phys 2212 test 3
micro or pico farads
(could be useful to check of answers are in right ballpark) what unit are practical capacitors usually measured in?
An external force must move the test charge against the electric field. Think about how gravity does work to move object towards its field, but cannot do work to move it away from the field. If someone were to move an object to move away from the gravitational field, they would being doing work and increasing potential energy (since it is a conservative force, as is the electric force).
A positive test charge is moved against electric field from one location to another. is work done by the field or an external force?
Decreases total resistance, Flow is divided between parallel resistors, thus increases current Adding resistors in parallel (how it affects resistance and current)
Adding resistors in parallel (how it affects resistance and current)
increases resistance, thus lowers current
Adding resistors in series (affect on resistance and current)
it is a scalar and this makes sense that it does not have a direction because it comes from an energy concept.
Is electric potential a scalar or a vector? why does this makes sense?
Kirchhoff's current law (1st Law) states that the current flowing into a node (or a junction) must be equal to the current flowing out of it. This is a consequence of charge conservation.
Kirchoff's Current Law
Kirchhoff's junction rule states that at any junction ( node ) in an electrical circuit, the sum of the currents flowing into that junction is equal to the sum of the currents flowing out of that junction. this is because of conservation of charge.
Kirchoff's Junction Rule
work is path independent, thus is potential (V=-w/q). the sum of all potential differences encountered while moving around a loop/ close path is zero. this is because energy is conserved and a charge around a closed path has ∆U=0.
Kirchoff's Loop Law
His voltage law states that for a closed loop series path the algebraic sum of all the voltages around any closed loop in a circuit is equal to zero.
Kirchoff's Voltage Law (KVL)
V=IR
Ohm's Law
we always use the magnitude of the charge, so the +Q is used.
a capacitor has an equal and opposite charge of Q. When performing calculations, is +Q or -Q used?
1/R = 1/R1 + 1/R2+...1/Rn
add resistors in parallel (equation)
R = R1+R2+...Rn
add resistors in series (equation)
it should be connected in series to measure the current in a wire. An ideal ammeter has zero resistance and is connected in series because objects in series experience the same current.
ammeter needs to connected in ... why?
yes! but the charges must be at rest.
can a conductor in electrostatic equilibrium be charged.
conductivity
current density depends on...
No! the terms refer to the same concept. Voltage is just used more colloquially to specify electric potential difference.
does voltage refer to something other than potential difference?
V = KQ/r²
electric potential of point charge (equation)
metals
electrons are the charge carriers in which type of material?
from E = -(gradient) V.
find electric field from electric potential
∆V = -( int ( from i to f) E dot ds ) the minus sign indicates that potential decreases along field direction
find electric potential difference from electric field
C= Q/∆Vc = ∈₀A/d
from the definition of capacitance, what is the capacitance of a parallel plate capacitor?
E = F/q and E = - (gradient) V
general relationships of electric field
moving them faster, having more of them per cubic meter, or by increasing the size of the pipe they're flowing through
how could the electron current be increased?
They differ in the fact that field is a vector field (because its a force concept) and potential is a scalar field (energy concept). However the idea that they convey are very similar, as they use the same method of describing a quantity of a source independent of a system. The equations that define the two concepts are very similar E=F/q and V = U/q (in both cases, the q's cancel and we are only left with source charge properties). The electric field is the force on a test charge divided by its charge for every location in space. The electric potential is the electric potential energy of a test charge divided by its charge for every location in space.
how do electric field and electric potential compare.
Ne = ie∆t
how do you find the number of electrons, Ne, that pass through a cross section during the time interval ∆t?
by connecting it to a battery! the work done by the battery charges the capacitor
how does a capacitor get charged?
A stretched spring holds the energy until we release it, then that potential energy is transformed into kinetic energy. A charged capacitor holds energy until we discharge it. Then the potential energy is transformed into kinetic energy of moving charges (current).
how is a charged capacitor analogous to a spring?
I = dQ/dt for a steady current, Q= I∆t
how is current defined as a rate?
to the negative end of the battery. field points to decreasing potential.
how is electric field oriented in a battery? why?
Simply, electric potential is the electric potential energy of a test charge divided by its charge for every location in space. Electric potential energy implies an interaction between more than one body, however potential is more of a quantification of the source charge's potential to interact with bodies.
how is electric potential different from electric potential energy?
the electric potential difference also gives the amount of work needed to move a unit charge from a reference point to a specific point against an electric field.
how is electric potential related to work?
EMF is the energy per unit charge exerted by an energy source. Potential difference is the energy released when the unit quantity of electricity passes from one point to another. Its a distinction made because the potential difference from an emf is not always equal unless the battery has no internal resistance and is an ideal battery
how is electromotive force (emf) different than potential difference
µe = Uc/Ad = (∈₀E²)/2
how is energy density of the electric field defined?
it is the inverse of conductivity
how is resistivity related to conductivity?
