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  • List some uses of capacitors.
  • Express in equation form the energy stored in a capacitor.
  • Explain the function of a defibrillator.

Most of us have seen dramatizations in which medical personnel use a defibrillator    to pass an electric current through a patient’s heart to get it to beat normally. (Review [link] .) Often realistic in detail, the person applying the shock directs another person to “make it 400 joules this time.” The energy delivered by the defibrillator is stored in a capacitor and can be adjusted to fit the situation. SI units of joules are often employed. Less dramatic is the use of capacitors in microelectronics, such as certain handheld calculators, to supply energy when batteries are charged. (See [link] .) Capacitors are also used to supply energy for flash lamps on cameras.

In an electronic calculator circuit the memory is preserved using large capacitors which store energy when the batteries are charged.
Energy stored in the large capacitor is used to preserve the memory of an electronic calculator when its batteries are charged. (credit: Kucharek, Wikimedia Commons)

Energy stored in a capacitor is electrical potential energy, and it is thus related to the charge Q size 12{Q} {} and voltage V size 12{V} {} on the capacitor. We must be careful when applying the equation for electrical potential energy Δ PE = q Δ V size 12{?"PE"=q?V} {} to a capacitor. Remember that Δ PE size 12{?"PE"} {} is the potential energy of a charge q size 12{q} {} going through a voltage Δ V size 12{?V} {} . But the capacitor starts with zero voltage and gradually comes up to its full voltage as it is charged. The first charge placed on a capacitor experiences a change in voltage Δ V = 0 size 12{?V=0} {} , since the capacitor has zero voltage when uncharged. The final charge placed on a capacitor experiences Δ V = V size 12{?V=V} {} , since the capacitor now has its full voltage V size 12{V} {} on it. The average voltage on the capacitor during the charging process is V / 2 size 12{V/2} {} , and so the average voltage experienced by the full charge q size 12{q} {} is V / 2 size 12{V/2} {} . Thus the energy stored in a capacitor, E cap size 12{E rSub { size 8{"cap"} } } {} , is

E cap = Q V 2 , size 12{E rSub { size 8{"cap"} } =Q { {V} over {2} } } {}

where Q size 12{Q} {} is the charge on a capacitor with a voltage V size 12{V} {} applied. (Note that the energy is not QV size 12{ ital "QV"} {} , but QV / 2 size 12{ ital "QV"/2} {} .) Charge and voltage are related to the capacitance C of a capacitor by Q = CV size 12{Q= ital "CV"} {} , and so the expression for E cap size 12{E rSub { size 8{"cap"} } } {} can be algebraically manipulated into three equivalent expressions:

E cap = QV 2 = CV 2 2 = Q 2 2 C , size 12{E rSub { size 8{"cap"} } = { { ital "QV"} over {2} } = { { ital "CV" rSup { size 8{2} } } over {2} } = { {Q rSup { size 8{2} } } over {2C} } } {}

where Q size 12{Q} {} is the charge and V size 12{V} {} the voltage on a capacitor C size 12{C} {} . The energy is in joules for a charge in coulombs, voltage in volts, and capacitance in farads.

Energy stored in capacitors

The energy stored in a capacitor can be expressed in three ways:

E cap = QV 2 = CV 2 2 = Q 2 2 C , size 12{E rSub { size 8{"cap"} } = { { ital "QV"} over {2} } = { { ital "CV" rSup { size 8{2} } } over {2} } = { {Q rSup { size 8{2} } } over {2C} } } {}

where Q size 12{Q} {} is the charge, V size 12{V} {} is the voltage, and C size 12{C} {} is the capacitance of the capacitor. The energy is in joules for a charge in coulombs, voltage in volts, and capacitance in farads.

In a defibrillator, the delivery of a large charge in a short burst to a set of paddles across a person’s chest can be a lifesaver. The person’s heart attack might have arisen from the onset of fast, irregular beating of the heart—cardiac or ventricular fibrillation. The application of a large shock of electrical energy can terminate the arrhythmia and allow the body’s pacemaker to resume normal patterns. Today it is common for ambulances to carry a defibrillator, which also uses an electrocardiogram to analyze the patient’s heartbeat pattern. Automated external defibrillators (AED) are found in many public places ( [link] ). These are designed to be used by lay persons. The device automatically diagnoses the patient’s heart condition and then applies the shock with appropriate energy and waveform. CPR is recommended in many cases before use of an AED.

