EK Physics Ch4 Electricity COPY Flashcards

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1
Q

1 Coulombs =

A

6.24 X 10^18 e

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2
Q

e =

A

1.60 X 10^-19 Coulombs

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3
Q

coulomb’s law

A
  • purpose is to predict what is the electrostatic force of attraction and repulsion of two charges! it states if I have two charges: so q1 and q2, distance btw two charges is r
  • law states that the force/magnitude of force can be repulsion force or attractive force, telling us direction of force, but magnitude of electrostatic force is proportional to product of magnitudes of the charges
  • Fe= k X [q1q2] absolute value of each/ r2
  • just like newton’s law of gravitation, proportional to product of two masses and inversely proportional to distance! same thing!
  • electrostatic force at close range much stronger, happening at atomic level or scale much stronger what we are used to operating at but there is a parallel* patterns in universe
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4
Q

insulators and conductors similarities

A
  • usually either an insulating material or conducting material!
  • similarities= both are composed of a huge number of atoms adn moelcules, these atoms and molecules are composed of a positively charged NUCLEUS
  • NEGATIVELY CHARGED swarm of electrons that swarm that nucleus
  • for both positively charged nuc cannot move! can wiggle from thermal vibrations cannot travel freely throughout material as long as solid, if fluid can move and migrate around, but for solid positively charged nuc is fixed
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5
Q

conductor vs insulators

difference

A
  • negatively charged electrons can move- there are electrons in conductor can move about relatively freely with almost no resistance
  • vs. insulators electrons cannot mvoe around freely, do not have the right energy levels or bands to move around freely, for insulators everything is basically stuck! e can jump around its own atom or share with another, but cant jump around to others
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6
Q

conductrs and insulators hooked up to battery…

A
  • conductors e could start migraating down teh line
  • but in an insulator electrons are sttuck
  • so for electrical materials all we care about are conductors, and insulators use if dont want electrical intearction
  • not totally true if set up insulator to battery, even though eelctrons cannot jump from atom to atom, can shift hte nucleus and cloud of electrons so get one side of atom more positive one side of atom more negative, set up so positive shifted from negative if get this material to do it creates overall electrical effect cna itneract with charges nearby and interact electrically even if charges cannot flow through insulator!
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7
Q

if add bunch of negative charges to insulator, what would happen. well since charges cannot move through insulator…

A

charges cannot flow through insualtor so stuck, can charge whole thing uniformally if i wanted to, spread out throughout the whole thing or bunched up on one side

charges are stuck

vs. conductor, if put extra negative charge on teh side of conductor, dont have to stay there if they dont want to, negatives repel each other like charges next to each other will not liek it, so one negative will try to get as far away from other negative as it can! cant jump off conductor that takes a lot more energy but can go to very edge, so thats what charges do for conductors, solid conducting material, extra charge on it all will reside on outside edge whether added extra negative or positive, always on otuside edge for conductor! can only add charge to outside edge for a conductor, if not on outside edge will quickly find its way to the edge becuase repel eachother!

how do you add a positive? take away a negative! if start off with amterial just as many positives or negative, like adding charge, take away negative, always resides on otuside edge of ocnductor becuase charges try to get away from each other as much as possible

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8
Q

what are good insulators?

A

wood

glass

most plasics

all can disrtibute charge and charge cannot flow through it, can stick charge on otuside edge and just stays there!

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9
Q

good conductors….

A

metals like gold, copper used becuase cheaper than gold, or any other metal silver works great

materials were charges can flow freely through them

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10
Q

if had two conducting rods made out of metal…

A

one net amount of negative cahrge, resides on otuside edge of conductor, other metal conducting rod has no charge on it, what would happen?

well charges want to get away from eachother as far as possible, so if some go onto the new rod adn some stay here can spread out even further so that is what would happen; if second rod bigger more would go onto second one becuase allows them to spread out even more

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11
Q

can charge something by induction!

A
  • this means bring charged rod near other piece of metal but dont touch it! well the engatives and positives in the other rod can move want to move as far away as possible form negative charges from new rod, so net amount of negative charges mvoe to the opposite side of one rid to get away from new rod to laeave total amoutn of charge on side near rod, deficet of electrons
  • e spread out
  • now these positives are closer to the negatives, so these postivies in the rod are attracting negatives* and the negatives repel the other negatives, dont cancel causes the rod to be attraced to the other rod
  • means if took charged rod and brought it to empty soda can and bring rod close can will start moving toward rod
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12
Q

how you charge by induction

A
  • example of two rods isnt charged by induction, charged by induction is when you take rod and stick in ground or connect it to ground, palce where can gain/steal/take infinitly amount of electrons or deposit electrons infinite number and ground would not care, like metal of your car can supply lots of electrons or take them thing will not notice or care
  • so now if bring metal rod with originally no net charge electrons now leave when attache dto ground, so then your rod is no longer uncharged has net amount of charge, not all going to leave still some electrons, but the rod that used to be uncharged now has a net amount of positive charge in it, charged this rod without even touching it because let negative electrons leave** if clever can cut the wire before take away thing that induced the charge, if now remove it far away, electrons negatives would have come back to rod, but cant rejoin positive becuase wire snapped, now stuck no way for these electrons to get back because you have cut the cord
  • calld charged by induction quick way to do it!
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13
Q

so with ballon and the wall…..

