Physics I: 9-12 Flashcards
opposite charges exert ___ forces
attractive
like charges exert ___ forces
repulsive
coulomb
fundamental unit of charge
insulator
does not easily distribute a charge over its surface
will not transfer that charge to another neutral object very well
ex: nonmetals
describe the electrons of insulators
tend to be closely linked with their respective nuclei
conductor
- charges distribute evenly upon its surface
- able to transfer and transport charges
- often used in circuits or electrochemical cells
- ex: metals, ionic (electrolyte) solutions
when placed one meter apart from each other, which will experience a greater acceleration: one coulomb of electrons or one coulomb of protons?
electrons will experience the greater acceleration because they are subject to the same force as the protons but have significantly smaller mass
what is the net charge of an object with one coulomb of electrons and 3 moles of neutrons?
net charge is -1 C
neutrons do not contribute charge
coulomb’s law quantifies…
the magnitude of the electrostatic force Fe
coulomb’s law eq
k = coulomb’s/electrostatic constant
permittivity of free space
ε0
how to know direction of electric force in coulomb’s law
unlike charges attract, like charges repel
force always along the line connecting the centers of the 2 charges
how is the magnitude of the electric force related to the square of the distance of separation?
inversely proportional
electric fields
exerts forces on other charges
electric fields are produced by
source charges (Q)
when a test charge (q) is placed in an electric field (E), it will experience
an electrostatic force (Fe) equal to qe
test charge
q
charge placed in the electric field
source charge
Q
creates the electric field
magnitude of electric field eq
E =
E = Fe/q = kQ / r2
divide coulomb’s law by q
direction of electric field vector is given as…
the direction that a positive test charge would move in the presence of the source charge
positive charges have electric field vectors that radiate…
outward (point away) from the charge
negative charges have electric field vectors that radiate…
inward (point toward) the charge
field lines
- imaginary lines that represent how a positive test charge would move in the presence of a source charge
- point away from positive charge
- point toward negative charge
where will positive test charges move in regard to the field lines?
move in the direction of the field lines
where will negative test charges move in regard to the field lines?
move in the direction opposite of field lines
what is the electric field midway between two negative charges in isolation?
electric field would be zero because the two charges are the same
in this case, the fields exerted by each charge at the midpoint will cancel out and there will be no electric field
electric potential energy
potential energy that is dependent on the relative position of one charge with respect to another charge
electric potential energy eq
U = kQq/r
if charges are like charges, then the potential energy will be _____
positive
if charges are unlike charges, then the potential energy will be _____
negative
electric field is defined as the amount of work…
amount of work necessary to move a test charge from infinity to a point in space in an electric field surrounding a source charge
electric potential energy of a system increases when
two like charges move toward each other or when two opposite charges move apart
electric potential energy of a system decreases when
two like charges move apart or when two opposite charges move toward each other
how does a change in electric potential energy from -4 J to -7 J reflect on the stability of a system?
A decrease in potential energy indicates that the system has become more stable.
how does electric potential energy change between two particles as the distance between them increases?
if both particles have the same charge, the electric potential energy decreases as the distance increases.
if the particles have opposite charges, then the electrical potential energy increases as distance increases.
electric potential
V
ratio of the magnitude of a charge’s electric potential energy to the magnitude of the charge itself
scalar
electric potential eq
V = U/q = kQ/r
how to determine electric potential sign
determined by source charge Q
how are electric potential and distance from the source charge related?
inversely proportional
positive charge moves from
+ to -
negative charges moves from
- to +
potential difference
voltage
change in electric potential that accompanies the movement of a test charge from one position to another
potential difference eq
ΔV = Vb - Va = Wab / q
Wab = work needed to move a test charge q through an electric field from point a to point b
positive charges will spontaneously move in the direction that __inc/dec__ their electric potential (__pos/neg__ voltage)
electric potential energy is __inc/dec__
decrease
negative
decreasing
negative charges will spontaneously move in the direction that __inc/dec__ their electric potential (__pos/neg__ voltage)
electric potential energy is __inc/dec__
increases
positive
decreasing
what is the difference between electric potential and voltage?
Electrical potential is the ratio of a charge’s electrical potential energy to the magnitude of the charge itself.
Voltage, or potential difference, is a measure of the change in electrical potential between two points, which provides an indication of the tendency toward movement in one direction or the other.
how will a charge that is placed at a point of zero electric potential move relative to a source charge?
A charge will move in such a way to minimize its potential energy. Placing a charge at a point of zero electrical potential does not indicate that there is zero potential difference, so the charge may or may not move-and if it moves, it may move toward or away from the source charge depending on the sign of the source charge and test charge.
