# 7.3 Energy stored in capacitors  (Page 2/3)

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## Capacitance in a heart defibrillator

A heart defibrillator delivers $4.00×{\text{10}}^{\text{2}}\phantom{\rule{0.25em}{0ex}}\text{J}$ of energy by discharging a capacitor initially at $1.00×{\text{10}}^{\text{4}}\phantom{\rule{0.25em}{0ex}}\text{V}$ . What is its capacitance?

Strategy

We are given ${E}_{\text{cap}}$ and $V$ , and we are asked to find the capacitance $C$ . Of the three expressions in the equation for ${E}_{\text{cap}}$ , the most convenient relationship is

${E}_{\text{cap}}=\frac{{\text{CV}}^{2}}{2}.$

Solution

Solving this expression for $C$ and entering the given values yields

$\begin{array}{lll}C& =& \frac{2{E}_{\text{cap}}}{{V}^{2}}=\frac{2\left(4\text{.}\text{00}×{\text{10}}^{2}\phantom{\rule{0.25em}{0ex}}\text{J}\right)}{\left(1\text{.}\text{00}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{V}{\right)}^{2}}=8\text{.}\text{00}×{\text{10}}^{–6}\phantom{\rule{0.25em}{0ex}}\text{F}\\ & =& \text{8}\text{.}\text{00 µF}\text{.}\end{array}$

Discussion

This is a fairly large, but manageable, capacitance at $1.00×{\text{10}}^{\text{4}}\phantom{\rule{0.25em}{0ex}}\text{V}$ .

## Section summary

• Capacitors are used in a variety of devices, including defibrillators, microelectronics such as calculators, and flash lamps, to supply energy.
• The energy stored in a capacitor can be expressed in three ways:
${E}_{\text{cap}}=\frac{\text{QV}}{2}=\frac{{\text{CV}}^{2}}{2}=\frac{{Q}^{2}}{2C},$
where $Q$ is the charge, $V$ is the voltage, and $C$ is the capacitance of the capacitor. The energy is in joules when the charge is in coulombs, voltage is in volts, and capacitance is in farads.

## Conceptual questions

How does the energy contained in a charged capacitor change when a dielectric is inserted, assuming the capacitor is isolated and its charge is constant? Does this imply that work was done?

What happens to the energy stored in a capacitor connected to a battery when a dielectric is inserted? Was work done in the process?

## Problems&Exercises

(a) What is the energy stored in the $\text{10.0 μF}$ capacitor of a heart defibrillator charged to $9.00×{\text{10}}^{\text{3}}\phantom{\rule{0.25em}{0ex}}\text{V}$ ? (b) Find the amount of stored charge.

(a) $\text{405 J}$

(b) $\text{90.0 mC}$

In open heart surgery, a much smaller amount of energy will defibrillate the heart. (a) What voltage is applied to the $\text{8.00 μF}$ capacitor of a heart defibrillator that stores 40.0 J of energy? (b) Find the amount of stored charge.

(a) 3.16 kV

(b) 25.3 mC

A $1\text{65 µF}$ capacitor is used in conjunction with a motor. How much energy is stored in it when 119 V is applied?

Suppose you have a 9.00 V battery, a $\text{2.00 μF}$ capacitor, and a $\text{7.40 μF}$ capacitor. (a) Find the charge and energy stored if the capacitors are connected to the battery in series. (b) Do the same for a parallel connection.

(a) $1.42×{\text{10}}^{\text{−5}}\phantom{\rule{0.25em}{0ex}}\text{C}$ , $6.38×{\text{10}}^{\text{−5}}\phantom{\rule{0.25em}{0ex}}\text{J}$

(b) $8.46×{\text{10}}^{\text{−5}}\phantom{\rule{0.25em}{0ex}}\text{C}$ , $3.81×{\text{10}}^{\text{−4}}\phantom{\rule{0.25em}{0ex}}\text{J}$

A nervous physicist worries that the two metal shelves of his wood frame bookcase might obtain a high voltage if charged by static electricity, perhaps produced by friction. (a) What is the capacitance of the empty shelves if they have area $1.00×{\text{10}}^{\text{2}}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{\text{2}}$ and are 0.200 m apart? (b) What is the voltage between them if opposite charges of magnitude 2.00 nC are placed on them? (c) To show that this voltage poses a small hazard, calculate the energy stored.

(a) $4\text{.}\text{43}×{\text{10}}^{–\text{12}}\phantom{\rule{0.25em}{0ex}}\text{F}$

(b) $\text{452}\phantom{\rule{0.25em}{0ex}}\text{V}$

(c) $4\text{.}\text{52}×{\text{10}}^{–7}\phantom{\rule{0.25em}{0ex}}\text{J}$

Show that for a given dielectric material the maximum energy a parallel plate capacitor can store is directly proportional to the volume of dielectric ( $\text{Volume =}\phantom{\rule{0.25em}{0ex}}A·d$ ). Note that the applied voltage is limited by the dielectric strength.

Construct Your Own Problem

Consider a heart defibrillator similar to that discussed in [link] . Construct a problem in which you examine the charge stored in the capacitor of a defibrillator as a function of stored energy. Among the things to be considered are the applied voltage and whether it should vary with energy to be delivered, the range of energies involved, and the capacitance of the defibrillator. You may also wish to consider the much smaller energy needed for defibrillation during open-heart surgery as a variation on this problem.

Unreasonable Results

(a) On a particular day, it takes $9.60×{\text{10}}^{\text{3}}\phantom{\rule{0.25em}{0ex}}\text{J}$ of electric energy to start a truck’s engine. Calculate the capacitance of a capacitor that could store that amount of energy at 12.0 V. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

(a) $\text{133}\phantom{\rule{0.25em}{0ex}}\text{F}$

(b) Such a capacitor would be too large to carry with a truck. The size of the capacitor would be enormous.

(c) It is unreasonable to assume that a capacitor can store the amount of energy needed.

#### Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
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Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
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Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
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LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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LITNING
scanning tunneling microscope
Sahil
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Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, College physics (engineering physics 2, tuas). OpenStax CNX. May 08, 2014 Download for free at http://legacy.cnx.org/content/col11649/1.2
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