A
  • take a balloon, charge it up by rubbing it against hair steels electrons becomes negatively charged
  • take it and put near wall or ceiling, if lucky sticks there- seiling is an insulating materials electrons arent being transfered but atom can reorient or poalrize! negatives in atom can shift to one side other side becomes mor epositive, causing net force btw ceiling and ballon because positives are a little closer to negatives in ballon
  • negatives and positives attracting, greater force than negatives repeling other engatives in ceiling
  • ballon also insulator made of rubber
  • ceilign attracting ballon and ballon attracting ceiling, so ballon can stick because of insulating material’s ability to polarize and cause electric attraction, can interact with somethign electric because atom can shift and polarize!
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14
Q

electric field

A
  • allows us to imagine that somehow the charge is affecting space around it in some way, creates field that whenever put another charge in that field can predict how field will impact charge
  • C’s law= force btw two charges =kq1Q2/r2
  • r=distance, can be d
  • E= kQ2(whatever charge is creating field) / r^2 or d^2
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15
Q

charge is

A

scalar

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16
Q

electric field is a

A

vector quantity! becuase vector quantity divided by scalar quantity charged, is vector quantiy!

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17
Q

electric field at a point

A

F = qE

units= N/C makes sense becuase Force divided by charge

The units of electric field are N/C. In this sense, the electric field is the force per unit charge that will be experienced by a charged particle entering the field. This implies an important relationship between electric fields and forces:

F = qE
In this case we are relating the vectors for the electric field and the resulting force, not just their magnitudes.

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18
Q

electric field 3

A

For a variety of reasons, it is often simpler to phrase problems in electrostatics in terms of electric fields rather than electric forces. An electric force is always between two charges, whereas an electric field emanates from a single charge. We say that a given charge creates an electric field and, whenever another charge enters this field, it will experience a force. At this point, there is no formal difference between the two descriptions; it is only a matter of convenience. The electric field of a point charge is:

E = kr q2

where q is the charge creating the electric field.

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19
Q

how to draw an electric field

A

Graphically, the effects of an electric field can be represented using field lines. Field lines point in the direction in which the force on a positive charge would be directed. In the picture below, a positive charge has field lines pointing away from it:

positive charge will accelerate outward at an every slowing rate! when really close to positive charge its very strong, as get far away field becomes weaker and weaker, radially outward! goes straight out away from charged cue, called electric field lines

This indicates that another positive charge would be repelled. Of course, a negative charge would experience a force in the opposite direction. The density of field lines represents the strength of the electric field. As we’d expect, the closer you get to the positive charge, the denser the field lines become. further lines go from center of positive charge, shorter vectors get!

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20
Q

Imagine we have a sphere that is negatively charged. The electric field would show that …..

A

that an imaginary positively charged particle is pulled towards the sphere by the electric force. The electric field would always point towards the sphere, because we always use an imaginary positively charged particle to determine the electric field. As we move away from the sphere, the electric field gets weaker and weaker.

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21
Q

electric potential energy

A

Electric potential energy is the energy that is needed to move a charge against an electric field. You need more energy to move a charge further in the electric field, but also more energy to move it through a stronger electric field.

Imagine that you have a huge negatively charged plate, with a little positively charged particle stuck to it through the electric force. There’s an electric field around the plate that’s pulling all positively charged objects toward it (while pushing other negatively charged objects away).

You take the positive particle, and start to pull it off the plate, against the pull of the electric field. It’s hard work, because the electric force is pulling them together. If you let the positive particle go, it would snap back to the negative plate, pulled by the electric force. The energy that you used to move the particle away from the plate is stored in the particle as electrical potential energy. It is the potential that the particle has to move when it’s let go.

If you pulled the positive particle further away from the plate, you would have to use more energy, so the charge would have more electrical potential energy stored in it. If we doubled the charge on the plate, again, you would need more energy to move the positive particle. If we doubled the charge on the positive particle, you would need more energy to move it. You get the idea.

Imagine that instead of a negatively charged plate, our plate is positively charged. Our positive particle would be pushed away from the plate since they are both positively charged. This time, we have to put in energy to try to move the particle closer to the plate, instead of to pull it away. The closer we try to move it to the plate, the more energy we have to put in, so the more electrical potential energy the particle would have.

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22
Q

what is electric potential?