T/F
the units of electric potential energy and electric potential are different
true
electric potential energy - J
electric potential - V
equipotential line
line on which the potential at every point is the same
the potential difference between any two points on an equipotential line is zero
equipotential lines and work
- no work is done when moving a test charge from one point on an equipotential line to another
- work will be done in moving a test charge from one line to another
- but the work depends only on the potential difference of the two lines (not on the pathway taken between them)
electric dipole
two charges of opposite sign separated by a fixed distance
dipole moment eq
p = qd
perpendicular bisector of the dipole
electric potential at any point along this plane is 0
in an external electric field, an electric dipole will experience
net toque until it is aligned with the electric field vector
what is the voltage between two points on an equipotential line? will this voltage cause a charge to move along the line?
no voltage, so no acceleration along the line
there is a potential difference between different sets of equipotential lines, which can cause particles to move and accelerate
what is the behavior of an electric dipole when exposed to an external electric field?
a dipole will rotate within an external electric field such that its dipole moment aligns with the field
True or false? Because the increasing distance between charged particles repelling each other will decrease the Electrostatic Force, they will also slow down as they move.
False. Because the increasing distance between charged particles repelling each other will decrease the Electrostatic Force, they will also have a lower acceleration (but still increase their velocity traveling away from each other).
In ______________, the positively charged nucleus cannot move around. In ______________, the negatively charged electrons cannot move around.
(A) insulators, insulators
(B) insulators, insulators and conductors
(C) insulators and conductors, insulators and conductors
(D) insulators and conductors, insulators
(D) insulators and conductors, insulators
In insulators and conductors, the positively charged nucleus cannot move around. In insulators, the negatively charged electrons cannot move around.
Compare the process of Charge by Conduction to Charge by Induction.
In Charge by Conduction, you charge a neutral object by physically touching a negatively-charged object to it.
In Charge by Induction a charge is induced by bringing a negatively charged object close to another object.
A Dielectric is a substance that is normally not polarized, but in an electric field, a small charge can be induced. This acts to stabilize the source charge, and can allow more charges to be stored. Which of the following could be a dielectric?
(A) Insulator
(B) Conductor
(C) Neither Insulator nor Conductor
(D) Both Insulator and Conductor
(A) Insulator
An Insulator is a Dielectric that is normally not polarized, but in an electric field, a small charge can be induced. This acts to stabilize the source charge, and can allow more charges to be stored.
Draw out how induction might result in two neutrally-charged metal balls becoming oppositely charged.
A “Ground” is an infinite reservoir for electrons. What does that mean? Give an example.
A “Ground” is an infinite reservoir for electrons, which means that it can accept an infinite number of electrons. An example would be the earth.
What equation can be used to relate Electric Field Strength (E) to Electrostatic Force (Fe)
Fe / q = E
Fe = Electrostatic Force q = Test Charge E = Electric Field Strength
True or false? Even if there are no other charges to affect, a single charge (the source charge) will still create an electric field.
True. Even if there are no other charges to affect, a single charge (the source charge) will still create an electric field.
What equation can be used to relate E to the distance between two charges?
E = k (Q / r^2)
E = Electric Field Strength Q = Source Charge r = Distance between Q and q
True or False? A charge is repelled from another charge. As the two charges get farther away from one another, they will move slower and slower.
False. A charge is repelled from another charge. As the two charges get farther away from one another, they will accelerate at a slower and slower rate due to the decreasing Electrostatic Force. Remember that Force is not directly related to velocity but rather acceleration.
What is the difference between Electric Potential and Electric Potential Energy?
Electric Potential Energy is the amount of energy required to move a charge from one location to another (units = J).
Electric Potential is the amount of energy required to move a charge from one location to another per unit charge (units = J/C).
What equation can be used to relate Electrostatic Force to Electric Potential Energy?
Fe = EPE/r (similar to F = mgh)
Fe = Electrostatic Force EPE = Electric Potential Energy r = Radius between the two charges
What equation can be used to relate Electric Potential Energy to Electric Potential?
EPE / q = V
EPE = Electric Potential Energy q = Charge V = Electric Potential
What equation is used to relate Electric Potential (V) to the Source Charge (Q)?
V = k (Q / r)
V = Electric Potential k = Coulomb's Constant (9⋅10^9) Q = Source Charge r = Radius between Q and q
A Test Charge (6.7⋅10^-14 C) is sitting 2.4⋅10^-3 meters away from a Source Charge. What is the Electrostatic Force (in N) between these two charges if the Voltage is equal to 4.3 V at that point?