Q=C∆V
how is the charge on a capacitor found?
the field is perpendicular to the surface.
how is the external electric field oriented at the surface of a conductor in electrostatic equilibrium?
both bulbs are equally bright, brightness determined by current and resistance, both bulbs have the same resistance so this cannot impact relative brightness. It may seem as though the current changes as it passes through the bulb, but it does not and therefore the brightness is the same for both bulbs. the rate of electrons leaving a lightbulb (or any other device) is exactly the same as the rate of electrons entering the lightbulb. Current does not change.
if two identical light bulbs are connected to two charged capacitor plates, how bright are the bulbs relative to each other?
it will remain charged unless or until a current allows positive charge to move back to the negative plate. An ideal capacitor in vacuum would stay charged forever.
if you were to disconnect the capacitor once it is fully charged, does the capacitor remain charged?
V = Vmax(1-e^(-t/RC)
in an rc circuit, what is the expression of voltage in terms of its maximum voltage?
Uc = ∈₀/2(Ad)E²
in terms of electric field, area, and distance we find that energy is stored in the capacitor is?
no! depends on the geometry of the lines, the field is strongest where the lines are closest (E = V/d).
is the electric field the same at all points on an equipotential line?
yes! because it is path independent and work can store electric potential energy
is the electric force a conservative force?
yes! this means that no work is required to move the charges along the line
is the potential the same at points on an equipotential line?
the negative plate and the negative terminal of the battery are at the same potential. this is because the negative capacitor plate, the upper wire, and the positive terminal of the battery for a single conductor in electrostatic equilibrium. Any two points in a conductor in electrostatic equilibrium are at the same potential.
once the capacitor is fully charged and charges are no longer in motion, what can be said about the potentials of the negative plate and the negative terminal of the battery?
the positive plate and the positive terminal of the battery are at the same potential. this is because the positive capacitor plate, the upper wire, and the positive terminal of the battery for a single conductor in electrostatic equilibrium. Any two points in a conductor in electrostatic equilibrium are at the same potential.
once the capacitor is fully charged and charges are no longer in motion, what can be said about the potentials of the positive plate and the positive terminal of the battery?
Uc = Q²/2C in terms of potential difference : 1/2C(∆Vc)² note how this is reminiscent to the potential energy of a spring U = 1/2k(∆x)²
potential energy stored by a capacitor is equal to?
electric field tangent to the equipotential is E is 0. E is perpendicular to the equipotential surfaces and points "downhill" in the direction of decreasing potential
properties of electric field
R=rho(L)/A
resistivity equation
simply, electric potential difference is created by seperated positive and negative charge. charging a capacitor by moving electrons from one plate to another created potential difference across a capacitor. Batteries are common sources of electric potential.
sources of electric potential
E = V/d (from V = Ed)
special case relationship of a constant electric field (equations)
increases
the capacitor voltage ________ as the charge seperation continues
larger
the equivalent capacitance of a parallel combination of capacitors is _____ than any single capacitor in the group
smaller
the equivalent capacitance of a series combination of capacitors is _____ than any single capacitor in the group
∆Vc = Ed
the potential difference across a parallel plate capacitor is related to the electric field inside by?
the structure of the metal, by any impurities, and by the temperature. metals conduct better at low temperatures than high temperatures.
the value of the conductivity is affected by...
the number of electrons over time interval ∆t is Ne = ie∆t. each electron has magnitude e, hence total Q = eNe. Therefore, I = Q/∆t=eNe/∆t=e(ie)
through which equation canconventional current, I, and electron current, ie ?
current!
what are the charges that move from the potential difference (battery) to the plates through the conducting wire called ?
either decrease the amount of charge, or decrease the charge's drift speed through the wire. Anything else would be destroying electrons, which is impossible through conservations of mass and charge
what are the only two ways to decrease the current, I? ( other than changing v and r?)
parallel capacitors (note that this is different from a parallel plate capacitor; this is capacitors connected in parallel) and series capacitors
what are the two basic combinations of capacitors?
electric field exerting force on charge carriers
what causes current?
it depends linearly. to double the current, you must double the electric field.
what dependence does current (and current density) have an electric field?
power, thus current and resistance
what does bulb brightness depend on?
only the geometry of the electrodes. the formula simply provides a way to solve for it.
what does capacitance depend on?
how reluctantly the electrons move in response to an electric field.
what does the resistivity of a material tell us?
