Download Chapter 27” You can`t resist being charged up about DC circuits!”

2015 AP Review Sheet
Final 2nd Trimester
Final Exam
2nd Trimester AP Physics C
2nd Trimester Final
Format: 35 Multiple Choice + three AP “like” Free Response
Free Response: Electric fields/Gauss’ Law, DC/RC circuits, Gravitation/Simple Harmonic Motion
Score is 50% Multiple Choice, 50 % Free Response
No penalty for guessing
Chapter 12 Equilibrium Only (Sections 1-5) (Takehome)
Chapter 13 Gravitation
Chapter 15 Simple Harmonic Motion
Chapter 21 Electric Charges
Chapter 22 Electric Fields
Chapter 23 Gauss' Law
Chapter 24 Electrical Energy
Chapter 25 Capacitance
Chapter 26 Current and Resistance
Chapter 27 Circuits
2015 AP Review Sheet
Final 2nd Trimester
Chapter 12 : Equilibrium
Notes < Take Home>
 Draw freebody for various systems at rest
 Write force equations (up=down/ right=left)
o Hinge is opposite tension and weight
 Write torque equations
o Don’t forget radius for each force!
o Make sure force is perpendicular to radius!

Chapter 13: Gravitation
Assigned Book Problems: (Q2, Q5, 1, 6,16,17,24,26,29,36,39, 43,49, 52, 55,64,93, 99a )
Notes <1-41>
 Know Kepler’s 3 laws <1>
1. Apply the 1st law (identify/draw new orbit) <2,3>
2. Apply the 2nd law (angular momentum conservation)<13d,39d>
mvr=mvr
3. Apply the third law (change orbits… what happens) <4,5,13c>
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Be able to derive Newton’s Law of Gravitation using Kepler’s 3rd law <6>
Know that the force due to gravity is equal and opposite on the two objects is equal
<7>
Find the gravitational force on an object given a system of objects
1. Treat gravitational force as a vector <8,9,10,11> (Q2,Q5,1,6)
2. Find where the gravitational force equals zero <9>
Use the gravitational force as a centripetal force <12,13b,14a> (43, 49, 52, 93)
R is radius of circle, r is distance center to center
1. Binary stars: Be careful with your R values!<17,18>(93)
2. Watch that r is radius of orbit NOT altitude <13>(49,52)
3. Find the period of a satellite<14a,4,5>(49)
4. Find mass of planet… know how to figure out meaning of slope<14b>(43)
5. Find velocity of a satellite<12,13a,15,18,39e>(49,52)
6. Find the centripetal acceleration <16,17a>
7. Find the moment of inertia of a system<17d>
2015 AP Review Sheet
Final 2nd Trimester
8. Find the angular momentum of a system (circular or elliptical) <17e,39c>

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Compare equations by dividing <15,16,23,24,25,26>
Find the force of gravity on an object inside a solid planet or shell<20a,21> (24)

Draw the force due to gravity as a function of distance inside/outside
planets/shells<20b,22>
Find the acceleration due to gravity <23,24,25> (17)



Be able to find the work done by the gravitational force <20c,30,31,32>
=K
Find the potential energy associated with the gravitational force (and graph!)
<33,34,35,39a>

Find the total energy of a satellite in an orbit<37,39b> (36, 39, 64)


Find work to change orbits <39f>
Find the escape speed for a planet-know derivation <40,41> (36)
Not on exam but you do need to know for May
 Force on point mass located along the axis of a ring <11>(99a)
 Force on a mass and extended mass <19>(16)
Chapter 15: Oscillations : Sine of the times!
(Homework assigned: Q1,Q2, 5,7,8,11,24,26,28,30,32,34,35,40,43,44,64,73,89)
<Notes 1-47>
 Be able to identify simple harmonic motion <1,2,3> (Q2)
o Know the definition of simple harmonic motion (use it to find angular frequency/period)
<3d,29,36,42,43> (Q2)