(A) 9.87⋅10^-12
(B) 4.32⋅10^-15
(C) 2.88⋅10^-13
(D) 1.20⋅10^-10
(D) 1.20⋅10^-10
EPE / q = V
EPE / (6.7⋅10^-14) = 4.3
EPE = (6.7⋅10^-14) x (4.3)
EPE = approx. 3⋅10^-13 J (actual: 2.881⋅10^-13)
Fe = EPE / r Fe = (3⋅10^-13) / (2.4⋅10^-3) Fe = approx. 1⋅10^-10 N (actual: 1.20⋅10^-10)
A Test Charge (6.7⋅10^-14 C) is sitting 2.4⋅10^-3 meters away from a Source Charge (4.2⋅10^-12 C). What is the Electric Potential Energy (in J) between these two charges?
(A) 4.55⋅10^-9
(B) 6.87⋅10^-10
(C) 2.23⋅10^-11
(D) 1.05⋅10^-12
(D) 1.05⋅10^-12
V = k (Q / r) V = (9⋅10^9) ((4.2⋅10^-12) / (2.4⋅10^-3)) V = (9⋅10^9) (approx. 2⋅10^-9 (actual: 1.75⋅10^-9)) V = approx. 18 (actual: 15.75)
EPE / q = V
EPE / 6.7⋅10^-14 = 18
EPE = 1⋅10^-12 J (actual: 1.05⋅10^-12)
Compare the Electrostatic Equations for F, E, EPE, and V.
b
b
a
b
b
a
b
a
magnetic field
created by any moving charge, whether a single electron traveling through space or a current through a conductive material
SI unit for magnetic field strength
tesla, T
1 T = ? gauss
104
diamagnetic
no unpaired electrons
no net magnetic field
slightly repelled by magnet (weakly antimagnetic)
paramagnetic
unpaired electrons
weakly magnetized in presence of external magnetic field
ex: aluminum, copper, gold
ferromagnetic
unpaired electrons
permanent atomic magnetic dipole
become strongly magnetized when exposed to a magnetic field or under certain temperatures
ex: iron, nickel, cobalt
magnitude of the magnetic field for an infinitely long and straight current-carrying wire
eq
B = µ0I / 2πr
B = magnetic field
I = current
r = distance from wire
what shape magnetic field do straight wires create?
concentric rings
magnitude of the magnetic field for a circular loop of current carrying wire
eq
B = µ0I / 2r
B = magnetic field
I = current
r = distance from wire
magnetic fields only exert forces on
other moving charges
lorentz force
sum of electrostatic and magnetic forces acting on a body
force on a moving charge eq
Fb = qvB sin theta
q = charge
v = velocity
B = magnitude of magnetic field
sin 0 =
0
sin 180 =
0
any charge moving parallel or antiparallel to the direction of the magnetic field will experience…
no force from the magnetic field
right hand rule for magnetic force
- thumb - velocity
- finger - field lines
- palm - force on a positive charge
magnetic force on a current carrying wire eq
Fb = ILB sin theta
I = current
L = length of wire
what are the requirements to have a nonzero electric field?
to create an electric field, one needs a charge
what are the requirements to have a nonzero magnetic field?
to create a magnetic field, one needs a moving charge
what are the requirements to have a nonzero magnetic force?
to create a magnetic force, one needs an external electric field acting on a charge moving any direction except parallel or antiparallel to the external field
Draw the magnetic field lines coming out of a simple bar magnet.
Which of the following is not one of the most common ferromagnetic materials?
(A) Zinc
(B) Iron
(C) Nickel
(D) Cobalt
(A) Zinc
The three most common ferromagnetic materials are Iron, Nickel and Cobalt.
A proton (q = 1.602⋅10^-19 C) is travelling through a magnetic field (B = .27 T) at an angle of 47° with a velocity of 4.5⋅10^7 m/s. What is the Magnetic Force acting on this proton?
(A) 1.42⋅10^-12
(B) 6.78⋅10^-13
(C) 9.22⋅10^-14
(D) 3.09⋅10^-15
(A) 1.42⋅10^-12
F = qvBsinθ F = (1.602⋅10^-19) (4.5⋅10^7)(.27)sin47° F = (1.602⋅10^-19) (4.5⋅10^7)(.27)(approx. √2/2 or .7 (actual: .731)) F = approx. 1.5⋅10^-12 (actual: 1.423⋅10^-12)
True or false? If the charged particle has no outside forces acting on it, then it will never create a magnetic field.
False. If the charge has no outside forces acting on it AND its initial velocity is 0, then it will never create a magnetic field.
Having no outside forces act on the charge just means it won’t accelerate, not that it will have no velocity.
Your professor makes an analogy comparing centripetal force to magnetic force. How are these two concepts related?
