Class 4: Electrostatics, Capacitors, Batteries, Resistors

insulators (dielectric)

(contrast to conductors) = a material that doesn't have free charges - electrons are tightly bound to their atoms and thus are not free to roam throughout the material - ex: rubber, glass, wood, paper, plastic

Kirchhoff's Laws

*For a circuit containing one battery as the voltage source, the sum of the voltage drops across the resistors in any complete path starting at the (+) terminal and ending at the (-) terminal matches the voltage of the battery. *The amount of current entering the parallel combination is equal to the sum of the currents that pass through all the individual resistors in the combination.

Electric Potential and Potential Energy

*only changes to electric potential matter (just like only changes in height in gravitational potential energy) - if an object moves "with nature" (i.e in the direction that gravity points), then potential energy decreases Wby-grav = +mgh deltaPEgrav = -mgh - if an object moves "against nature", then potential energy increases Wagainst-grav = +mgh deltaPEgrav = +mgh

All of the following kinematics statements must be true EXCEPT: A. an object can have zero average velocity with nonzero average speed. B. an object can have constant speed but nonzero acceleration. C. the total distance traveled by an object is the magnitude of its displacement vector. D. it is impossible for an object to change its position while having zero average velocity.

- Choice A is possible for any closed path (initial and final positions the same) - choice B corresponds to uniform circular motion - choice D is true because a change in position is a displacement (and average velocity is the magnitude of displacement per unit time). Hence, choice C isn't necessarily true: Total distance is a scalar that accounts for the path taken between initial and final positions, whereas displacement is a vector pointing from the initial position to the final position. Unless the path from point A to point B is a straight line, total distance will be greater than the magnitude of displacement.

The horizontal component of velocity in ideal projectile motion determines which of the following? I. total range II. maximum height III. time of flight A. I only B. I and II only C. I and III only D. I, II, and III

- The horizontal component of velocity in projectile motion determines the total horizontal displacement, i.e., the range. - Because all of the acceleration is in the vertical direction, the vertical component of velocity determines maximum height and time of flight, eliminating II and III. While it is true that the range depends on the time of flight according to dx = vxt, the time in this equation is the same time that is determined by the vertical component.

Energy stored by a capacitor equation

- When a capacitor is charged, it also stores energy

Change in Electrical Potential Energy (J)

- a charge experiences no change in potential energy when its initial and final positions are at the same potential - the path taken by the charge is irrelevant. Like the gravitational force, the electric force is conservative; all that matters is where the charge began and where it ended; the specific path it takes doesn't matter - positively charged particles naturally tend toward lower potential and negatively charged particles tend toward higher potential - "moving with nature" = (-) deltaPE

The electric field strength at a point at a distance from a source charge is NOT dependent on which of the following? A. The sign of the source charge B. The nature of the medium surrounding the source charge C. The magnitude of the source charge D. The distance from the source charge

- absolute value symbols - E clearly depends on both the magnitude of the source charge Q and the distance r from Q; this eliminates choices "the magnitude of the source charge" and "the distance from the source charge". - The sign of the source charge affects only the direction of the electric field vectors; they will point away from the source charge if it is positive and toward the source charge if it is negative. The sign of the source charge does not affect the strength of the field. Thus, "the sign of the source charge" must be the answer. - (Note on the choice "the nature of the medium surrounding the source charge": The field created by the source charge is indeed affected by the nature of the medium surrounding it. For example, consider the case of a dielectric placed between two charged plates of a parallel plate capacitor, with the battery no longer attached. The presence of the insulating material will decrease the strength of the electric field created by the plates. The same would be true if a point charge were placed inside an insulating material. The equation E = kQ/r2 assumes that the source charge is in vacuum.)

Electric charge

- an atom is composed of a central nucleus (which is itself composed of protons and neutrons) surrounded by a cloud of one or more electrons - the fact that an atom is held together as a single unit is due to the fact that protons and electrons have a special property: they carry electric charge, which gives rise to an attractive force between them protons carry + charge electrons carry - charge neutrons have no electric charge

Electric charge summary

- can be positive or negative (unlike mass, length, speed)

video: Electric Potential Energy summary

- electric potential energy obeys the same relations as potential energy does generally: work done on the system can raise its value, and its change equals the negative change in KE - remember that for a negative charge, and increase in electric potential (V) energy corresponds to a decrease in electric potential energy (electrons move toward higher potential)

electric potential (V) vs electric field

- equipotential = equal potential because the potential is the same at every point on them (Q=1/r and r= same distance) - as we move around the circle, the electric field changes (because the direction of E changes), but the potential doesn't change

video: dielectric

- if inserted between the plates of a capacitor increases its capacitance by a factor of the dielectric number, k - inserting or removing a dielectric requires positive or negative work depending upon whether the charged capacitor is connected to a battery or not. Consider which quantity is constant in the equation for PE