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Know what happens if a spring is cut in half, put in parallel, series<3a,b,c> (26)
Know how to find acceleration at any position of SHM<3d>(Q1)
o From an acceleration vs time graph be able to identify where mass is :
amplitude/equilibrium
o From an acceleration vs time graph be able to identify if mass is moving left/right
Energy is NOT conserved during inelastic collisions! (35)<12>
Know the energy conversions for SHM<4-12> (7,28,30,32,34,35,64,89)
o Be able to use conservation of energy to solve problems
(7,28,30,32,34,35,64,89)<6,11,12>
2015 AP Review Sheet
Final 2nd Trimester
o
Be able to draw kinetic energy/potential energy as a function of position or time
<5,14,15,20>(30,32)
o Know where in the motion the following are max or zero: velocity, kinetic energy,
potential energy, force, acceleration <4,8,9,10>
 Know how to find potential energy from a variable force<7>
F=Ax2
W=1/3 Ax3
 Given a spring with attached mass determine:
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
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

o
the period of motion, (5,7,8,26,89)<22,23,24,26,32>
o
o
o
o
o
maximum acceleration,(24) <30>
a=-kA/m where A is amplitude
the maximum speed,(7,89)
the mass, (28)
the amplitude, (5,24,30,35,89)<25,30,32>
frequency (5,7,8,26,28,89)
o
angular frequency (7,8)<21>
o spring constant (7,28,32)
o Force (7)
F=-kx
Given an equation of position as a function of time determine <16,17,18,19,28,31> (11,34,64)
o
o the displacement at a given time,
o acceleration at a point,
o frequency,
o period,
o amplitude,
o speed at a point,
o time to reach a point,
o maximum acceleration
Write equations for position, velocity, and acceleration as a function of time<13,18,19,27>
(11,34)
o
o
o
Find amplitude that a block can have so that it doesn’t slip<30>(24)
Know what motion results if an object follows SHM in both x and y directions<16,17,31>
Know the difference between finding equilibrium (FORCES) and finding maximum compression
(ENERGY) (89)<23,25,32>
Simple Pendulum – period equation- <,33-35,37-41>(40)
o Recognize the difference between a simple pendulum and a mass on a spring
o Simple Pendulum -know derivation
o
Physical Pendulum: calculate rotational inertia, center of mass, period
(43,44)<36,43,44,45>
2015 AP Review Sheet
Final 2nd Trimester
where x is the center of mass to the pivot point
o
Torsion Pendulum (73)<42>
Calculus Review Exam
To power rule or to not power rule... that is the question
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I put an example for each objective below
Given position as a function of time
x=3t2+5
o Be able to find instantaneous velocity
 v=6t m/s
o Be able to find kinetic energy
 K=1/2 m (6t)^2
o Instantaneous acceleration
 a=6 m/s2
o Net force
 F= m(6)
Given a velocity as a function of time
v=3t-6
o Be able to find total distance traveled for a given time interval
 x=1.5t2-6t
 for 1 to 2 seconds put in 2 for t then subtract and put 1 in for t
 x=-6+4.5=-1.5m
o Be able to find instantaneous acceleration
 a=3 m/s2
o Be able to find instantaneous force
 F=m3
o Be able to find work
 (no power rule necessary!) W = 1/2mvf 2-1/2 mvi 2
Given an acceleration as a function of time equation a=4t3
o Be able to find where a particle is located at a given time t
 v=t4+ initial velocity

x=(1/5)t5 +v0t+ initial position
Given an angular position as a function of time t4+5t-2
o Be able to find the instantaneous speed
 =24t3+5

v=R where R is radius
Given a potential energy as a function of position U=7x2+4x
o Be able to find force
 Negative sign specifically tested for! F=-14x-4
Given a force as a function of position equation F=-2x3
o Be able to find potential energy
 U=(1/2)x4
o Be able to find work
 W=-(1/2)x4
Given a force as a function of time equation F =3t+5; mass =2 kg
2015 AP Review Sheet
Final 2nd Trimester