When magnetic force acts on a charge, it causes it to change directions in a way that makes it go in a circle.
a
a
a
Fb = qvB sin theta
b
current
I
- movement of charge that occurs between two points that have different electrical potentials
- movement of positive charge from high potential end of voltage source to low potential end
- reality: electrons move from low potential to high potential
metallic conductivity
- relies on uniform movement of free electrons in metallic bonds
- metal atoms can easily lose one or more of their outer electrons -> make them free to move around other metal atoms
electrolytic conductivity
relies on the ion concentration of a solution
depends on the strength of the solution
magnitude of current in terms of charge eq
I = Q/Δt
where do electrons move in a current
electrons move from lower electrical potential to higher electrical potential
potential difference (voltage) can be produced by…
electrical generator, galvanic (voltaic cell)
electromotive force
emf
voltage when no charge is moving between the two terminals of a cell that are at different potential values
kirchhoff’s junction rule
at any point or junction in a circuit, the sum of th currents directed into that point equals the sum of currents directed away from that point
Iinto junction = Ileaving junction
kirchhoff’s loop rule
around any closed circuit loop, the sum of voltage sources will always be equal to the sum of voltage (potential) drops
Vsource = Vdrop
provide the SI units of current
amperes (C/s)
voltage SI units
volts (J/C)
electromotive force SI units
volts (J/C)
conductivity SI units
siemens (S)
which likely has a higher conductivity: 1 M glucose or 0.25M NaCl? why?
NaCl because it is a salt and will increase the ion content of the water
glucose does not dissociate
resistance
R
the opposition within any material to the movement and flow of charge
materials that offer almost no resistance are called
conductors
materials that offer very high resistance are called
insulators
resistors
conductive materials that offer amounts of resistance
middle
resistance eq
R = ρL / A
ρ = resistivity
L = length of resistor
A = cross sectional area
resistivity
ρ
intrinsic resistance to current flow in a material
how is the resistance of a resistor related to its length?
directly/linearly proportional
how is the reissitance related to the cross sectional area of the resistor?
inversely proportional
the wider the resistor, the ___ current that can flow
more
how is temperature related to resistance?
proportionally
most conductors have greater resistance at higher temperature due to increased thermal oscillation
ohm’s law
for a given resistance, the magnitude of the current through a resistor is proportional to the voltage drop across the resistor
V = IR
voltage drop between any two points in a circuit eq
V = IR
V = voltage drop
R = magnitude of resistance
what happens when a cell is discharging?
- it supplies current
- current flows from the positive, higher potential end of the cell, around the circuit to the negative, lower potential end
power eq in terms of work and time
P = W / t = ΔE / t
power of a resistor eq
P = IV = IR2 = V2/R
resistors in series
all current must pass sequentially through each resistor connected in a linear arrangement
resistors in parallel
current divides to pass through resistors separately
describe what happens to resistors in series
as the electrons flow through each resistor, energy is dissipated, and there is a voltage drop associated with each resistor
Rs increases as more resistors are added
Rs _____ as more resistors are added
increases
voltage and resistance eqs
resistors in series
Vs = V1 + V2 + V3 + … + Vn
Rs = R1 + R2 + R3 + … + Rn
Rp ___ as more resistors are added
decreases
describe what happens to resistors in parallel
voltage drop by each division of current is the same bc all pathways originate from a common point and end at a common point
current will be largest through the pathways with the lowest resistance
voltage and resistance eqs
resistors in parallel
Vp = V1 + V2 + V3 + … + Vn
1/Rp = 1/R1 + 1/R2 + 1/R3 + … + 1/Rn
when n identical resistors are wired in parallel, the total resistance =
R/n
for equal resistances, the current flowing through each of the resistors =
Itotal/n
when approaching circuit problems, you need to find:
total voltage, total resistance, total current
to find the total current, find the total resistance first
what four physical quantities determine the resistance of a resistor?
- resistivity
- length
- cross sectional area
- temperature
capacitors
have the ability to store and discharge electrical potential energy
capacitance
C
in parallel plate capacitors
determined by the area of the plates and the distance between the plates
capacitance eq
C = Q/V
magnitude of electric field eq
E = V/d
d = distance between the plates
potential energy stored in a capacitor eq
U = 1/2 CV2
dielectric material
insulators placed between the plates of a capacitor that increase capacitance by a factor equal to the material’s dielectric constant
capacitance due to dielectric material eq
C’ = κC
C’ = new capacitance
can a dielectric material decrease the capacitance?