A

The electric potential, or voltage, is the difference in potential energy per unit charge between two locations in an electric field. When we talked about electric field, we chose a location and then asked what the electric force would do to an imaginary positively charged particle if we put one there. To find the electrical potential at a chosen spot, we ask how much the electrical potential energy of an imaginary positively charged particle would change if we moved it there. Just like when we talked about electric field, we don’t actually have to place a positively charged particle at our chosen spot to know how much electrical potential energy it would have.

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23
Q

What if our plate was positively charged?

A

A positively charged particle would be pushed away from the plate. This is the exact opposite of the last case. Near the plate the electrical potential is high and far from the plate the electrical potential is low.

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24
Q

Let’s say we have a negatively charged plate.

A

We know that a positively charged particle will be pulled towards it. That means we know that if we choose a spot near the plate to place our imaginary positively charged particle, it would have a little bit of electrical potential energy, and if we choose a spot further away, our imaginary positively charged particle would have more electrical potential energy. So we can say that near the negative plate the electrical potential is low, and further from the negative plate the electrical potential is high.

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25
Q

cell membranes- electrical potential

A

The membranes that surround your cells are comprised of thin layers of molecules that stick together to form a continuous, two-dimensional sheet. The sheet is held together because the molecules that form the membrane have special distributions of electric charges that allow them to stick together without dissolving in the water surrounding the cell.

Because the membrane is held together by the attraction of opposite charges, it is possible to overcome this attraction by applying a large electric potential across the membrane.

In some cells, applied electric potentials are used to open and close the cell membrane in order to allow nutrients and waste to enter and exit the cell. In nerve cells, the electric potential across the membrane can be easily changed, allowing the cells to carry messages encoded in their membrane potential.

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26
Q

electric potential energy vs electric potential

A

electrical potential energy is assocaited with a charge. its associated with a particle that has some charge, only that particle has some eenrgy. its how much total work is needed to mvoe it from one point to another, the difference in X J, associated with a particle

vs.

electric potential which is assocaited with a positioN!

can figure out electric potentil energy by multiply electric potential X charge. how much work per unit charge does it take to move any charge per unit charge from point A to point B, this is indepdent on size of particle, depends on position so would be liek 12 J divided by 2 C, = 6 J/C which is the same thing as 6 volts!

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27
Q

voltage

A

regardless of how small or big, what the difference in potential enegy would be if at two different points, so comparing points in space!

electric potential V- abstract number associated with points in space

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28
Q

how do electrons move through

A

Electrons actually move very slowly through direct current (DC) electric circuits. Remember that DC is the simple circuit you get when you connect something like a battery to a lightbulb to make a flashlight: the transfer of energy between the battery and the bulb is due to the kinetic energy of the electrons that move through the wires of the circuit.

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29
Q

After MgCl2 dissolves in a neutrally charged solvent, what is the net charge of the solution?

A

=The solution remains neutrally charged.

The law of conservation of charge states that the net charge of an isolated system remains constant.

When the ions are added to a neutrally charged solvent like water, the overall solution remains the same.

MgCl2 dissolves into one +2 cation and two -1 anions.

The only way to change the net charge of a system is to introduce a charge from elsewhere, or to remove a charge from the system. In this closed system, the resulting Mg2+ cation and Cl- anions will yield an overall neutral charge.

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30
Q

In the figure below, spheres q1 ,q2 , and q3 have the same positive charge magnitude. Which of the following is a possible direction for the net electric field vector on q4?

A

The superposition principle means that the net electric field vector is the sum of all individual electric field vector arrows made by each charge’s interaction with the charge being affected.

If q1​ and q2​ have the same positive charge magnitude, then their electric field vector arrows should cancel out in the horizontal direction. This will occur whether q4​ has a positive or negative charge.

Since there is no other charge to influence the direction of the net electric field vector in the horizontal direction, the correct vector direction should not be angled toward the left or the right. An arrow that points straight up or straight down are possible directions for the net electric field vector.

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31
Q

In five seconds, a point charge moves from position A to position B as shown in the diagram below. Which one of the following two paths require the most energy?

A

The amount of time is not relevant to this problem.

In electrostatics, energy is determined by product of the point charge magnitude, the displacement of the point charge, and the value of the electric field, for a constant field in the direction of displacement:

W=Fd

W=qEd

When the displacement is the same for both paths of a point charge along a constant electric field, the energy expended is equivalent.

so the answer is that both paths require an equal amount of energy b/c work is independent of the path

32
Q

A constant electric field moves a positive point charge from one position to another position so that the change in electric potential is −450 V. Which of the following must increase during this movement?

A

= the charge’s velocity

According to the question stem, there is an electric potential difference between the two positions.

The negative change in electric potential indicates that the point charge moves from a position of higher electric potential to a position of lower electric potential.

