19.1 Electric potential energy: potential difference  (Page 3/10)

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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 $\Delta V={V}_{\text{B}}{\mathrm{–V}}_{\text{A}}=\text{+12 V}$ and the charge $q$ is negative, so that $\text{ΔPE}=q\Delta V$ 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 runs 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 moved in 1.00 s. The charge moved is related to voltage and energy through the equation $\text{ΔPE}=q\Delta V$ . A 30.0 W lamp uses 30.0 joules per second. Since the battery loses energy, we have $\text{ΔPE}=\text{–30.0 J}$ and, since the electrons are going from the negative terminal to the positive, we see that $\Delta V=\text{+12.0 V}$ .

Solution

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

$q=\frac{\text{ΔPE}}{\Delta V}\text{.}$

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

$q=\frac{\text{–30.0 J}}{\text{+12.0 V}}=\frac{\text{–30.0 J}}{\text{+12.0 J/C}}=–2.50 C.$

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

${\text{n}}_{\text{e}}=\frac{–2.50 C}{–1.60×{\text{10}}^{\text{–19}}\phantom{\rule{0.25em}{0ex}}{\text{C/e}}^{–}}=1.56×{\text{10}}^{\text{19}}\phantom{\rule{0.25em}{0ex}}\text{electrons.}$

Discussion

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.

The electron volt

The energy per electron is very small in macroscopic situations like that in the previous example—a tiny fraction of a joule. But on a submicroscopic scale, such energy per particle (electron, proton, or ion) can be of great importance. For example, even a tiny fraction of a joule can be great enough for these particles to destroy organic molecules and harm living tissue. The particle may do its damage by direct collision, or it may create harmful x rays, which can also inflict damage. It is useful to have an energy unit related to submicroscopic effects. [link] shows a situation related to the definition of such an energy unit. An electron is accelerated between two charged metal plates as it might be in an old-model television tube or oscilloscope. The electron is given kinetic energy that is later converted to another form—light in the television tube, for example. (Note that downhill for the electron is uphill for a positive charge.) Since energy is related to voltage by $\text{ΔPE}=q\Delta V,$ we can think of the joule as a coulomb-volt.

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
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Abdu
Describe an experiment to determine short half life
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Hassan
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Emmanuel
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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
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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
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Kelly
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Kalilu
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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.
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