never
constant can never be less than 1
dielectrics in isolated capacitors
- shields the opposite charges from eachoterh
- increase in capacitance arises from decrease in voltage
dielectrics in circuit capacitors
increase in capacitance arises from increasee in stored charge
Cs ___ as more capacitors are added
decreases
Cp ___ as more capacitors are added
increases
describe what happens to capacitors in series
- capacitors must share the voltage drop in the loop and therefore cannot store as much charge
- group of capacitors act like one equivalent capacitor with a larger distance between its plates
- inc distance = smaller capacitance
voltage and capacitance eqs
capacitors in series
Vs = V1 + V2 + V3 + … + Vn
1/Cs = 1/C1 + 1/C2 + 1/C3 + … + 1/Cn
voltage and capacitance eqs
capacitors in parallel
Vp = V1 + V2 + V3 + … + Vn
Cp = C1 + C2 + C3 + … + Cn
assuming the plates are attached by a conducting material, how does a capacitor behave after the voltage source has been removed from a circuit?
the capacitor discharges, providing a current in the opposite direction of the initial current
ammeters
inserted in a series in a circuit to measure current
have negligible resistance
voltmeter
inserted in parallel in a circuit to measure a voltage drop
have very large resistances
ohmmeters
inserted around a resistive element to measure resistance
have negligible resistance
When you draw a battery, the larger line indicates that it is positive or negative?
The larger line in a battery symbol indicates that it is positive.
What equation typifies the definition of Current (I)?
I = ΔQ / Δt
I = Current ΔQ = Change in charge Δt = Change in time
True or False? Charges move more slowly through a resistor than through the rest of the circuit.
False. Charges move at the same speed throughout the entire circuit. Adding a resistor will cause the entire circuit as a whole to have a slower current.
What equation is used to relate the Current (I1, I2, etc) across all of the resistors to the total Current (It) of a circuit when resistors are in series?
It = I1 = I2 = In
The total Voltage for a circuit with resistors in parallel is equal to 3.2 V. If R1 = 2.3 Ω, R2 = 6.5 Ω, and R3 = 9.7 Ω, what is the current that is going through R3 (I3)?
(A) 3.29
(B) 1.33
(C) 2.04
(D) 0.33
(D) 0.33
V3 = Vt V3 = 3.2 V
V3 = I3R3 3.2 = I3(9.7) I3 = 3.2 / 9.7 I3 = 0.33 C/s
You have a simple circuit that contains a single resistor. If you increase the voltage, which of the following is true?
I. Resistance increases.
II. Current increases.
III. Capacitance increases.
(A) I Only
(B) II Only
(C) I and II Only
(D) II and III Only
(B) II Only
If you increase the voltage, the current will increase. Resistance (if it is an Ohmic material) will remain the same as it is a property that is dependent solely on the resistor and not on the battery or wire of the circuit.
How are Resistivity (ρ) and Conductivity (σ) related?
ρ = 1/σ
True or false? Nonionic solutions will always have a higher Resistivity than Ionic solutions.
True. Nonionic solutions will always have a higher Resistivity than ionic solutions.
The converse is also true: Ionic Solutions always have a higher Conductivity than Nonionic solutions.
What happens to resistance as the area of the resistor is increased? Why?
Resistance will decrease as area increases due to the increased number of paths that the electrons can take through the resistive material.
What happens to resistance as the length of the resistor is increased? Why?
Resistance will increase as length increases due to the longer amount of time that the electrons will need to travel through resistive material.
The Electrolytic Resistivity refers to what?
The resistivity of a liquid that can conduct electricity.
Fill in the blanks: Resistors in ______________ must have the same Voltage, but may have different currents. Resistors in __________ must have the same current, but may have different Voltages.
(A) Series, Parallel
(B) Parallel, Series
(C) Series, Non-Ohmic Circuits
(D) Parallel, Non-Ohmic Circuits
(B) Parallel, Series
Resistors in Parallel must have the same Voltage, but may have different currents. Resistors in Series must have the same current, but may have different Voltages.
Draw the symbol for a capacitor in a circuit.
True or False. The plates charge this way because the positive terminal will send out protons to the plate it is attached to while the negative terminal will send out electrons to the plate it is attached to.
False. Protons do not move! The electrons from the plate attached to the positive terminal will be attracted to the positive terminal, sent through the battery, and then pushed away from the negative terminal to the plate attached to the negative terminal.
True or False? Capacitor Plate A is parallel and opposite to Plate B. If Plate A is twice the thickness of Plate B, it will store twice as much charge.
False. No matter their size or shape, 2 plates parallel and opposite of each other will always store equal and opposite amounts of charge.
You increase the charge on a Capacitor; therefore, the:
I. Capacitance increases
II. Voltage increases
III. Resistance increases
(A) I Only
(B) II Only
(C) I and II Only
(D) II and III Only
(B) II Only
You increase the charge on a Capacitor; therefore, the Voltage increases. The capacitance (just like resistance) will only change if you change its intrinsic characteristics.
Which of the following best describes the electric field between parallel capacitor plates?
(A) Unpredictable
(B) Linear
(C) Radial
(D) Uniform
(D) Uniform
There will be a uniform electric field between the parallel Capacitor plates, due to the separation and alignment of charges.