The point charge displacement as a result of a constant electric field indicates that the point charge moves to a more favorable, downstream position. This indicates that the charge loses potential energy and gains kinetic energy during the movement.

Just like a ball dropped from a height due to the force of gravity, the point charge moves to its new location due to the force generated by the electric field on the charge. In both situations, the object being moved will increase in velocity during its movement.

33
Q

The magnitude of the electric force experienced by a point charge aaa distance ddd away from a source charge is affected by which of the following?

A

= the value of distance, d

The sign of the source charge affects only the direction of the electric force (either towards or away from a source charge), it does not affect the magnitude.

Similarly, the sign of the point charge affects only the direction of the electric force and not its magnitude.

The mass of an object is important for determining gravitational force, not electrostatic force. The electric force of a single point charge q at a distance d away from a source charge Q is given by the equation F=k (q1Q2/d^2). The signs of both charges will only affect the overall sign on the force value. The distance d is the only answer choice that affects the magnitude of the electric force.

34
Q

Sphere A and B have the same mass and charge magnitudes. They are placed a distance rrr away from each other so that gravitational forces and electrostatic forces allow both spheres to be in equilibrium. What would occur if sphere A doubled in charge?

A

the answer is both spheres would move away from each other with the same force!

In order for the two spheres to be in equilibrium, the forces on each sphere must cancel out. Drawing a free-body diagram will visually demonstrate the forces on each sphere.

The gravitational force can only act to attract both spheres toward each other. Therefore the electrostatic force in this situation must repel the spheres away from each other.

The formula for electrostatic force is FE=k0 Qq/r^2. Doubling the charge of sphere A will double the repulsive electrostatic force but not change the attractive gravitational force measurably since the added charge would have such a small mass.

The electrostatic force experienced by each sphere is the same because the electrostatic force equally accounts for the source charge as well as the point charge in the determination of its magnitude. Therefore, the spheres will move away from each other with the same force.

35
Q

Ohm’s law

A

V = IR

*voltage is electric potential, its potential energy per unit charged*(volts)

36
Q

current

A

I

= the amount of charge per unit time (amoutn of charge /water flowing through pipe at given time); how much charge flowing past a point in a circuit* in a sec

I = Q/t

37
Q

current 2

A

Current is the amount of charge that moves past a particular point in the circuit in a given unit of time. The unit of current is the Ampere (denoted by a capital “A”), which breaks down into C/s. By convention, the direction of current flow in a circuit is from the positive terminal of the battery toward the negative terminal, as if the current consists of moving positive charges. This is the direction in which positive current would flow, even though, in reality, only negatively charged electrons are actually moving.

38
Q

resistance

A

something that would keep charge from flowing at arbitrarily high rate, something that would impede water goind down pipe like narrowing of the pipe, narrowing of pipe is analogus to resistance

= PE (voltage) converte to ke flow of water through pipe, now every point in pipe water flowing pass will be lwoer becasue of bottle neck, narrowing analogous to resistance how much charge flow impeded*

unit OHMS! greek letter omega!

39
Q

amps

A

for current, Q (charge)/ time

40
Q

what is the direction of hte current?

A

Benjamin Franklin didn’t know about electrons when working on circuits, what he labeled as charge was flowing in his studies of electricity he denoted current as going from positive to negative terminal so its + to negtive, even though its opposite of flow of electrons**

as will see later, current doesnt always involve electrons*

remember voltage difference in how bad electrons want to get from one point to anotehr**

41
Q

resistors in series

A

Voltage total= equals potential drop across all devices, electrons really want to get to end, so go through resistance and experience a potential drop, each resistor a little less eager to get to end, voltage drop across each of the devices*

Vtotal= V1+V2+V3

all I are the same!!! all current through entire circuit is the same!

Rtotal= R1+R2+R3…..

42
Q

Resistors in parallel

A

For a circuit with resistors in parallel, the total or equivalent resistance is given by:

1/R total= 1/R1 + 1/R2 + 1/R3….

**current flows positive to negative, but really electrons flowing in other direction*

current going into the branch is equal to current going out of branch!

43
Q

resistance 2

A

REMEMBER IT IS A CONSTANT, resistivity is constant! will stay the same not changing material make up, size or dimensions that number that is the resistance is a constant if truly ohmic material! same no matter what voltage or current you put through it

  • if inc length of resistor, resistance will go up
  • if inc area, make larger diameter cylinder, current more room to flow through, bigger area to flow through not as restrictive, means resistance should go down! if put in mathematical formula, R should depend on length should be directly proportional to length, if inc area should get less resistance becuase more room to flow! resistance of resistors is inversely proportional to cross sectional areas!

geoemtry determines resistance as well as what mateiral is made of, some mateirals offer better resistance than others, nonemtals typically offer more resistance and metals offer no resistance

irs resistvity* bigger resivity of material more it naturally resists flow through it! the resistivity of copper will be small, resistivity of something like rubber is huge, can be in order of 10 ^13 huge range of possible resistivities** so bigger resisitivity bigger resistance