Resistance equation (Ohm's Law)

- if you have greater resistance it will require more voltage to get the same current - metal wire and rubber wire have different resistances; this is why touching a metal to the two terminal ends of a battery you get a current, but not with the rubber - metals have low intrinsic resistance - insulators (like rubber) have high intrinsic resistance to the flow of charge - insulators have very few free electrons, there's going to be basically no current, even with an applied voltage = why we get essentially 0 current with rubber wire

Properties of conductors

- imagine we place a whole bunch of electrons on a piece of metal. It is now negatively charged. Since the electrons repel each other, they'll want to get as far away from each other as possible. As a result, all this excess charge moves (rapidly) to the surface. - any net charge on a conductor resides on its surface - since there's no excess charge within the body of the conductor, there cannot be an electrostatic field inside a conductor - you can block out external electric fields by simply surrounding yourself with metal; the free charges in the metal will move to the surface to shield the interior and keep E = 0 inside

Current in a conductor equation

- induced by voltage across the conductor (voltage creates a current) - amount of charge that moves past a certain point per unit time **Q = n(+-e) still can use to plug into current equation [I] = A = ampere = C/s = Coulomb/sec - direction of current flow defined by the movement of positive charge (opposite the direction of electron flow) *voltage causes current to flow (charges don't just start moving and that is what causes the potential difference; the charges are ALREADY moving but the voltage introduces the general trend for positive and negative charges to move about their respective potentials = current) **the charges that flow in a current are ALREADY in the wire: they are not supplied by the voltage source

value of elementary charge

- measured in Coulombs (C) - when an atom (or any other object) contains the same # of e as p, its total charge is 0 = the object is electrically neutral - an object is charged when there's an imbalance between the # of e and p - when #e > #p the object is negatively charged - when #p > #e the object is positively charged - if a neutral atom has electrons removed or added, we say that it has been ionized, and the resulting electrically charged atom = ion - a positively charged ion = cation - a negatively charged ion = anion

electric potential (V)

- no direction because scalar quantity (also no absolute value symbols like in the electric field equation) - the potential is the same at every point that is a distance r from Q = equipotentials (has no direction like E field) - if Q is (+) charge, then the values of the potential due to this source charge are also (+) (if Q is positive the kQ/r is positive) - the sign of the potential (+/-) is not an indication of a direction, because potential is scalar and has no direction

Direction of electric field

- positive charges want to move in the direction of the electric field [E] - negative charges want to move opposite the direction of the electric field [E]

Electric field lines from a point charge

- the electric field lines exit from positive and enter negative charges. - Since the axon is negatively charged, the electric field lines will be entering the axon - superposition applies: figure out what the electric field due to one charge is, add that to the electric field due to another charge and calculate the net electric field E=kQ/r^2 [E] = N/C=V/m

Without air resistance, an object dropped from a plane flying at constant speed in a straight horizontal line will A. fall straight down to the ground in a vertical line. B. move ahead of the plane. C. remain vertically under the plane. D. quickly lag behind the plane.

-remain vertically under the plane. In the absence of any additional forces like air resistance, the only acceleration for an ideal projectile is gravity, acting straight down. Since the object begins with some horizontal speed from the plane, choice A can be eliminated. Since gravity is perpendicular to the initial velocity, the horizontal velocity will not be impacted and the plane and object will remain in a vertical line, eliminating choices B and D. Since the motion of the projectile is a composition of the vertically accelerated motion (the free falling object) and the horizontal motion at constant velocity, the projectile will remain under the plane so long as the plane doesn't accelerate.

Two copper wires are tested for resistance. The first wire is longer and thinner than the second wire. Which wire has the higher resistivity? A. The first wire, because resistance increases with increased length and decreased area. B. The second wire, because resistance increases with decreased length and increased area. C. Neither wire, because resistivity depends only on the material, and both wires are made of copper. D. It cannot be determined without knowing the voltage and current, because Ohm's law defines resistance as a ratio of voltage over current.