What is the equation for Capacitance in terms of its intrinsic characteristics?
C = ε₀ (A / d)
C = Capacitance ε₀ = Permittivity of Dielectric (8.84⋅10^-12) A = Area of each plate d = Distance between the two plates
What equation can be used to calculate the total amount of energy produced by a capacitor when it is discharged in terms of the charge built up on one of the capacitor plates?
E = Q(V/2)
E = Total Energy produced by Capacitor Q = Charge on one plate of capacitor V = Voltage difference between the two plates of a capacitor
d
c
c
b
b
c
You have three capacitors in series (C1 = 2.6 F, C2 = 7.4 F, C3 = 2.2 F) and connected to a battery (V = 13.3 V). What is the voltage across C3?
(A) 3.12
(B) 6.05
(C) 13.24
(D) 19.44
(B) 6.05
1/Ceq = 1/C1 + 1/C2 + 1/C3 1/Ceq = 1/2.6 + 1/7.4 + 1/2.2 1/Ceq = approx. 1 (actual: .974) Ceq = approx. 1 (actual: 1.03)
Ceq = Q / V 1.03 = Q / 13.3 Q = approx. 13.3 (actual: 13.7)
C3 = Q / V3 2.2 = 13.3 / V3 V3 = approx. 6 (actual: 6.05)
Recall the equation for the charge on a Capacitor. What happens to the Capacitance if the Charge is doubled?
(A) The Capacitance Quadruples
(B) The Capacitance Doubles
(C) The Capacitance stays the same
(D) The Capacitance is cut in half
(C) The Capacitance stays the same
The equation for charge on a Capacitor is Q = CV. Capacitance is constant for a given Capacitor, so if charge doubles, then the voltage would double.
You have three capacitors in parallel (C1 = 2.6 F, C2 = 7.4 F, C3 = 2.2 F) and connected to a battery (V = 13.3 V). What is the voltage across C3?
(A) 2.56
(B) 7.09
(C) 13.30
(D) 21.34
(C) 13.30
The voltage across each capacitor is exactly the same in a parallel configuration.
Why is the voltage across each capacitor exactly the same for each capacitor in a parallel configuration?
The voltage across each capacitor is exactly the same as the overall voltage because each capacitor is directly linked to the battery and every spot along a wire that isn’t interrupted by either a resistor or a capacitor will have the exact same voltage in it.
You have three capacitors in parallel (C1 = 2.6 F, C2 = 7.4 F, C3 = 2.2 F) and connected to a battery (V = 13.3 V). What is the charge on a plate of C3?
(A) 12.27
(B) 18.79
(C) 29.26
(D) 48.30
(C) 29.26
C3 = Q3 / V 2.2 = Q3 / 13.3 Q3 = approx. 30 (actual: 29.26)
Which of the following are the main purposes for a Capacitor on the MCAT?
I. Creating uniform Electric Fields
II. Regulating the movement of Charges within a Circuit
III. Storing Electrical Potential Energy
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(C) I and III only
The main purposes of a Capacitor on the MCAT are to create Uniform Electric Fields and Storing EPE.
Write out the equation for the Electrical Potential Energy stored by a Capacitor.
PE = 1/2QV
PE = Potential Energy stored by Capacitor Q = Charge V = Voltage difference between the two plates of a capacitor
What is a Dielectric? Why do we place Dielectrics between capacitor plates?
A Dielectric is a non-conducting (insulating) material. We place them between capacitor plates to prevent them from touching, which if they did touch, they would no longer store charge but rather just be part of the circuit, allowing charge to flow through them.
When a capacitor remains connected to a battery, adding a dielectric will:
I. Increase the voltage
II. Increase the charge
III. Increase the capacitance
(A) I Only
(B) III Only
(C) I and III Only
(D) II and III Only
(D) II and III Only
A dielectric will increase the capacitance of a capacitor, which will allow more charge to build up on the capacitor. This is because the induced polarization within the dielectric will effectively cancel out the charges on the plates, making the voltage difference between the two plates smaller. The battery will then add more charge to the plates in order to once again make the voltages equal, leaving the voltage unchanged while increasing the number of charges on each plate.