44
Q

resistivity

A

formula

R= p L/A

resisitivity will change by= length, resistivity or area

units= ohms X meters

45
Q

conductivity

A

how much something allows current, inversely proportional to resistivity

row = 1/ sigma (conductivity)

conductivty (sigma)= 1/row

something great conductor bad resistor

46
Q

difference btw voltage and current

A

current flows through a point

BUT voltage is across two points!! difference in electric potential of two points, why hook up volt meters in parallel; need huge resistance 100s to milliosn of ohms key idea do not want to disturb thing mesuring

can;t ask whats voltage through a point? no

can ask- whats voltage across two points in a circuit, that question makes sense!

voltmeters huge resistance

47
Q

voltmeter vs ammeter

A

voltmeter hooked up in parallel to circuit element want to determine vltage across

ammeter hooked up in series

48
Q

what is a capacitor?

A

Capacitors store energy by holding apart pairs of opposite charges. Since a positive charge and a negative charge attract each other and naturally want to come together, when they are held a fixed distance apart (for example, by a gap of insulating material such as air), their mutual attraction stores potential energy that is released if they are re-united. The simplest design for a capacitor is a parallel-plate, which consists of two metal plates with a gap between them: electrons are placed onto one plate (the negative plate), while an equal amount of electrons are removed from the other plate (the positive plate).

49
Q

capacitor 1

A
  • made up of two pieces of conducting materials like metals separated from each other!!!

JOB IS TO STORE CHARGE*

if connect two pieces of metal to a battery those two pieces of metal can store charge** once batteyr connected negative charges on lone side get attacked to postive terminal of battery, and that causes that pice of metal to become positively charge with less negatives than it does positives, piece of metal on left becomes negatively charg has more negatives than it does positive*

both pieces of metal have same magnitude of charge* if on + 6 C then other metal plate -6 C***

50
Q

capacigtor 2

A
  • even if diff sizes and shapes have to store equal adn opposite amount of charge
  • negative charges move, positive charge just sits there, negative charge attracted to positve erminal of battery start to get attracted to positive piece of metal as well* once this happens process stops and accumulated charge just sits there on pieces of metal, charges continue to sit there even when remove battery*
51
Q

C

A

how good that capacitor is at storing charge**8

C= Q (charge stored on capacitor) / voltage (across capacitor)

technically net charge should be zero, Q refers to magnitude of charge on one side of the capacitor, what voltage refers to in this formula whne a capaciotr stores charge it creates a voltage and difference in electric potential** high near psotive charges and low near negative charges**

units= Coulombs/Volt= Farad

52
Q

Capacitance is constnat

A

charge inc voltage also inc!

only way to change it is change physical set up, like material or make it farther apart, cant do it by changing ratio that makes capacitance

As you may recall, charges create electric field lines that point away from positive charges and towards negative charges. In a parallel-plate capacitor, the electric field lines point straight across the gap between the two plates. We know that electric fields and voltage differences go hand-in-hand, and so it also turns out that the two plates are at different voltages. The size of this voltage difference (V) is related to the charges on the two plates (Q):

Q= C V

The constant C is called the capacitance. It determines how much of a charge difference the capacitor holds when a certain voltage is applied. If a capacitor has very high capacitance, then a small difference in plate voltage will lead to a huge difference in the number of electrons (total charge Q) on the two plates.

53
Q

type of energy stored in a capacitor

A

electrical potential energy!

54
Q

energy of a capacitor=

A

1/2QV

*its 1/2 because during discharge all of the charges will not drop during total initial voltage v, all charges transfered after initial drops from less AND LESS voltage

each time charge gets transfered dec amount of charge stored on capacitor as voltage of capacitor keeps dec charge keeps decreasing*

or E=1/2CV^2

55
Q

capacitors in series

A

remember C=Qcharge/V-voltage

=1/Ceq= 1/C1 + 1/C2 + 1/C3

*when battery jooked up negative charge starts to flow, negative charge flows from right side of capacitor 1 to left side of capciotr 2, makes negative charge flow from right side of capcitor etc…. keeps flowing

because of way charging process works, all capacitors must have same amount of charge stored on them! no where else for charge to go but onto the next capaciotr in the line, good news means for capacitors in series charge stored on every capacitor will be the same, if found charge on one capacitor found charge on all other capaciotrs*

trick can use= imagine replacing all 3 capaciotrs with single equilvaent capaciotor**

56
Q

capacitors in parallel

A

Ceq= C1+C2+C3*

capacitance of capciotr is proportional to area of capacitance plate*

57
Q

dielectic 1

A

a nonconducting mateiral prevents pieces of metal from touching each otehr! which is important because if pieces of metal were touchign no charge would get stored! it will alawys inc capatiance of that capaciotr as logn as material is non conducting doesnt even matter what it is as logn as you do nto change area btw plates, inserting nonconducting material will always inc capatiance****

why does inc capaitance= charges stuck on plate negatives dont have a path to get back to positives so even after removing battery, voltage remains teh same that cahrge dit up, then place dielectic in btw capatiance, when placed in between plates negative charges in dieletic get attracted to positve sof capacitor, negatives cannot travel because dieletic is a nonconducting material, causing atoms to become poalrized in dielectic, atom stretches one end becomes overall negative adn one end becomes overall positive!

