom{\rule{0.2em}{0ex}}\text{C}\right)\left(12.0\phantom{\rule{0.2em}{0ex}}\text{V}\right)=\left(5000\phantom{\rule{0.2em}{0ex}}\text{C}\right)\left(12.0\phantom{\rule{0.2em}{0ex}}\text{J/C}\right)=\phantom{\rule{0.2em}{0ex}}6.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\phantom{\rule{0.2em}{0ex}}\text{J}\text{.}$

Similarly, for the car battery, $q=60,000\phantom{\rule{0.2em}{0ex}}\text{C}$ and

$\text{Δ}{U}_{\text{car}}=\left(60,000\phantom{\rule{0.2em}{0ex}}\text{C}\right)\left(12.0\phantom{\rule{0.2em}{0ex}}\text{V}\right)=7.20\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{J}\text{.}$

## Significance

Voltage and energy are related, but they are not the same thing. The voltages of the batteries are identical, but the energy supplied by each is quite different. A car battery has a much larger engine to start than a motorcycle. 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 depleted 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.

Check Your Understanding How much energy does a 1.5-V AAA battery have that can move 100 C?

$\text{Δ}U=q\text{Δ}V=\left(100\phantom{\rule{0.2em}{0ex}}\text{C}\right)\left(1.5\phantom{\rule{0.2em}{0ex}}\text{V}\right)=150\phantom{\rule{0.2em}{0ex}}\text{J}$

Note that the energies calculated in the previous example are absolute values. The change in potential energy for the battery is negative, since it loses energy. These batteries, like many electrical systems, actually move negative charge—electrons in particular. The batteries repel electrons from their negative terminals ( A ) through whatever circuitry is involved and attract them to their positive terminals ( B ), as shown in [link] . The change in potential is $\text{Δ}V={V}_{B}-{V}_{A}=+12\phantom{\rule{0.2em}{0ex}}\text{V}$ and the charge q is negative, so that $\text{Δ}U=q\text{Δ}V$ is negative, meaning the potential energy of the battery has decreased when q has moved from A to B .

## How many electrons move through a headlight each second?

When a 12.0-V car battery powers a single 30.0-W headlight, how many electrons pass through it each second?

## Strategy

To find the number of electrons, we must first find the charge that moves in 1.00 s. The charge moved is related to voltage and energy through the equations $\text{Δ}U=q\text{Δ}V.$ A 30.0-W lamp uses 30.0 joules per second. Since the battery loses energy, we have $\text{Δ}U=-30\phantom{\rule{0.2em}{0ex}}\text{J}$ and, since the electrons are going from the negative terminal to the positive, we see that $\text{Δ}V=\text{+12.0}\phantom{\rule{0.2em}{0ex}}\text{V}\text{.}$

## Solution

To find the charge q moved, we solve the equation $\text{Δ}U=q\text{Δ}V:$

$q=\frac{\text{Δ}U}{\text{Δ}V}.$

Entering the values for $\text{Δ}U$ and $\text{Δ}V$ , we get

$q=\frac{-30.0\phantom{\rule{0.2em}{0ex}}\text{J}}{+12.0\phantom{\rule{0.2em}{0ex}}\text{V}}=\frac{-30.0\phantom{\rule{0.2em}{0ex}}\text{J}}{+12.0\phantom{\rule{0.2em}{0ex}}\text{J/C}}=-2.50\phantom{\rule{0.2em}{0ex}}\text{C}\text{.}$

The number of electrons ${n}_{e}$ is the total charge divided by the charge per electron. That is,

${n}_{e}=\frac{-2.50\phantom{\rule{0.2em}{0ex}}\text{C}}{-1.60\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{\phantom{\rule{0.2em}{0ex}}10}^{-19}\phantom{\rule{0.2em}{0ex}}{\text{C/e}}^{-}}=1.56\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{\phantom{\rule{0.2em}{0ex}}10}^{19}\phantom{\rule{0.2em}{0ex}}\text{electrons}\text{.}$

## Significance

This is a very large number. It is no wonder that we do not ordinarily observe individual electrons with so many being present in ordinary systems. In fact, electricity had been in use for many decades before it was determined that the moving charges in many circumstances were negative. Positive charge moving in the opposite direction of negative charge often produces identical effects; this makes it difficult to determine which is moving or whether both are moving.

