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AP Physics – Electric Forces, Fields, Energy and Capacitance – Chapter 16-17 Chapter 16 - Reading pp. 501-527 - text HW #2,9,12,21,23,26,43,45,46,47,61,65 Chapter 17 - Reading pp. 535-562 - text HW #1,4,10,11,15,16,21,22,29,30,31,37, 40,46,48,69,70 16.1 - Static Electricity and charging by rubbing

What happens when a neutral rubber rod is rubbed by neutral fur?

Electrons are transferred from the fur to the rubber rod. As a result, the rubber rod becomes ____ charged and the fur becomes ____ charged.

What happens when a neutral glass rod is rubbed by neutral silk?

Electrons are transferred from the glass rod to the silk. As a result, the glass rod becomes ____ charged and the silk becomes ____ charged. Historical note: Thanks to Ben Franklin’s work in the 1700s, research in the field of electrostatics exploded. Unfortunately, there is one assumption in his theory we are stuck with today: Conventional (positive current) flow. Franklin put forth a fluid theory of electricity. When he rubbed silk on glass, he theorized a that the silk had excess electrical fluid, which he called “positive” and the glass was deficient in electrical fluid, so it would readily accept the electrical fluid from the silk. It would get positive, leaving the silk negative. Thus, positive flow was born. It was not until 1898 when JJ Thompson discovered the electron that scientists started to determine that it was electron flow in metal wire that accounted for current. Thus, conventional flow was was born. Some say he chose wrong, others say he just chose. And in choosing, he unknowingly gave educators to discuss many common electrical misconceptions like:

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16.2 – Electrical conductors and Electrical Insulators Electrical Conductors – materials that allow electric charges to move through them. Examples: metals (mobile electrons) (Aluminum used in long distance power lines, copper in local lines)

graphite (delocalized electrons in pi bonds between planar layers),

Ionic solutions (mobile ions in solution)

Electrical Insulators – materials that do not allow movement of electric charge.

Examples: molecular materials like wood, plastic, rubber and ceramics Con Ed Substation – Tuckahoe Road Modular suspension insulators

What is Charge? Charge is an intrinsic property of a material similar to mass. Objects with mass are affected by gravitational forces and fields. Objects with charge are affected by electric forces and fields. The SI unit of charge? The coulomb (C) What is the elementary charge? 1 e = ______________ How many elementary charges are in 1C of charge?

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What are the possible allowable charges an object can have? The allowable charges must be whole number multiples of the elementary charge. Which charges can be found on an object? 8.0C 8.0e 8.5e 8.5C 8.0 x 10-19C 8.5 x 10-19C 8.0 x 10-20C 8.5 x 10-6C

Particle Charge(C) Charge (e) Mass (u) Mass (kg)

Proton +1.6 x 10-19 C +1 e 1 u 1.67 x 10-27 kg

Neutron 0 C 0 e 1 u 1.67 x 10-27 kg

Electron -1.6 x 10-19 C -1 e 1/1836u 9.11 x 10-31 kg

What is an electroscope? An electroscope is a device that detects electric charge.

Gold leaf electroscope Braun Electroscope

Now go home and review the next two pages of notes on behavior of electroscopes and methods of charging. You must be able to explain the behavior of and movement of charge in charged and uncharged electroscopes. You also need to be able to qualitatively explain the steps and outcome of each method of charging.

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Uncharged and charged electroscopes behave differently.

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Rules of Attraction Make all demos predictive: Demo: magic soda can, magic wood, water stream vs. mineral oil, Charge balloons on students hair and have one repel the other. Demo: pith ball charging – what’s the charge Demo: Van de Graaff generator, determine its charge Demo: Leyden Jar Extra credit Video: Taking clothes out of the dryer in complete darkness

16.3 Charles Augustin Coulomb’s Law (1785) Coulomb discovered an inverse square relationship between electrostatic force and distance between charges that was similar to Newton’s Law of Universal Gravitation. Let’s say two charges q1 and q2 are separated by a distance r. Each exerts an electrostatic force on the other. Draw the forces: F12 = Force on q1 due to q2 F21 = Force on q2 due to q1

What’s the relationship between F12 and F21? They are EQUAL! Coulomb’s equation:

Where k = 9 x 109 Nm2 C2

Opposite charges attract.

Like charges repel.

Charged objects ALWAYS attract NEUTRAL OBJECTS.

Note: the only true test that proves an object is charged is _____________.

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r

qkqFe

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#1) A proton and an electron are separated by a distance of 1.2 Angstroms. Find the magnitude of the electrostatic force that each particle exerts on each other. #2) q1 = 5 nC , q2 = -6 nC, q3 = 6 nC

(A) Find the net electrostatic force on q1. (B) Find the net electrostatic force on q2.

+

+ _

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#3)

In terms of k and L, find the electrostatic force on the charge in the center of the square of side length L. #4) Point C is equidistant from charges q1 and q2

(A) At which approximate point could a positive charge q3 be placed so that the net force on it is zero? (B) Calculate the exact position of q3. (5.86m from q2, 4.14m from q1) Charge q1 is now replaced with a -1C charge. (C) Repeat parts A and B.

Now go home and do HW chapter 16 #2,9,12

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16.5 Electric Fields Gravitational force and electrostatic force are different than contact forces (tension, normal force, friction) in that they are “action at a distance” forces. So how does one charged particle interact through space to act on another charged particle? Michael Faraday in the 1830s came up with an interesting idea that electrostatic forces acted through space via a medium called the electric field such that:

When a charged body is placed in an electric field, it experiences a ________. An electric field has an electric field strength E in units of N/C Equations: Note: the second equation makes more physical sense as the Force F experienced by a particle in an electric field is proportional to the particle’s charge and the strength of the field it is in.