o Be able to find when an object comes to rest (instantaneous velocity of zero)
 a=1.5t+2.5
 v=.75t2+2.5t +initial velocity
 0=.75t2+2.5t +initial velocity
 Solve for t
Be able to identify if a pair of equations is for
o A particle moving with zero acceleration (constant velocity)
 X=At
 Y=Bt
o A particle moving in projectile motion (one is constant velocity the other is
acceleration)
 X=At
 Y=Bt2
o A particle moving with constant speed and nonzero acceleration (circle)
 X=Acost
 Y=Bsint
Not a ton of math but lots of concepts!
Chapter 21: Electric Forces : Let’s get charged up!
(Homework assigned: Ch 21 problems Q1, Q8, 4,13,25,44,52,54a,63)
< Notes : 1-25>
 How many electrons are in a charge? How much mass for a charge?<2,12>(25,52)
 Know Coulomb’s Law and be able to apply it.<3-13>(Q1,4,13,25,44,54a)
o
o
o
o
o
o
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
Watch your r value!<3b,6,7>(54a)
Apply Newton’s 3rd Law to charges attracting and repelling <4,12>(4,13)
Figure out what happens to force when charge/distance changes <5,11>
Know that the force inside a charged object is zero, just like gravity! <7>
Calculate the magnitude and direction of the force on a positive or negative
charge due to other specified point charges.<8,9,10,11>(Q1,13,63)
 Find where the electrostatic force is zero<13>(Q1,63)
o Analyze the motion of a particle of specified charge and mass under the
influence of an electrostatic force.<11> F=ma
o Add vectors!<6,9,10,13> (13,44,63)
Know that conductor’s and insulator’s electrons act differently <14,15.16,17> (52)
Be able to apply Newton’s 2nd Law to a hanging sphere of charge <16>(54a)
Know the types of charging<18>(52)
o Conduction/ Electrification by contact (4,52)
 Determine charge after objects touch (4,52) <20,21,22,23,24>
o Induction
 Describe the process of charging by induction<17,18,20,23,24>(Q8)
 Explain why a neutral object is attracted to a charged object<18>(52)
2015 AP Review Sheet
Final 2nd Trimester

Know what grounding is and that it doesn’t necessarily neutralize objects.<19>(Q8)
Chapter 22 Electric fields “Can you Field these notes? They are electric!
(Homework assigned: Ch 22 Problems Q1,Q2,Q4,8a,11,14, 40,48,49,50,77a)
Notes <26-44>
 Understand the concept of electric field, be able to:
o Define it in terms of the force on a test charge. <26,28,32> (40,48,49,50,77a)
o
o Describe and calculate the electric field of a single point charge.<26>

o
o
o
o
o
Calculate the magnitude and direction of the force on a positive or negative charge placed
in a specified field. <27,29,30,31,32,33,34,35>(Q1,40,48,49,50,77a)
 Be able to describe the motion of the a charged particle placed in an
electric field <27,33c>(Q1,49,50)
 Know that the force is with the field for positives and against for negatives
<29,30,31> (40,48,50,77a)
 Be able to draw a freebody with the force due to the electric field as one vector
(especially sphere hanging ) <32,33>(77a)
 Be able to solve a projectile problem with a charge in an electric field
<34>(48,49,50)
 Be able to solve for force, acceleration, displacement using two dimensional
electric field <35> (48,50)
Draw electric fields for various charge distributions
<36,37,38,39,40,41,42>(Q2,Q4,8a,11,14)
Perform vector addition to find the electric field at a point in space due to
charges<40,41,42>(Q2,Q4,8a,11,14)
Find where the electric field is zero due to two point charges(8a)<39>
Use the principle of superposition (adding vectors) to calculate by integration <45-51>
 The electric field due to a line of charge (just like gravitation, rotational inertia,
center of mass)

The electric field at the center of a circular arc of charge (gravitation too!)

The electric field on the axis of a thin ring of charge (gravitation too!)