58
Q

dielectic 2

A

REDUCES VOLTAGE BTW CAPACiTIOr PALTES** reduces voltage because even thoguh still just as many charges onc apacitance plate, contribution to charges across plates are being canceled* soem charges on capacitor palte are having their contributon negated becuase negative charge right next to them now, so reduces voltage becuase of poliarzation of capaitance

capatiance will inc if voltage dec and cahrge stays the same

SO CAPATIANCE INC***** by lowering voltage*

59
Q

dielectic constant 3

A

INC capacitance by storing more charge! ALWAYS TRUE, k (dielectic constant) is always greater than 1***

inc capaitane because dec voltage**, total charges same but their contribution across plate partially canceled; voltage dec because of polarization of charges* C= Q/V so divide by smaller number will inc C

Dielectrics are materials that don’t allow current to flow. They are more often called insulators because they are the exact opposite of conductors. But usually when people call insulators “dielectrics,” it’s because they want to draw attention to a special property shared by all insulators: polarizability.

In a dielectric, the charges are valence electrons that are stuck inside atoms of a crystal or polymer, and so current doesn’t flow at all. The electric field, however, still exerts a force on the charges. While the individual electrons remain tied to their parent atoms, they prefer to stay on the side of the atom that’s closer to the positive terminal. You can imagine the electrons wanting to jump off their parent atoms, but instead remaining leashed to them by the electrostatic forces that bind valence electrons to the nucleus:

60
Q

dielectric 4

A

Just like a spring, the force that causes electrons to orbit the nucleus provides a restoring force that counteracts the force exerted by the external electric field from the battery. So as the battery’s electric field pushes the electrons further and further towards one side of the atom, the restoring force in the opposite direction that pulls them back towards the nucleus gradually increases. The final position of the electrons corresponds to when these two forces (the one from the nucleus and the one from the battery) balance each other out.

Because the external field causes the electrons in each atom to congregate on one side of the nucleus, the atoms are polarized, meaning they have a positive pole and a negative pole that are oriented with the direction of the electric field.

That said, if a large enough electric field is applied to a dielectric, the forces that want to push the electrons can actually overcome the force that tethers them to the atomic nucleus, resulting in the electrons being ripped off their leashes. Large electric fields ionize the atoms of a dielectric. This means large electric fields create free charges (electrons in this case) that are able to move freely through the material and carry current. This process is called dielectric breakdown because the dielectric transitions from being an insulator to a conductor. In most real-world capacitors, dielectric breakdown results in a spark and damage to the capacitor.

61
Q

dielectric 5

A

The presence of a dielectric in the gap of a parallel-plate capacitor increases the total capacitance.

The dielectric constant, k, is a property of the specific dielectric being used; it indicates how much the capacitance increases when a given dielectric is used. The higher the dielectric constant, the better a material functions as an insulator—for example, rubber has a very high dielectric constant, and so it is often used a protective coating around high voltage wires because its high k makes it a very poor conductor.

Common dielectrics include wood (k = 2), beeswax (k = 4), glass (k = 5), and plastic (k = 5). The capacitors inside consumer electronics like your computer usually use plastic as a dielectric because of its low cost and high dielectric constant value, allowing the capacitors to be made really small.

The presence of a dielectric increases the capacitance because it actually decreases the electric field inside the capacitor by a factor of the dielectric constant. When all of the atoms in a dielectric polarize, they end up creating a field that points in the opposite direction to the applied field, resulting in a smaller field electric field: look on image

The presence of a dielectric between the two plates actually decreases the electric field inside the capacitor. This should tell you a lot about the way that sticking dielectrics in capacitors messes with their properties: capacitors store energy within their electric fields, and so changing that field changes everything!

62
Q

dielectic ex 1

A

For example, imagine that you’ve charged up your favorite parallel plate capacitor to a voltage of 6V across the plates. This 6V difference corresponds to an electric field between the plates, which is the voltage divided by the distance between the plates, d. If you have a huge capacitor with a plate separation of 1 cm, that’s an electric field of 6 V/cm. But imagine that you stick a big chunk of beeswax (k = 3) into your capacitor after it’s been fully charged and disconnected from the battery. All of the sudden, the charges on the molecules in the beeswax will shift and orient themselves in such a way that they partly cancel out the original field. Because the total amount of polarization is related to the dielectric constant, your capacitor now has an internal field of only 6/3 = 2 V/cm. Since the plate separation is the same, this corresponds to a new capacitor voltage of only 2V!