Questions & Answers

what is temperature
Adeleye Reply
temperature is the measure of degree of hotness or coldness of a body. measured in kelvin
Ahmad
a characteristic which tells hotness or coldness of a body
babar
Average kinetic energy of an object
Kym
average kinetic energy of the particles in an object
Kym
A measure of the quantity of heat contained in an object which arises from the average kinetic energy of the constituent particles of that object. It can be measured using thermometers. It has a unit of kelvin in the thermodynamic scale and degree Celsius in the Celsius scale.
ibrahim
Mass of air bubble in material medium is negative. why?
Hrithik Reply
a car move 6m. what is the acceleration?
Umaru Reply
depends how long
Peter
What is the simplest explanation on the difference of principle, law and a theory
Kym Reply
how did the value of gravitational constant came give me the explanation
Varun Reply
how did the value of gravitational constant 6.67×10°-11Nm2kg-2
Varun
A steel ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.45 m. (a) Calculate its velocity just before it strikes the floor.
Kris Reply
9.8m/s?
Muhammad
Sqrt(2*1.5m*9.81m/s^2)
Richard
0.5m* mate.
Muhammad
0.05 I meant.
Muhammad
Guess your solution is correct considering the ball fall from 1.5m height initially.
Muhammad
Sqrt(2*1.5m*9.81m/s^2)
Deepak
How can we compare different combinations of capacitors?
Prakash Reply
find the dimension of acceleration if it's unit is ms-2
Happiness Reply
lt^-2
Ahmad
b=-2 ,a =1
Ahmad
M^0 L^1T^-2
Sneha
what is botany
Masha
it is a branch of science which deal with the study of plants animals and environment
Varun
what is work
Sunday Reply
a boy moving with an initial velocity of 2m\s and finally canes to rest with a velocity of 3m\s square at times 10se calculate it acceleration
Sunday
.
Abdul
6.6 lol 😁😁
Abdul
show ur work
Sunday
sorry..the answer is -10
Abdul
your question is wrong
Abdul
If the boy is coming to rest then how the hell will his final velocity be 3 it'll be zero
Abdul
re-write the question
Nicolas
men i -10 isn't correct.
Stephen
using v=u + at
Stephen
1/10
Happy
ya..1/10 is very correct..
Stephen
hnn
Happy
how did the value 6.67×10°-11Nm2kg2 came tell me please
Varun
Work is the product of force and distance
Kym
physicist
Michael
what is longitudinal wave
Badmus Reply
A longitudinal wave is wave which moves parallel or along the direction of propagation.
sahil
longitudinal wave in liquid is square root of bulk of modulus by density of liquid
harishree
Is British mathematical units the same as the United States units?(like inches, cm, ext.)
Nina Reply
We use SI units: kg, m etc but the US sometimes refer to inches etc as British units even though we no longer use them.
Richard
Thanks, just what I needed to know.
Nina
What is the advantage of a diffraction grating over a double slit in dispersing light into a spectrum?
Uditha Reply
can I ask questions?
Boniface Reply
yes.
Abdul
Yes
Albert
sure
Ajali
yeap
Sani
yesssss
bilal
hello guys
Ibitayo
when you will ask the question
Ana
anybody can ask here
bichu
is free energy possible with magnets?
joel
no
Mr.
you could construct an aparatus that might have a slightly higher 'energy profit' than energy used, but you would havw to maintain the machine, and most likely keep it in a vacuum, for no air resistance, and cool it, so chances are quite slim.
Mr.
calculate the force, p, required to just make a 6kg object move along the horizontal surface where the coefficient of friction is 0.25
Gbolahan
Yes ask
Albert
if a man travel 7km 30degree east of North then 10km east find the resultant displacement
Ajali Reply
11km
Dohn
disagree. Displacement is the hypotenuse length of the final position to the starting position. Find x,y components of each leg of journey to determine final position, then use final components to calculate the displacement.
Daniel
1.The giant star Betelgeuse emits radiant energy at a rate of 10exponent4 times greater than our sun, where as it surface temperature is only half (2900k) that of our sun. Estimate the radius of Betelgeuse assuming e=1, the sun's radius is s=7*10exponent8metres
James Reply
2. A ceramic teapot (e=0.20) and a shiny one (e=0.10), each hold 0.25 l of at 95degrees. A. Estimate the temperature rate of heat loss from each B. Estimate the temperature drop after 30mins for each. Consider only radiation and assume the surrounding at 20degrees
James
Practice Key Terms 1

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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