The electric field due to a disk of charge (could be gravitation too!)
r=
Lots of concepts!
(excess charge/types of charging/motion of charges due to electric force or field /electroscopes/
grounding/ charged objects touching/hanging spheres/projectile motion)
Drawing vectors and vector addition
Mass and charge of electron/proton given on formula sheet
2015 AP Review Sheet
Final 2nd Trimester
Chapter 23 Gauss’ Law
Notes <1- 33>
(Homework assigned Chapter 23: Q1, Q3, Q6, 3, 5, 12, 13, 18, 19, 21, 44,47, 59,63,68,69,71,79 )
Understand the relationship between electric field and electric flux, be able to <2-9>
o Calculate the flux of an electric field through an arbitrary surface or of a field uniform in
magnitude over a Gaussian surface and perpendicular to it.<2,3,4,5,6> (Q1,12,44)
o
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


Calculate the flux of the electric field through a rectangle when the field is perpendicular
to the rectangle and a function of one coordinate only. <3,6> (Q3,3)
o State and apply the relationship between flux and the electric field. <2-8>
(Q3,5,18,19,44)
o Know that the electric field at any arbitrary point depends on all charges in the area but
the electric flux/field for the outside charges reduces to zero for an enclosed surface
<7,9>(Q1,12)
Understand the nature of electric fields in and around conductors, be able to:
o Explain the mechanics responsible for the absence of electric field inside a conductor,
and know that all excess charge must reside on the surface of the conductor.<11-16>
o the field outside the conductor must be perpendicular to the surface.<17,18>
Understand induced charge and electrostatic shielding, be able to
o Explain why there can be no electric field in a charge-free region completely surrounded
by a single conductor, and recognize consequences of this result.<11-15> (Q6,12,18)
o Explain why the electric field outside a closed conducting surface cannot depend on the
precise location of charge in the space enclosed by the conductor, and identify
consequences of this result. <12>
Be able to use induction for conductors and find the charge on the inside and outside surfaces of
shells <12,13,14> (21,59,79)
Understand Gauss’s Law, be able to:
o State the law in integral form, and apply it qualitatively to relate flux and electric charge
for a specified surface. <10,19>
o Apply Gauss’ law, along with symmetry arguments, to determine the electric field
 For a line of charge <26,27>
: A=2πrL

for a plane of charge,<28>(41)
: A=2A

for a inside spherical charge distribution(concentric spheres!)
<19,21,22,23>(47,51)
E=0 inside conductors!!!!!
2015 AP Review Sheet
Final 2nd Trimester
Outside: all the charge is enclosed

For a cylindrically symmetric charge distribution (insulator)
V= πr2 L
A=2πrL

Oppositely-charged parallel plates. (no integration necessary due to uniform E)
<32>(36)
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
Conducting sphere (Inside and outside!) <42-47,49-51>(63,67)
 Draw graph of electric field inside and outside
 Inside E=0
Insulating sphere (Inside and outside!) <52-54,57>(93)
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V=4/3 πr3 : A=4πr2
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o
Cylinder of charge <56>
 Draw graph of electric potential/electric field inside and outside<56>

Non-uniform <56g>(32a)
Draw the electric field as a function of distance for a variety of charge distributions
<20,22e,32a>
Chapter 24 Electric Potential
Notes <1-57> Assigned Homework (Q9,4,16,17,23,24,31,32a,34,35,36,41,45,47,63,67,90,91,93,101,108)
 Understand the concept of electric potential, be able to:
o calculate how much work is required to establish the charge system. <3,5>(41)
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o
Calculate the electrostatic potential energy of a system of two or more point
charges<6a,7>
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o
Determine the electric potential in the vicinity of one or more point charges.
<11,12,13,14,16,36>(45,90)

o
Find where the potential is zero due to two point charges <12,13>(16,17)

