# 7.1 Capacitors and dielectrics  (Page 6/12)

 Page 6 / 12

## Phet explorations: capacitor lab

Explore how a capacitor works! Change the size of the plates and add a dielectric to see the effect on capacitance. Change the voltage and see charges built up on the plates. Observe the electric field in the capacitor. Measure the voltage and the electric field.

## Section summary

• A capacitor is a device used to store charge.
• The amount of charge $Q$ a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
• The capacitance $C$ is the amount of charge stored per volt , or
$C=\frac{Q}{V}.$
• The capacitance of a parallel plate capacitor is $C={\epsilon }_{0}\phantom{\rule{0.15em}{0ex}}\frac{A}{d}$ , when the plates are separated by air or free space. ${\epsilon }_{\text{0}}\phantom{\rule{0.25em}{0ex}}$ is called the permittivity of free space.
• A parallel plate capacitor with a dielectric between its plates has a capacitance given by
$C={\mathrm{\kappa \epsilon }}_{0}\phantom{\rule{0.25em}{0ex}}\frac{A}{d},$
where $\kappa$ is the dielectric constant of the material.
• The maximum electric field strength above which an insulating material begins to break down and conduct is called dielectric strength.

## Conceptual questions

Does the capacitance of a device depend on the applied voltage? What about the charge stored in it?

Use the characteristics of the Coulomb force to explain why capacitance should be proportional to the plate area of a capacitor. Similarly, explain why capacitance should be inversely proportional to the separation between plates.

Give the reason why a dielectric material increases capacitance compared with what it would be with air between the plates of a capacitor. What is the independent reason that a dielectric material also allows a greater voltage to be applied to a capacitor? (The dielectric thus increases $C$ and permits a greater $V$ .)

How does the polar character of water molecules help to explain water’s relatively large dielectric constant? ( [link] )

Sparks will occur between the plates of an air-filled capacitor at lower voltage when the air is humid than when dry. Explain why, considering the polar character of water molecules.

Water has a large dielectric constant, but it is rarely used in capacitors. Explain why.

Membranes in living cells, including those in humans, are characterized by a separation of charge across the membrane. Effectively, the membranes are thus charged capacitors with important functions related to the potential difference across the membrane. Is energy required to separate these charges in living membranes and, if so, is its source the metabolization of food energy or some other source?

## Problems&Exercises

What charge is stored in a $\text{180 µF}\phantom{\rule{0.25em}{0ex}}$ capacitor when 120 V is applied to it?

$\text{21}\text{.}6\phantom{\rule{0.25em}{0ex}}\text{mC}$

Find the charge stored when 5.50 V is applied to an 8.00 pF capacitor.

What charge is stored in the capacitor in [link] ?

$\text{80}\text{.}0\phantom{\rule{0.25em}{0ex}}\text{mC}$

Calculate the voltage applied to a $2\text{.}\text{00 µF}$ capacitor when it holds $3\text{.}\text{10 µC}$ of charge.

What voltage must be applied to an 8.00 nF capacitor to store 0.160 mC of charge?

20.0 kV

What capacitance is needed to store $3\text{.}\text{00 µC}$ of charge at a voltage of 120 V?

What is the capacitance of a large Van de Graaff generator’s terminal, given that it stores 8.00 mC of charge at a voltage of 12.0 MV?

$\text{667}\phantom{\rule{0.25em}{0ex}}\text{pF}$

Find the capacitance of a parallel plate capacitor having plates of area $5\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}$ that are separated by 0.100 mm of Teflon.

(a)What is the capacitance of a parallel plate capacitor having plates of area ${\text{1.50 m}}^{2}$ that are separated by 0.0200 mm of neoprene rubber? (b) What charge does it hold when 9.00 V is applied to it?

(a) $4\text{.}\text{4 µF}$

(b) $4\text{.}0×{\text{10}}^{–5}\phantom{\rule{0.25em}{0ex}}\text{C}$

Integrated Concepts

A prankster applies 450 V to an $\text{80}\text{.}0 µF$ capacitor and then tosses it to an unsuspecting victim. The victim’s finger is burned by the discharge of the capacitor through 0.200 g of flesh. What is the temperature increase of the flesh? Is it reasonable to assume no phase change?

Unreasonable Results

(a) A certain parallel plate capacitor has plates of area ${\text{4.00 m}}^{2}$ , separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage? (b) What is unreasonable about this result? (c) Which assumptions are responsible or inconsistent?

(a) 14.2 kV

(b) The voltage is unreasonably large, more than 100 times the breakdown voltage of nylon.

(c) The assumed charge is unreasonably large and cannot be stored in a capacitor of these dimensions.

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
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
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
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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