c
a
c
B
c
b
electrochemical cells
contained systems in which redox reactions occur
3 types: galvanic cells, electrolytic cells, concentration cells
electrodes
strips of metal or other conductive materials placed in an electrolyte solution
where oxidation and reduction take place
anode
site of oxidation
attracts anions
cathode
site of reduction
attracts cations
electrons flow from __anode/cathode__ to __anode/cathode__
anode to cathode
(alphabetical order)
current flows from __anode/cathode__ to __anode/cathode__
cathode to anode
emf > 0
cell is able to release energy (ΔG<0) -> spontaneous
emf < 0
cell must absorb energy (ΔG > 0) - nonspontaneous
galvanic cells
aka voltaic cells
house spontaneous reactions with a positive electromotive force
electrolytic cells
house nonspontaneous reactions with a negative electromotive force
require input of energy
can be used to create useful products through electrolysis
concentration cells
specialized form of galvanic cell in which both electrodes are made of the same material
concentration gradient between the two solutions causes the movement of charge (instead of potential difference)
makeup of galvanic cell
- two electrodes of distinct chemical identity - placed in separate compartment called half cells
- electrodes connected by conductive material
- ex: copper wire
- electrolyte solution surrounds each of the electrodes
electrolyte
composed of cations and anions
surrounds the electrodes in galvanic cells
salt bridge
inert salt that connects the two solutions around electrodes
permits the exchange of cations and anions
what would happen to galvanic cell without a salt bridge?
reaction would stop because an excess positive charge would build up on the anode, and an excess negative charge would build up on the cathode
cell diagram notation
anode | anode solution (concentration) || cathode solution (concentration) | cathode
|| = presence of salt bridge or other barrier
= phase boundary
electrolysis
redox reaction driven by an eternal voltage source
makeup of electrolytic cell in comparison to galvanic cell
external voltage source (battery)
half reactions don’t need to be separated into different compartments because the desired reaction is nonspontaneous
reactions that involves the transfer of n electrons per atom M
Mn+ + n e- –> M (s)
one mole of metal M (s) will be produced if n moles of electrons are supplied to one of Mn+
electrodeposition eq
helps determine the number of moles of element being deposited on a plate
mol M = It/nF
mol M = amount of metal ion being deposited at a specific electrode
I = current
t = time
n = number of electron equivalents for a specific metal ion
F = faraday constant
how to calculate the voltage in concentration cell
nernst eq
rechargeable cell/battery
electrochemical cells that can experience charging (electrolytic) and discharging (galvanic) states
ranked by energy density
lead-acid battery
- when discharging: consist of a Pb anode and a PbO2 cathode in a concentrated sulfuric acid solution
- when charging: PbSO4- plated electrodes are dissociated to restore the original Pb and PbO2 electrodes and concentrate the electrolyte
- have low energy density
energy density
measure of a battery’s ability to produce power as a function of its weight
nickel-cadmium batteries (Ni-Cd)
- when discharging: Cd anode and NiO(OH) cathode in a concentrated KOH solution
- when charging: Ni(OH)2 and Cd(OH)2 plated electrodes are dissociated to restore the of ones and concentrate the electrolyte
- have higher energy density that lead acid batteries
nickel-metal hydride (NiMH) batteries
today replace Ni-Cd batters bc they have higher energy density, are more cost-effective, and are significantly less toxic
surge current
above average current transiently released at the beginning of the discharge phase
wanes rapidly until a stable current is achieved
anode of galvanic cell is considered the __pos/neg__ electrode bc…
negative electrode because it is the source of electrons
cathod of galvanic cell is considered the __pos/neg__ electrode
positive electrode
anode of electrolytic cell is considered the __pos/neg__ electrode bc…
positive bc it is attached to the positive pole of the external voltage source and attracts anions from the solution
cathode of electrolytic cell is considered the __pos/neg__ electrode bc…
negative electrode bc its attached to the negative pole of the external voltage source and attracts cations
cathode attracts…
cations
anode attracts…
anions
isoelectric focusing
technique used o separate amino acids or polypeptides based on their isoelectric points (pI)
which type of cell has a positive ΔG?
electrolytic cells
which type of cell has a positive Ecell?
galvanic cells
reduction potential
quantifies the tendency for a species to gain electrons and be reduced
the higher the reduction potential…
the more a given species wants to be reduced - the more likely it is to be reduced
standard reduction potential
E°red
calculated by comparison to the standard hydrogen electrode (SHE) under standard conditions
standard electromotive force
emf or E°cell
the difference in standard reduction potential between the two half cells
for galvanic cells, the difference of the reduction potentials of the two half reactions is __pos/neg__
positive
for electrolytic cells, the difference of the reduction potentials of the two half reactions is __pos/neg__
negative
for galvanic cells the electrode with the more positive reduction potential is the __anode/cathode__
cathode
species with stronger tendency to gain elections is actually doing so - spontaneous rxn
for galvanic cells the electrode with the less positive reduction potential is the __anode/cathode__
anode
species with stronger tendency to gain elections is actually doing so - spontaneous rxn
for electrolytic cells, the electrode with the more positive reduction potential is the __anode/cathode__
anode
bc it is forced to be oxidized by the external voltage source
for electrolytic cells, the electrode with the less positive reduction potential is the __anode/cathode__
cathode
bc it is forced to be reduced by the external voltage source
standard electromotive force eq in terms of reduction potentials
E°cell = E°red,cathode - E°red,anode
if a cell’s electromotive force is denoted as positive value, what does that mean?