2 positions because it is a scalar quantity!
2015 AP Review Sheet
Final 2nd Trimester
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
Know your formulas!<8>
Understand the concept of electric potential difference, be able to:
o Calculate the electrical work done on a charge or use conservation of energy to determine
the speed of a charge that moves through a specified potential difference.
<19,33,34,35,39>(47)
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o
o
o
o
o
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Calculate the work done on a charge when moving in an equipotential diagram
<22,23,24,56f>(4)
 W=qV
Determine the direction and approximate magnitude of the electric field at various
positions given a sketch of equipotentials. <20,21,22>(91)
 Downhill!
Draw equipotential surfaces for given charge distributions <20,21,32,56>(91)
 Point charges= circles
plane of charge = planes
Use integration to determine electric potential difference between two points on a line,
given electric field strength as a function of position along that line.<27,30>(35)

Use a derivative to find the electric field given the electric potential as a function of
position<27,28,29,36>(34)

Derive expressions for electric potential as a function of position (This means using Gauss’ Law
first!).
o Oppositely-charged parallel plates. (no integration necessary due to uniform E) <32>(36)

V=-Ed
o
o
o

U=qV=1/2 mv2
Conducting sphere (Inside and outside!) <42-47,49-51>(63,67)
 Draw graph of electric potential/electric field inside and outside
 Inside E=0 and V=constant=kQ/R
Insulating sphere (Inside and outside!) <52-54,57>(93)

Cylinder of charge <56>
 Draw graph of electric potential/electric field inside and outside<56>

 Non-uniform <56g>(32a)

 Empty space (93)
Use the principle of superposition to calculate by integration the electric field and the
electric potential
o
o
o
on the axis of a thin ring of charge, <37,38,39>(23,101)
at the center of a circular arc of charge. <41>(24,31)
r is from charge to point in space,

r is from charge to point in space,
Chapter 25 : Capacitance Notes “You must have the capacitor to charge up for this Chapter! Or you
have no potential! “(1-38) Homework <2,5, 9,11,12,29,32,34,35,43,46a,53ab>
 draw a diagram for a circuit using arrows for conventional current (electric field direction)
(5)
2015 AP Review Sheet
Final 2nd Trimester

Know what capacitance depends on and be able to find the capacitance for a parallel plate
capacitor (7,8,9) <2,5>

Find the energy stored by a capacitor (10,11,12)<29,32>

Describe the electric field inside the capacitor, and relate the strength of this field to
the potential difference between the plates and the plate separation. (6)
o V=Ed
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Know what happens when the distance between the plates increases with and without a battery
(14)<35>
o Battery maintains electric potential difference
o No battery means charge is trapped on capacitor
Be able to find a new capacitance with a dielectric (with and without battery)
(15,16,18,19,20,21,22,24) <42,45>
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Be able to find the capacitance if a metal is placed between the two parallel plates (17)
Be able to add capacitors in series and or parallel (25-36) <9,11,12>
 Series: Q=, V+
 Parallel: Q+, V=
o Find charge on any individual capacitor
o Find electric potential difference across any individual capacitor
o Find energy stored by combination or individual