What is differential form of Gauss's law?
help me out on this question the permittivity of diamond is 1.46*10^-10.( a)what is the dielectric of diamond (b) what its susceptibility
a body is projected vertically upward of 30kmp/h how long will it take to reach a point 0.5km bellow e point of projection
i have to say. who cares. lol. why know that t all
Jeff
is this just a chat app about the openstax book?
kya ye b.sc ka hai agar haa to konsa part
what is charge quantization
it means that the total charge of a body will always be the integral multiples of basic unit charge ( e ) q = ne n : no of electrons or protons e : basic unit charge 1e = 1.602×10^-19
Riya
is the time quantized ? how ?
Mehmet
What do you meanby the statement,"Is the time quantized"
Mayowa
Can you give an explanation.
Mayowa
there are some comment on the time -quantized..
Mehmet
time is integer of the planck time, discrete..
Mehmet
planck time is travel in planck lenght of light..
Mehmet
it's says that charges does not occur in continuous form rather they are integral multiple of the elementary charge of an electron.
Tamoghna
it is just like bohr's theory. Which was angular momentum of electron is intral multiple of h/2π
determine absolute zero
The properties of a system during a reversible constant pressure non-flow process at P= 1.6bar, changes from constant volume of 0.3m³/kg at 20°C to a volume of 0.55m³/kg at 260°C. its constant pressure process is 3.205KJ/kg°C Determine: 1. Heat added, Work done, Change in Internal Energy and Change in Enthalpy
U can easily calculate work done by 2.303log(v2/v1)
Abhishek
Amount of heat added through q=ncv^delta t
Abhishek
Change in internal energy through q=Q-w
Abhishek
please how do dey get 5/9 in the conversion of Celsius and Fahrenheit
what is copper loss
this is the energy dissipated(usually in the form of heat energy) in conductors such as wires and coils due to the flow of current against the resistance of the material used in winding the coil.
Henry
it is the work done in moving a charge to a point from infinity against electric field
what is the weight of the earth in space
As w=mg where m is mass and g is gravitational force... Now if we consider the earth is in gravitational pull of sun we have to use the value of "g" of sun, so we can find the weight of eaeth in sun with reference to sun...
Prince
g is not gravitacional forcé, is acceleration of gravity of earth and is assumed constante. the "sun g" can not be constant and you should use Newton gravity forcé. by the way its not the "weight" the physical quantity that matters, is the mass
Jorge
Yeah got it... Earth and moon have specific value of g... But in case of sun ☀ it is just a huge sphere of gas...
Prince
Thats why it can't have a constant value of g ....
Prince
not true. you must know Newton gravity Law . even a cloud of gas it has mass thats al matters. and the distsnce from the center of mass of the cloud and the center of the mass of the earth
Jorge
please why is the first law of thermodynamics greater than the second
every law is important, but first law is conservation of energy, this state is the basic in physics, in this case first law is more important than other laws..
Mehmet
First Law describes o energy is changed from one form to another but not destroyed, but that second Law talk about entropy of a system increasing gradually
Mayowa
first law describes not destroyer energy to changed the form, but second law describes the fluid drection that is entropy. in this case first law is more basic accorging to me...
Mehmet
define electric image.obtain expression for electric intensity at any point on earthed conducting infinite plane due to a point charge Q placed at a distance D from it.
explain the lack of symmetry in the field of the parallel capacitor
pls. explain the lack of symmetry in the field of the parallel capacitor
Phoebe