63
Q

dielectic ex 2

A

Another way to think about this is to remember that Q = CV, where Q is the charge of the capacitor, V is the voltage difference across the two plates, and C is the capacitance. For this setup, Q is fixed because the capacitor is not connected to any power source that can change the relative amount of charge on the two plates. Since adding the dielectric increases C by a factor of 3, the voltage must decrease by a factor of three in order to keep Q the same. You can now plug the new values of Q, C, V into the equation for the energy stored in a capacitor, E = 1/2 C V^2, and determine that the energy stored in the capacitor also decreases by a factor of 3.

The situation is very different when you leave the capacitor connected to the 6V battery as you insert the dielectric. This time the voltage, V, is fixed at 6V in the equation Q = CV, and so when you add the dielectric and cause the capacitance to jump by a factor of 3, the difference in charge across the two plates, Q, also increases by a factor of 3. In this situation, using the formula E = 1/2 C V^2 reveals that the energy stored in the capacitor actually increases by a factor of three.

64
Q

lightning

A

If you’re ever in danger of being struck by lightning, sometimes all of the hairs on your head will stand on end until your head looks like a giant puff ball. This usually provides a good warning that you should immediately take shelter or move away from where you are and take cover indoors. It turns out that the reason for this odd effect is that your hair itself is a dielectric!

When you’re dealing with the kinds of voltages found in lightning strikes, the soggy ground beneath you is pretty conductive, and your body is, too. But your hair is not conductive. Human hair is such a good insulator that it actually used to be used as shielding in some old-school electrostatic machines. Thus if lightning is about to strike you, your hair acts like the dielectric in a capacitor, where the two conducting plates are the clouds (which have a huge negative charge) and the soggy ground below (which builds up a large positive charge due to induction). Thus, as charge builds up in the cloud, an electric field builds up in your hair. But unlike the glass or plastic inside a parallel-plate capacitor, the strands of your hair can easily move around individually, and so the electric field causes them to rise up, towards the clouds. Just like the individual electrons in a polarizable dielectric, the charges in them want to complete the circuit and travel up to the clouds, but they can’t quite make it because they are tethered to your head!

When lightning eventually does strike, it serves as a sort of dielectric breakdown in which current can suddenly flow through the air and your hair, through your body, and into the ground—so be sure to make a run for it before that happens!

65
Q

Capacitors and energy

A

Once opposite charges have been placed on either side of a parallel-plate capacitor, the charges can be used to do work by allowing them to move towards each other through a circuit. This usually requires them to travel through a circuit (as current) and perform some task, like illuminating a light bulb, along the way. The total energy that can be extracted from a fully charged capacitor is also related to the capacitance and voltage,

E = 1/2 CV^2

If you attach a capacitor (with capacitance C) to a battery (at voltage V), it will slowly develop a charge on each plate (Q) as electrons build up on one plate and then exit the other. Once you remove the battery, this difference in charge between the two plates remains indefinitely, until the capacitor is connected to a circuit (such as a light bulb) through which it can discharge. Once this occurs, charges will slowly pass out of one plate of the capacitor, move through the circuit, and onto the other plate. Capacitors function a lot like rechargeable batteries. The main difference is a capacitor’s ability to store energy doesn’t come from chemical reactions, but rather from the way that its physical design allows it to hold negative and positive charges apart. This makes capacitors very fast at charging and discharging, much faster than batteries. They are essential for applications where rapid bursts of current are needed, such as camera flashes.

66
Q

Do capacitors store charge?

A

Capacitors do not store charge. Capacitors actually store an imbalance of charge. If one plate of a capacitor has 1 coulomb of charge stored on it, the other plate will have -1 coulomb, making the total charge (added up across both plates) zero. If you short circuit the capacitor by connecting the two plates with a wire of negligible resistance, you’ll see a sudden rush of current (depending on the size of the capacitor, this can result in sparks) as the electrons on the -1 coulomb plate rush onto the +1 coulomb plate. This sudden rush of current releases all the energy that’s stored in the capacitor.

To help us understand parallel plate capacitors, consider this situation. Imagine you start with two metal plates with no difference of charge (Q= 0). You attach a battery, which at first adds a single electron to one side of the capacitor. The electron has an electric field that repels other electrons, and this field reaches through space and pushes on the electrons in the other plate, causing that plate to acquire an induced positive charge. Now your first plate has a charge of -1e, and the far plate has a charge of +1e, where e is the way we normally write the elementary charge of a single electron.