Q = (∈₀A/d ) ∆Vc
what equation results from combining the relationship between potential difference across a parallel plate capacitor to the electric field and the definition of the parallel plate capacitor?
parallel capacitors each have the same potential difference ∆Vc. kirchoff's voltage law. since they have they have the same potential difference, if the capacitance differs, so the charge on them must differ due to Q = C∆Vc
what fact allows us the determine the equivalent capacitance of parallel capacitors?
series capacitors have the same charge, Q
what fact allows us the determine the equivalent capacitance of series capacitors?
two equally, but oppositely charged electrodes. the two electrodes have zero net charge, but the separation between them creates a potential difference.
what is a capacitor?
the most common definition is a force with the property that the total work done in moving a particle between two points is independent of the path taken, but that explanation holds no merit (to me) without context. A conservative force results in potential energy (work is related to energy by W = ∆Emech aka work energy theorem). We can define a potential energy for any conservative force, just as we did for the gravitational force. For example, when you wind up a toy, an egg timer, or an old-fashioned watch, you do work against its spring and store energy in it. (We treat these springs as ideal, in that we assume there is no friction and no production of thermal energy.) This stored energy is recoverable as work, and it is useful to think of it as potential energy contained in the spring. Indeed, the reason that the spring has this characteristic is that its force is conservative.
what is a conservative force?
a conductor through which electricity enters or leaves an object, substance, or region
what is an electrode?
the number of electrons per second
what is electron current, ie? (concept not equation)
ie = ne(A)vd
what is electron current, ie? (equation not concept)
farad, named after Faraday 1F = 1C/V
what is the SI unit for capacitance?
a vector field associated with each point in space when charge is present in any form
what is the conceptual definition of electric field?
Conventional Current assumes that current flows out of the positive terminal, through the circuit and into the negative terminal of the source. Electron Flow is what actually happens and electrons flow out of the negative terminal, through the circuit and into the positive terminal of the source.
what is the difference between conventional current and electron current?
E = Q/∈₀A; A being the surface area of the plates
what is the electric field inside a parallel plate capacitor equal to ?
it is zero as the charges are free to move and "kill" the electric field. thus, any two points inside a conductor in electrostatic equilibrium are the same (non zero) potential.
what is the electric field of an interior point of a conductor in electrostatic equilibrium?
J = current density= 1/A = ne(e)vd = σE using the definition of drift speed to be : (e(tau)E)/m J can be replaced with that definition the part of this expressions sans the field is only dependent on the conducting material (this is the conductivity)
what is the equation for current density?
C = C1+C2+C3+...
what is the equivalent capacitance of parallel capacitors?
Ceq = (1/C1 +1/C2 + 1/C3 +...)^-1
what is the equivalent capacitance of series capacitors?
σ=(ne(e²)tau)/m
what is the expression for conductivity of a material?
drift speed, vd
what is the net motion of current through a wire?
it is the capacitance of the two electrodes; C = Q/∆Vc (capacitor voltage)
what is the proportionality constant called in the relationship between charge and potential difference of a capacitor? what is it equal to?
I=JA
what is the relationship between current and current density?
ampere, A which equal 1C/s
what is the unit for current?
they point to an increasing negative number, in direction of decreasing potential
what kind of value do electric field lines of a negative charge point to?
at d = 0, the potential is some positive value and the field lines point to zero which is at d = infinity (decreasing potential)
what kind of value do electric field lines of a positive charge point to?
the current must be the same at all points in a current-carrying wire. a junction does not change this reasoning, the current going into a junction is equal to the current going out.
what observation (due to conservation of charge) leads to kirchoff's junction rule?
they are directly proportional with a proportionality constant, C.
what relationship do charge and potential difference of a capacitor share?
when ∆Vc = ∆Vbattery. the growing positive charge on the upper capacitor plate exerts a repulsive force on new charges flowing toward the plat. eventually, the capacitor charge gets so large that no new charges can arrive. at this point the capacitor is fully charged.
when does current stop flowing from the battery in a circuit containing a capacitor?
NO! potential is scalar, so we do not take the magnitude. The negative does not refer to direction, but rather quantity.
when we say that electric field lines point toward decreasing potential, are we referring the magnitude of potential?
sharp points because the charge density is indeed higher at sharper regions.
where is the electric field the largest on a surface
the electric field
where is the potential energy of a capacitor stored?
work energy theorm. ∆V = ∆U/q. W = ∆KE + ∆U. We are not accelerating the object, so ∆V = ∆W/q.
which theorem relates electric potential and work?
simplest form of capacitor made of two metal plates fixed at a distance and parallel to each other. An infinite parallel plate capacitor forms a uniform electric field at all points. Any ol capacitor can be made from any two electrodes and do not have to be parallel. All capacitors must have zero net charge.
why are parallel plate capacitors a special case?
the "positive end" of the circuit is a conductor in electrostatic equilibrium, same with the "negative side". Thus, the plates match the potential differences of their ends of the batteries.
why does charge stop flowing to the capacitor when ∆Vc = ∆Vbattery?
electron current requires knowing the exact amount of electrons
why is conventional current more practical to use?
the direction the current is defined to be (by conventional current) in which positive charges seem to move. The direction of the current is the same as the direction of the internal electric field. The direction of conventional current is opposite to the motion of the charge carrying electrons.
why is important to note that currents were known and studied before we discovered that electrons carried that charge?
it can be charged slowly, but release the energy quickly. a mechanical analogy would be using a crank to stretch the spring the spring of a catapult, the quickly releasing the launch an object. a camera flash A defibrilator.
why would someone use a capacitor?