C. Neither wire, because resistivity depends only on the material, and both wires are made of copper. Resistivity is a measure of a material's intrinsic resistance, and is dependent only on the material itself. Since both wires are made of copper, the resistivity of each wire will be the same. - Note that answer choice A would be correct if the question were asking for resistance (BUT ASKING FOR RESISTIVITY = HOW MUCH A MATERIAL OPPOSES THE FLOW OF CHARGE THROUGH IT). Note that answer choice D correctly states Ohm's law, but is incorrect because resistance is determined by the wire and is fixed for Ohmic materials, regardless of the voltage and current.

Electric field in a capacitor equation

Charges on a capacitor create a uniform electric field between the plates - both V and d are constants (distance isn't going to change between the plates like a radius term would) **An important use of capacitors is to create constant electric fields, which can be used to accelerate charged particles to known energies

Superposition of forces

Configurations of multiple charges create a net force on a single charge that is the vector sum of the force contributions from the interaction with each additional charge - if you have a set of 4 charges, and you want the net force on one of them, you will have three pairs of charges that each include the charge you are focused on. Must add the vectors ; 3 forces together - charges further away from the charge you are measuring are weaker forces

Electric Charge and Force

Coulomb's Law Fe = kQq/r^2 - attractive or repulsive - relatively strong force - inverse square law - this fore is stronger than the Fg Newton's Law of Gravitation - only attractive - relatively weak force - also inverse square law

Point charge Q is at the origin of a cartesian coordinate grid and has a charge of 2 nC. Point charge A is at the location (0 m, 3 m) on the grid and has a charge of -3 C. Point charge B is at the location (3 m, 0 m) on the grid and has a charge of -4 C. What is the magnitude of the net force acting on point charge Q? A. 2 N B. 5 N C. 10 N Correct Answer D. 14 N

. The principle of superposition states that the net electric force on a charge due to a collection of other charges is equal to the sum of the individual forces that each charge alone exerts. Force is a vector, so the sum is found using vector addition. The equation to calculate the magnitude of the force between two point charges is F = k|Q||q| / r2. The force from charge A on charge Q is FA = (9 × 109)(2 × 10-9)(3) / 32 = 6 N. This is an attractive force (since the charges have opposite signs) so the direction of the force of charge A on charge Q is up (along the y-axis). The force from charge B on charge Q is FB = (9 × 109)(2 × 10-9)(4) / 32 = 8 N. This is an attractive force (since the charges have opposite signs) so the direction of the force of charge B on charge Q is right (along the x-axis). Adding these two perpendicular vectors creates a 6-8-10 right triangle, and the net force on charge Q is the hypotenuse of the triangle, 10 N.

Resistance equation

= How much an object (a wire) opposes the flow of charge through it [R] = ohms *resistors use up energy in a circuit (light bulb, toaster oven); typically as heat or light

Capacitor (units?)

= circuit elements used to store charge and energy (rapidly stores and discharges charge) - two conducting surfaces separated by an insulator (dielectric) [C] = F = farads C = 1/distance between plates k = 1 for vacuum and air k > 1 for other insulators **capacitors charge by being connected to a battery

Conductor

= material in which charges move freely - there is no net movement of charge (since all positive and negative charges are moving constantly) so current = 0 How do you get a current through the wire? - introduce a potential difference - high on one side and low on the other - positive charges (protons) move to regions of lower potential = -PE - negative charges (electrons) move to regions of higher potential = +PE *applying this potential difference (voltage) across a conductor induces a net movement of charge (i.e a current)

Uniform electric field

= same magnitude and direction at all points within the region, then the electrostatic force and the particles acceleration will be uniform - big 5 kinematics equations can be used to solve for final velocity, time etc. - W=Fdcostheta can also be used to calculate the work done by or against the electrostatic force to move a charge from one position to another - a large conducting plate that is charged (or a parallel plate capacitor) creates an electric field that is approximately uniform

Batteries

= source of voltage (potential difference that forces charge, aka electrons, to move) - maintains constant voltage **not source of charge/current** positive terminal = higher potential negative terminal = lower potential voltage of battery, V = change in potential between the + and - terminals

Source charge

= the charge that creates an electric field whether or not there's another charge in the field to feel it **it takes 2 charges to create an electric force, but it only takes 1 charge (the source charge) to create an electric field

Total electric charge is always conserved

= the total amount of charge before any process must always be equal to the total amount of charge afterward - this doesn't mean that electric charge cannot be created or destroyed

electromotive force (emf)