Now imagine repeating this process over and over, until a considerable amount of negative charge has built up on one plate and induced an equal positive charge on the other plate. At some point, the existing negative charge on the first plate will be so repulsive that it prevents you from adding any more negative charges to that plate. In this case the capacitor is fully charged. This maximum charge Q corresponds to the final voltage of the charged capacitor in the relation Q= C V.

67
Q

Distance on capacitor

A

The further apart the two plates are, the less the free electrons on the far plate feel the push of the electrons that you’re adding to the negative plate, making it harder to add more negative charges to the negative plate. If the plates were infinitely far apart, you would just be adding negative charges to an already negative metal surface, which would be pretty hard. If the plates were very close to each other or even touching, you essentially would be making current flow through a short circuit, which would be easy. This means that the capacitance of a parallel plate must be inversely related to the plate separation.

68
Q

area

A

It’s a lot easier to add charge to a capacitor if the parallel plates have a huge area. Two wide metal plates would give two repelling like charges a greater range to spread out across the plate, making it easier to add a lot more negative charge to one plate. Likewise, a very small plate area would cause the electrons to get cramped together earlier, making it harder to get a large difference in charge for a given voltage. From this we can guess that the capacitance of a parallel plate must be related to the plate areas

69
Q

These two principles (area and distance) can be expressed as the parallel-plate capacitor formula:

A

C = ɛ A/d

A is the area of the plates, and d is the distance between the plates. ɛ is a constant called the permittivity, which determines how easily the air between the plates allows an electric field to form. If a different insulating material is used inside the gap, this constant will have a different value, and so materials with a higher value of this constant generally make better capacitors.

70
Q

Cardiac defibrillators

A

Sometimes the regular rhythm of your heart pumping blood around your body stops beating regularly. It turns out that the most effective way to make the heart start ticking regularly is simply to shock it with a giant capacitor. When a patient’s heart beats too fast or doesn’t beat in the correct sequence (called fibrillation), paramedics attach two electrodes to the patient’s chest. These electrodes are connected to a defibrillator, which consists of a battery and a giant capacitor. When paramedics use defibrillators, batteries slowly charge the capacitor by adding electrons to one plate and pulling an equal number of electrons off of the other plate. Once the capacitor is charged to the set voltage, paramedics rapidly discharge the capacitor through the electrodes on the patient’s chest in hopes of resetting the heart beat.

71
Q

Suppose two parallel plates are inserted into a solution, and the current that passes between them for a known potential difference is used to measure the electrolytic resistivity of the solution. How would this resistivity change if the area of both of the two plates was doubled, at a fixed separation distance?

A

The measured resistance is given by the relation R = rho L/A, where A is the plate area, L is the plate separation, and ρ (rho) is the resistivity.

If the plate area were doubled, the resistance measured would decrease by a factor of 2.

The resistivity is found by dividing the resistance by the area and separation of the plates, and so this factor of two would cancel out.

Resistivity is an intrinsic property of a medium, and so it remains the same when the area of the plates is changed. ANSWER= IT WOULD REMAIN THE SAME

72
Q

An unusual alloy has a resistivity of 4 X 10-8 Ohms meters. Suppose that a hollow pipe is made from this alloy that has an inner diameter of 2 meters and an outer diameter of 4 meters. What is the total resistance of a 10meter length of this pipe?

A

Resistance is given by the relation R=ρ A/L

The cross-sectional area of the hollow pipe is just the enclosed area of the outer diameter minus the enclosed area of the inner diameter.

The cross-sectional area is A = pi (2)2 - pi (1)2 = 3 pi= 9m2. R = 4 X10-8 10/9 = 4 X 10-8 Ohms.

73
Q

Which of the following would be the resistance of an ideal voltmeter, which could measure a circuit while affecting it the least?

A

A voltmeter is placed in parallel with the portion of the circuit for which potential difference is to be measured.

In order to avoid perturbing the circuit, the voltmeter must draw no current.

The voltmeter draws minimal current when it has maximal resistance due to Ohm’s law.

The ideal resistance of a perfect voltmeter would be ∞, infinity.

74
Q

Which of the following would be the resistance an ideal ammeter, which could measure a circuit while affecting it the least?

A

A ammeter is placed in series with the portion of the circuit for which current is to be measured. In order to avoid affecting the flow of electrons through the circuit, the ammeter must itself not obstruct the flow of electrons.

The ammeter obstructs the least current when it has minimal resistance due to Ohm’s law.

The ideal resistance of a perfect ammeter would be 0.

75
Q

law of conservation of charge

A

saying cannot have charges magically appear or disappear however much charge you start with is the amount of charge you have in teh end, said that when did parallel circuits adn series circuits lets think about what’s going on with series circuit, current same becuase no where else for charge to go except from all resistors that is law of conservation of charge

parallel circuit- currents have to add up becuase however much charge have has to get divided by branches but cant gain some or lose some magically* shouldn’t really be that earth shattering a thing, it should be like that makes common sense