cell is spontaneous (Galvanic)
if a cell’s electromotive force is denoted as negative value, what does that mean?
cell is nonspontaneous (electrolytic)
- electrolytic bc neg emf
- galvanic bc pos emf
when E°cell is positive, ΔG° is:
type of electrochemical cell:
negative
galvanic cell
when E°cell is negative, ΔG° is:
type of electrochemical cell:
positive
electrolytic cell
when E°cell is 0, ΔG° is:
type of electrochemical cell:
0
concentration cell
nernst eq describes…
the relationship between the concentration of species in a solution under nonstandard conditions and the electromotive force
when Keq > 1, E°cell is
positive
when Keq < 1, E°cell is
negative
when Keq = 1, E°cell is
0
eq relating ΔG° and emf
ΔG° = -nFE°cell
n = number of moles of electrons exchanged
simplified nernst eq
Ecell = E°cell - (0.0592/n)logQ
E°cell = emf under standard conditions
n = number of moles of electrons
Q = reaction quotient
standard change in free energy from equilibrium constant eq
ΔG° = -RTlnKeq
free energy change under nonstandard conditions eq
ΔG = ΔG° + RTlnQ
What is the purpose of a salt bridge?
The purpose of a salt bridge is to neutralize the charges in the solutions that are either becoming positive or negative as the reaction proceeds. This allows the reaction to continue moving forward.
For a Redox Reaction to be spontaneous, which of the following must its voltage be?
(A) Positive
(B) Zero
(C) Non-Zero [positive or negative]
(D) Negative
(A) Positive
For a Redox Reaction to be spontaneous, the voltage must be positive.
What equation can be used to determine the Standard Cell Potential for a Galvanic Cell?
E°cell = E°red (cathode) - E°red (anode)
True or false? The deposition of the metal from the electrolyte solution onto the cathode is called Galvanization, explaining the alternate name for these cells.
True. The deposition of the metal from the electrolyte solution onto the cathode is called Galvanization, explaining the alternate name for these cells.
You are reducing copper, and decide to double the number of moles of copper that you are reducing. If you do so, the:
I. ∆G° will double
II. E°red for copper will double
III. K will double
(A) I Only
(B) II Only
(C) I and II Only
(D) I and III Only
(A) I Only
You are reducing copper, and decide to double the number of moles of copper that you are reducing. If you do so, the ∆G° will double and n will double, leaving the E°red as the same value according to the relationship ∆G° = -nFE°cell. K will not change according to the relationship -nFE°cell = -RTlnK.
Cu2+ (E°red = .34) and Zn2+ (E°red = -.76) are both part of a Galvanic Cell. What is the equilibrium constant K for this cell?
(A) 3.05⋅10^6
(B) 8.90⋅10^14
(C) 6.03⋅10^33
(D) 1.59⋅10^37
(D) 1.59⋅10^37
E°cell = E°red (cathode) - E°red (anode) E°cell = .34 - -.76 E°cell = 1.10
E°cell = (.0592 / n)logK 1.10 = (.0592 / 2)logK logK = approx. 40 (actual: 37.2) K = approx. 1⋅10^40 (actual: 1.59⋅10^37)
The Nernst Equation allows us to relate E°cell to Ecell. Write out this equation.
Ecell = E°cell - (.0592 / n)logQ
Cu2+ (E°red = .34) with a concentration of 3.2⋅10^-3 M and Zn2+ (E°red = -.76) with a concentration of 4⋅10^-5 M are both part of a Galvanic Cell. What is Ecell for this cell under these conditions?
(A) .54
(B) .95
(C) 1.06
(D) 1.16
(D) 1.16
E°cell = E°red (cathode) - E°red (anode) E°cell = .34 - -.76 E°cell = 1.10
Ecell = E°cell - (.0592 / n)logQ Ecell = 1.1 - (.0592 / 2)log(4⋅10^-5 / 3.2⋅10^-3) Ecell = 1.1 - (.0296)log(approx. .01 (actual: .0125) Ecell = 1.1 - (.0296)(approx. -2 (actual: -1.903)) Ecell = 1.1 - (.approx. -.05 (actual: -.056)) Ecell = approx. 1.15 (actual: 1.156)
True or false? Concentration cells often overshoot their equilibrium point where concentrations are equal, reversing which electrode is the cathode and anode and reversing the current.
False. Concentration Cells will work until equal concentrations in each compartment is achieved, and then there is no Electrical Potential Energy or the ability to do further work.
b
B
c
A
A
B
A
D