= the voltage that creates a current, since it is the cause that sets the charges into motion in a preferred direction (charges are present and moving, but their movement cancels out, when voltage is not present) - calling it a "force" isn't really correct, it's a voltage

Gravitational analogy

A positively charged particle can be thought of as any mass; it naturally "falls downward" when released from rest. A negatively charged particle can be thought of as a helium balloon - it "rise upward". The electric field can be thought of as g, which is a vector that points downward toward the center of the earth. - positively charged particles therefore naturally move in the direction of E (the electric field) - negatively charged particles naturally move opposite of E The potential can be thought of as the height above the ground - positively charged particles naturally move toward lower potential (they fall towards the ground, losing height) - negatively charged particles move toward higher potential (they rise up, moving away from gravity and the electric field, gaining height) *negative potentials can be thought of as "heights" below ground. The same rules apply

A spherical metal ball has a charge of Q. Which of the following is NOT a possible value of Q? A. 8.0 × 10-20 C B. 1.6 × 10-19 C C. 8.0 × 10-18 C D. 1.6 × 10-17 C

A. 8.0 × 10-20 C q=n9+/-e) Charge is quantized, so the charge on any object must be a whole number multiple of the elementary charge, 1.6 × 10-19 C. Only answer choice A represents a fraction of an elementary charge, and therefore cannot be a possible value. solving for n = A. 8.0 × 10-20 C/1.6 x 10^-19 = 0.5 which is a fraction and the others are whole numbers

A test charge of -3 C moves in a 180° arc from point A to point B on the opposite side of a source charge Q on an equipotential line. If the potential at point A is -6000 V, what is the change in potential energy as the test charge moves to point B? A. -36 kJ B. 0 kJ C. 36 kJ D. 18 kJ

B. 0 kJ Correct Answer . The change in potential energy can be found using the equation ΔPE = qV where V is the change in potential. In this case, the charge is moving along an equipotential, so there is no change in potential and no change in potential energy. Algebraically, ΔPE = (-3)(0) = 0 J.

Two charges, Q1 = -3.2 × 10-10 C and Q2 = +6.4 × 10-9 C, are separated by a distance of 1 cm. Let F12 be the magnitude of the electrostatic force felt by Q1 due to Q2, and let F21 be the magnitude of the electrostatic force felt by Q2 due to Q1. Evaluate the ratio F12 / F21. A. 12.8 B. 0.05 C. 1.00 D. 20

By Newton's Third Law, F12 and F21 form an action-reaction pair. Therefore, the ratio of their magnitudes equals 1; all the numbers given in the question are irrelevant.

Two cars of equal mass are traveling opposite directions on a highway. If one is moving twice as fast as the other, what is the relationship between their kinetic energies? A. One is a quarter of the value and the opposite sign of the other. B. One is half the value and the opposite sign of the other. C. One is a quarter the value and the same sign as the other. D. One is half the value and the same sign as the other.

C. Kinetic energy is always a positive scalar value or zero, so choices A and B are eliminated. It is also proportional to the square of the speed, so if the speed doubles and mass is the same, the kinetic energy will change by a factor of four.

test charge q is released from rest at point A and accelerates toward point B. If the charge on q is negative, all of the following are true EXCEPT: A. The potential energy decreases as q moves from point A to point B. B. The kinetic energy increases as q moves from point A to point B. C. The work done by the electric field is positive as q moves from point A to point B. D. The potential at point B is less than the potential at point A.

D. The potential at point B is less than the potential at point A. A. The potential energy decreases as q moves from point A to point B. -Since the charge is gaining kinetic energy, it is losing potential energy, eliminating choice A. B. The kinetic energy increases as q moves from point A to point B. - The charge accelerates from rest to point B, so there is a gain in kinetic energy, eliminating choice B. C. The work done by the electric field is positive as q moves from point A to point B. -By the work-energy theorem, the work done by the field is opposite the change in potential energy, so the work done by the electric field must be positive, eliminating choice C D. The potential at point B is less than the potential at point A. - Since the change in potential energy is ΔPE = qV and both ΔPE and q are negative, then V must be positive. This means the potential at point B must be greater than the potential at point A, making choice D false and the correct answer.

