# 19.7 Energy stored in capacitors

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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.

Energy stored in a capacitor is electrical potential energy, and it is thus related to the charge $Q$ and voltage $V$ on the capacitor. We must be careful when applying the equation for electrical potential energy $\text{Δ}\text{PE}=q\text{Δ}V\phantom{\rule{0.25em}{0ex}}$ to a capacitor. Remember that $\text{Δ}\text{PE}$ is the potential energy of a charge $q$ going through a voltage $\text{Δ}V$ . 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 $\text{Δ}V=0$ , since the capacitor has zero voltage when uncharged. The final charge placed on a capacitor experiences $\text{Δ}V=V$ , since the capacitor now has its full voltage $V$ on it. The average voltage on the capacitor during the charging process is $V/2$ , and so the average voltage experienced by the full charge $q$ is $V/2$ . Thus the energy stored in a capacitor, ${E}_{\text{cap}}$ , is

${E}_{\text{cap}}=\frac{QV}{2},$

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

${E}_{\text{cap}}=\frac{\text{QV}}{2}=\frac{{\text{CV}}^{2}}{2}=\frac{{Q}^{2}}{2C},$

where $Q$ is the charge and $V$ the voltage on a capacitor $C$ . 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:

${E}_{\text{cap}}=\frac{\text{QV}}{2}=\frac{{\text{CV}}^{2}}{2}=\frac{{Q}^{2}}{2C},$

where $Q$ is the charge, $V$ is the voltage, and $C$ is the capacitance of the capacitor. The energy is in joules 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.

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branch of science which deals with matter energy and their relationship between them
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sound is directly proportional to the temperature.
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convex lens brings rays of light to a focus while concave diverges rays of light
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it depends on the size
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each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties; in particular, a radioactive form of an element. "some elements have only one stable isotope
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A wave is a disturbance which travels through the medium transferring energy from one form to another without causing any permanent displacement of d medium itself
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Light is a form o wave
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Neurons communicate by sending message through nerves in coordination
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light has dual nature, particle as well as wave. when we want to explain phenomena like Interference of light, then we consider light as wave.
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particles of light are like small packets of energy called photons, and flow or motion of photons is wave like
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light is just the energy of which photons emit
Matthew
the wave is how they travel
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photons do not emitt energy, they are energy. They are massless particles.
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a wave is a disturbance through the medium. Have you ever thrown a stone in still water? the disturbance produced travels in form of wave, the wave produced by throwing stone in still water are circular in nature.
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when would it ever be at rest
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a wave is a disturbance of which energy travels
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that's darkness. darkness has no mass because the photons within in aren't moving or producing energy
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effective mass of photons only comes into picture when we consider it accelerating in gravitational field, mass of photon has no meaning as it is always travelling with speed of light and is never at rest. with that high speed, Energy and momentum are equivalent. and darkness is absense of photons.
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darkness is absense of light. not the presence of 'resting photons'. photons are never at rest.
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this theory is presented in Einsteins theory of special relativity
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A.The velocity Vo for the streamline flow of liquid in a small tube depends on the radius r of the tube,the density and the viscosity iter of the liquid .use the dimensional analysis to obtain an expression for the velocity . B.Given that Vo =r square ×p all over 4×iter ×l
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A.The velocity Vo for the streamline flow of liquid in a small tube depends on the radius r of the tube,the density (rho)and the viscosity (iter)of the liquid. Use the method of dimensional analysis to obtain an expression for the velocity . B.Given that Vo =r square x p all over 4 x iter x l
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Matthew, photons ARE light. there is no such thing as a photon that isn't moving. in fact the speed they move at is called C (for constant) in physics. through a vacuum they always travel at this speed no matter what. they can not slow down; except in another medium.
The reason why a photon can go at this speed is BECAUSE it had no mass. nothing can go this speed or faster because it needs to have no mass or negative mass. that's why it's called the constant.
when a photon hits something that is opaque, this is the only way to "stop"it. it isn't merely stopped but absorbed and turned into heat energy, then the remaining energy is reflected in different wavelengths. that reflection is what we call color. the darker something is, the less photons are ther
e. complete blackness is the absolute absence of photons altogether. I believe what you're referring to is not speed, but wavelength, which is indirectly proportional to the amount of energy a particular photon is made up of.
in order for a photon to have zero wavelength, it must (at least theoretically) have infinite energy.
about mass: you may have photons confused with electrons. elections have a mass so small that people say they are without mass, but they do. it is called electron mass or Me-.
you may also be getting electrons and photons confused because of the cherenkov effect. that is what happens when a particle travels faster than light IN THAT PARTICULAR MEDIUM. I emphasize that because no other particle besides photons can go the speed of c.
when a particle goes faster than light in a particular medium, a blue light is emitted, called cherenkov radiation. this is why nuclear reactors glow blue.
nuclear reactors release so much energy that when they emit electrons, those electrons are given enough energy to go faster than light in that medium (in this case water), releasing blue light. if you put the reactor in air or a vacuum, this effect wouldn't happen because the speed of light in air
is very close to c, which is the universal speed limit. I'd you did go faster than c, time would go backwards and you would have infinite theoretical mass and probably spagghettify, like with a black hole.
*if
*electrons
light waves can travel through a vacuum, and do not require a medium. In empty space, the wave does not dissipate (grow smaller) no matter how far it travels, because the wave is not interacting with anything else.
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