Be able to use Gauss’ Law to find electric field inside and outside a

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o Parallel plate capacitor (4)
o Cylindrical capacitor (37) <43,46>
o Spherical capacitor (38) <53>
Be able to find the potential difference between plates of a
o Parallel plate capacitor (6,23)
o Cylindrical capacitor (37) <43,46>
o Spherical capacitor (38) <53>
Be able to use C=Q/V to determine the capacitance of a
o Parallel plate capacitor (7)
o Cylindrical capacitor (37) <43,46>
o Spherical capacitor. (38) <53>
Chapter 26 Current and Resistance
Homework assigned<Q1,Q2,Q7,Q10,4,12,16,18,23,43,50,53>
Notes Chapter 26 (all)
 Know what current is<Q1>
o Draw conventional current (electric field = downhill) (2,3)
o I=dq/dt (2,6a)
o Ammeter (4)
o Find number of electrons (charge/1.6x10-19C) (6b)
o Area of current vs time (7)<Q2>
 Are wires charged? How fast do charges move in wires? (9)
 Use drift velocity equation I=vDnAe (12-14)<Q2,4>
2015 AP Review Sheet
Final 2nd Trimester
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Use current density equation J=I/A (15,18)<4,16>
Know when area changes how it impacts: current density, electric field, current, drift velocity,
number of charges per unit volume, resistance (16,17)<Q7,Q10>
Be able to do power rule to find current (19)<12,50>
Be able to use ohm’s law and write some “ohmisms” (20-22)<16,43,53>
Know the four characteristics that resistance depends on and why (23-24)
o Ratios! (25)<18,23>
How is resistivity different from resistance? (26)
o Use the definition of resistivity ρ=E/J
o Use V=Ex
o Use J=I/A
o Use R=ρL/A<16,53>
Be able to (27)
o Graph data
o Draw Best fit line
o Calculate Slope using two points on the line
o Use slope to solve for unknown quantity (watch units!)
Be able to calculate the rate of energy dissipation
o Power (29,31)<43,53>
o
o
o
Slope of a energy vs time graph(30)
Find energy using power (33)<43>
Use equation one of the three equations with something held constant (34-36)
Chapter 27” You can’t resist being charged up about DC circuits!”
Homework Assigned <Q6,Q8,6,12,31,40,51,55,64,65,67,70,79,89,94,97,100 >
Notes Chapter 27 (all)
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
Know the difference between terminal voltage and emf.(1,2,3,4) ε-Ir=IR
ε+Ir=IR
Recognize if a battery is providing energy or absorbing energy based on the direction of the
current (1,2,3,4)
What happens when batteries are in series and parallel? (5,6)<100>
o Be able to look at battery orientation to see if voltages add or subtract (6)
Series vs parallel(7) <31,40,51,79>
o Be able to recognize if resistors are in series (one finger… NO FORKs) or parallel
o Know when resistors have the same voltage (parallel) or current(series- flows thru
wires)
o Know when electric potential (series- splits at forks)/current (parallel) adds up
Know what resistance depends on so that you know what happens for resistors in series
and parallel(7) R=ρL/A
Be able to find equivalent resistance, voltage, current, power for a circuit or an individual
resistor (8-17,19,20)<31,40,51,79,100>
Know what the brightness of a lightbulb depends on (13,14)… Power but if R is equal than
can use I
Determine what will happen when a switch is closed in a circuit (12,13,14)
2015 AP Review Sheet
Final 2nd Trimester


Know what happens when circuit has a short circuit (13,41)… R=0 so I = max
Know what ammeters , voltmeters and fuses measure and how to place them in circuits.
o State whether the resistance of each is high or low. (18)
o Identify or show correct methods of connecting meters into circuits in order to
measure voltage or current. (60,61)
 Be able to do Kirchhoff’s loop rule (21-28)<Q6,Q8,6,12,94>
o Find current<70>
o Determine resistance (24,26)<12>
o Potential difference across two given points(25,27)<6,12>
o Power/energy(28)<12>
 Know that no current in a wire is due to no potential difference across the wire , this
includes Wheatstone! (29-33,71a)<55,89>
 Be able to use Kirchhoff’s junction rule (34-36)
 RC circuits (37-71)
o Charging (37-42)
 When the switch is first closed the capacitor V=0 (acts like closed
switch)<65,97>
 Short circuit if no resistor is with the capacitor (41)
 Resistors in series and parallel (39)
 After a long time capacitor is fully charged V=Vmax(open switch)<65,94>
 Current follows complete path (40,42,43)
 Voltage is equal in parallel!(43)
 Be able to write a loop rule for charging and discharging (differential equation)
(45,62,71b)<64>
 Be able to solve differential equation for charge as a function of time(47,64)
q=Cε(1-e-t/RC)
q=Cεe-t/RC


o Take the derivative to find current as a function of time(49,66)<67>
o Find voltage as a function of time (48,50,65,67)<64>
o Find Max charge, current(53b)<64>
o Find time for a specific charge(53c)
o Find power as a function of time (71c)<64>
o Find energy from power (71d)
Graph voltage of capacitor, voltage of resistor, charge on capacitor, current all as a function
of time(51,54b,55-57,68)
Know what time constant is and be able to use it (53,54a,69,70) τ=RC