Two pulleys--one mounted in the ceiling, another anchored to a mass M suspended above the ground below--have a rope looped over them three complete times, so that there are six strands of rope running between the two pulleys. One end of the rope is tied to the center of the top pulley, the other is being held by a man standing next to the mass. The man pulls down with a tension T on that strand of rope causing the mass to rise at a constant speed. What is the net force pulling up on the bottom pulley? A. Mg B. Mg / 3 C. Mg / 6 D. Mg - T

Mg This is an easy problem to over-think, so consider the equilibrium of the system. The net force acting on the mass M must be zero, so the total tension force up for all the strands together is Mg. Note that the question is not asking for the force of tension

A positive test charge q is released from rest at point x. The value of the potential at x is 1000 V. If there are no other external forces and q accelerates to point y, which of the following is true? The electric potential at point y is lower than at point x and q is losing potential energy or The electric potential at point y is lower than at point x and q is gaining potential energy

The electric potential at point y is lower than at point x and q is losing potential energy If q is accelerating from rest toward point y, then it is gaining kinetic energy and losing potential energy, eliminating choices C and D. The change in potential energy is ΔPE = qV, and since q is positive and potential energy change is negative, the change in potential must be negative. Thus the potential at point y must be less than the potential at point x, eliminating choices B and D. Note that the value of the potential at point x is not needed.

A double tackle machine is a two-pulley system with the upper pulley attached to the ceiling and the lower pulley attached to a mass, with four strands of rope running between the two pulleys. What is the mechanical advantage of a double tackle machine lifting a mass M? A. 1 B. 2 C. 3 D. 4

The mechanical advantage of any simple machine such as a ramp, lever, or pulley system is defined as the ratio of the of the resistance force to the effort force. The resistance force is the weight Mg, whereas the tension in the four strands of rope is Mg / 4, so the mechanical advantage is Mg / (Mg / 4) = 4.

The Principle of Superposition

The net electric force on a charge (q) due to a collection of other charges (Q's) is equal to the sum of the individual forces that each of the Q's along exerts on q

A capacitor of capacitance C0 is fully charged by a battery of voltage V0, then disconnected from the battery. How much work is required to pull the plates of the charged capacitor apart to three times their original separation? A. -4C0V0^2/9 B.C0V0^2 C. 3C0V0^2/2 D. -C0V0^2/3

The work done on a system, in this case the charged and disconnected capacitor, is given by W = ΔPE. Because the capacitor is disconnected and cannot gain or lose charge, the best formula to use for its potential energy is PE = Q2/2C. Because C is inversely proportional to d, the separation between the plates, tripling the separation of the plates reduces the capacitance to (1/3)C0. Thus W = ΔPE = PEf - PEi = Q^2/(2/3)C0 - Q^2/2C0 = 2Q^2/2C0 = C0V0^2.

Drag is a force that acts on any object moving through a fluid. The drag force is always directed opposite the velocity of the object. Suppose a ball is thrown straight up into the air and a few seconds later it is caught. From the moment the ball leaves the thrower's hand to the instant before it is caught, what can be said definitively about the work done by drag? A. Wdrag > 0 B. Wdrag = 0 C. Wdrag < 0 D. The work done by drag over the flight is equal to the negative of the work done by gravity.

Wdrag < 0 The key point here is that the drag force is always directed opposite the motion of an object, so that over any segment of a path, it is doing negative work. Note that gravity would do zero work in this case because the object began and ended at the same height.

Charge on a capacitor equation

When connected to a battery in a closed circuit, capacitor will store charge Q = the charge; not the sum of the negative and positive charge because that would be zero; rather the total positive and total negative separately V = the voltage difference between the two plates of the capacitor, not necessarily the voltage of a battery the circuit (if system is in equilibrium then voltage difference will be the same as the battery)

A person is standing on the side of a hill. What is true of the person's weight and the normal force acting on his feet? A. They are equal and opposite and an action-reaction pair. B. They are equal and opposite but not an action-reaction pair. C. They are not equal and opposite but are an action-reaction pair. D. They are not equal and opposite and are not an action-reaction pair.

When standing on an incline, a person experiences three forces: weight, the normal force perpendicular to the surface of the incline, and static friction uphill. The sum of these three forces must be zero, so no two of them can sum to zero. Additionally, all three of these forces are acting on one body, not acting on two bodies as Newton's third law dictates for an action-reaction pair. They are not equal and opposite and are not an action-reaction pair.

Electric fields

a vector field (has mag and dir) created by source charge(s) = charge(s) creating the electric field; they're the source of the electric field - other nearby charges near the source charge that created the electric field will experience a force because of the field NOT because of the source charge ex: source charge = spider, while web = electric field *electric field vectors always point away from positive source charges and toward negative ones *the closer we are to the source charge, the stronger the resulting electric force a test charge would feel (bc Coulomb's law is an inverse-square law) FE=qE - q is scalar *whenever q is negative, the force F-on-q will always point in the direction opposite to the electric field *FE is in the same direction as E for +q

The area between a velocity versus time curve and the horizontal time axis from a time t1 to a time t2 represents what physical quantity? A. Displacement between t1 and t2 B. Average speed between t1 and t2 C. Final velocity at t2 D. Average acceleration from t1 to t2

a. The area under a curve has units of the product of the axes. In this case, because velocity is defined as displacement over a duration, the product of velocity and duration must be displacement.

For conductors

charge rests on the outer surface and the electric field inside is zero

Conductor

contains charges that are free to roam throughout the material - metals are the classic and most important conductors. In a metal, one or more valence electrons per atom are not strongly bound to any particular atom and are thus free to roam. If a metal is placed in an electric field, these free charges (called conduction electrons) will move in response to the field - another example of a conductor would be a solution that contains lots of dissolved ions (i.e saltwater)

Resistors in series have the same

current

A hollow metal sphere of radius 0.5 m has a net charge of 2.0 x 10^-6C. A solid metal sphere has a radius 0.5 m and a net charge of 4.0 x 10^-6C. The centers of the spheres are placed a distance of 2m apart and equilibrium is established. Compared to the electric field at the center of the hollow sphere, the electric field at the center of the solid sphere is; a. 2x the magnitude b. 4x the magnitude c. half the magnitude d. equal in magnitude

d = equal in magnitude The electric field inside of an electrostatic conductor is always zero. Therefore the electric fields at the centers of the solid and hollow sphere are both equal in magnitude

Electric field lines (are they vectors?)

electric field lines summarize all the electric field vectors in space - electric field at any point is tangent to the field line - strength of the electric field corresponds to the density of the field lines picture shows an electric dipole field **Electric field lines are not vectors, but they do indicate the directions of the electric field vectors (the tangents to the electric field lines) and magnitude (how close together the electric field lines are in the region) **notice how the lines are curved - vectors must be straight

Electric field vs. electric potential

electric field or electric potential can equal zero when the other is nonzero - must consider how electric potential is changing

Coulomb's Law

electric force between charged objects depends on the distance between the objects and the magnitude of the charges. GIVES MAGNITUDE NOT DIRECTION

Charge is Quantized

q = n(+/- e) since an object can become charged only by gaining or losing electrons or protons, the charge on an object can only be a whole number of +/- electrons, charge is quantized n = a whole number q or Q = electric charge

A metal sphere with no net charge is placed near a positive source charge. All of the following are true EXCEPT: A. The electric field inside the sphere will not be zero because the sphere has an uneven charge distribution. Correct Answer B. The sphere will be attracted to the source charge. Your Answer C. The net electric force between the sphere and the source charge is not zero. D. The source charge will force the electrons on the sphere to move.

think of sphere as a conductor The sphere is a conductor (metal) so when the positive source charge is placed near it, the free electrons in the metal will be attracted to it, and they will move to be near it. This makes choice D true and therefore incorrect. The movement of electrons creates a negative charge on the side of the sphere closest to the source charge and a positive charge on the far side of the sphere. Since the negative charge is closer to the positive source charge, there will be a net attraction between the source charge and the sphere, making choice B true and therefore incorrect. The attraction is the result of an electric force, making choice C true and therefore incorrect. Since the sphere now has a positively charged side and a negatively charged side, there is an induced electric field within it that perfectly cancels the external field (this is the field-focused way of explaining why the charges redistribute in a conductor, to cancel the external field). This makes choice A false, and the correct answer.

Resistors in parallel have the same

voltage

If the charged capacitor were separated from the battery... (what equation should you use and what is being held constant?)...how much work would it take to pull the capacitor plates apart to twice their original separation (what sign is work?)?

want work - C is changing - V is changing because separated from battery = no longer constant voltage - Q is constant because if capacitor plates are no longer connected by any wire then there is no way for current to flow (charge cannot move) use PE = Q^2/2C Won-system = +deltaPE because -(-PE) = +PE **If the capacitor is connected to a battery, V is constant, so use the form 1/2CV^2 ***If the capacitor is disconnected from battery, current cannot flow and Q is constant, so use the form Q^2/2C

Power Dissipated by a resistor: Joule heating law

when current passes through a resistor, the resistor gets hot; it dissipates heat. The rate at which it dissipates heat energy is the power dissipated by the resistor