Note: Electric field strength is a________ Quantity. More on this later. #5) An electron is placed in an electric field. If the electron experiences a force of 6.4 x 10-17 N to the right, what is the magnitude and direction of the electric field strength at that point.

16.6 Electric Field Lines Direction Rule:

The direction of an electric field at a point in space is determined by placing a theoretical positive test charge at that point. The direction in which the positive charge moves is the direction of the field.

q

FE qEF

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#6) Draw the electric field around the following: A) an isolated positive charge. B) an isolated negative charge Electric Field Lines between two charged bodies #7) (A) Draw the electric field lines between:

(B)

(C)

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#8 ) A +6-C charge is placed in a UNIFORM electric field of magnitude 300 N/C. Find the magnitude and direction of the force on this charge.

(B) Repeat for a charge of -6 C. Remember:

Positive charges “swim” in the ___________ direction of the electric field. Negative charges “swim” in the ___________ direction of the electric field. Finding the Electric Field at a distance r away from an isolated point charge Given: An isolated point charge with charge Q Derive the equation to find the magnitude of the electric field due to charge Q on a positive test charge q at a point that is a distance r away from charge Q.

qEF 2r

kqQF

2r

kqQqE

2r

kQE

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#9) Calculate the magnitude and direction of the electric field at a point p which is 30 cm to the right of a point charge Q = - 3 x 10-6 C #10) A proton and an electron are separated by a distance of 1.2 Angstroms. Find the magnitude of the electrostatic force exerted on the electron using and Note: Now you see why we use Coulomb’s law.

#11) Calculate the magnitude and direction of the electric field at point p. Q1 = -50µC Q2 = +50µC

qEF

2r

kQE

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#12) If Q1 = -1nC and the electric field at point M is 60 N/C to the right, find the magnitude and sign of charge Q2.

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#13) (A) If Q1 = -50nC and Q2 = +30nC find the net electric field at the origin.

(B) A third charge Q3 = +20nC is brought to the origin. What is the force on Q3 due to the other two charges? Now go home and do HW chapter 16 #21,23,26,43

+

_

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16 – 6 Electric Field Lines revisited #14) (A) Draw the electric field due to an isolated point charge +Q. (B) Now, draw the electric field around charge +2Q.

Note: the number of electric field lines is proportional to the magnitude of the charge.

The electric field has the greatest magnitude where the density of the lines per unit area is greatest.

#15) Draw the electric field: A)

B)

Now go home and do HW – chapter 16 #45,46,47,61,65

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16–7 Conductors in Electrostatic Equilibrium When there is no net motion of charge in a conductor, such as a hollow, positively charged metallic sphere on an insulating stand, the conductor is said to be in electrostatic equilibrium. Studies of such objects have led to four important observations:

1) The electric field inside the sphere is _____________. 2) Any excess charges on the conductors reside entirely ____________. 3) The electric field just outside a charged conductor is _____________ to the conductor’s surface. 4) On an irregularly shaped conductor, the charge per unit area is greatest at locations where the curvature of the surface is greatest (such as at sharp points). Useful application: The Faraday Cage. Note: besides having zero electric field inside, which keeps external charge from passing through the cage, It also will keep out electromagnetic radiation, as long as the cage is thick enough and any openings are much smaller than the wavelength of the electromagnetic radiation. Faraday Cages in everyday life DEMO: The Cage – make cell phone call to student check for dead zone Typical RF signal 800-1000 MHz VIDEO: FARADAY CAGE DEMO: Glass/Metal jar with nickel/matchstick #16) Graph the Electric Field vs. distance from center of a hollow sphere for a charged sphere of radius r.(repeat for a solid sphere)

Now go home and do HW – CHAPTER 16 additional Problems

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AP Physics – Electrical Energy and Capacitance – Chapter 17 Chapter 17 - Reading pp. 535-562 - text HW #1,4,10,11,15,16,21,22,29,30,31,37, 40,46,48,69,70 Chapter 16 was the electrical version of Newton’s Laws of motion. Chapter 17 is the electrical version of the energy unit. 17.1 Potential Difference and Electrical Potential Energy Two parallel plates are connected to a battery as shown: What happens?

A UNIFORM electric field is set up between the plates.

#17) (A) If a +3-C charge is placed at points A, B, or C, where would it experience the greatest force? (B) What about a -3-C charge? (B) At what point would the positive charge have the greatest electrical potential energy? Think of “dropping” an object and conservation of energy. Would it fall from A to C, or C to A? (C) At what point would the negative charge have the greatest electrical potential energy?

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Potential difference defined:

If a positive charge is placed at point A, it will have ________electrical potential energy. If it is moved from point A to B, which has _________ electrical potential energy, _________ must be done to move this + charge to change the charge’s ______________________________. Potential Difference: The potential difference between two points is defined as the change in the electrical potential energy (work) per unit charge when a positive charge is moved from a point of low PE to high PE. (Units: _______) Equation 1: or Note: If a positive charge is moved from A to B, the work is (+ -).

If a positive charge is moved from B to A, the work is (+ -).

If a negative charge is moved from A to B, the work is (+ -).

If a negative charge is moved from B to A, the work is (+ -).

q

WV

q

PEVVV AB

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Equation 2: Since W = Fd , derive another expression for the electric field E, in terms of the potential difference.

and: thus:

Note: Valid for uniform electric fields, only. Unit Check: What, Bananas? Review of Units Write the unit for the following: Electrical potential energy ______ Electric field ______ or _______ (See above equations) Potential difference _______ or ______ Electrical Potential _______ (at two different points, used to find ∆V) Potential ______ (for lazy physicists) Potential drop ______ (used when discussing circuits) Voltage ______ (voltage of a battery is the potential difference between terminals)

qEFFdW qEdW EdV

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#18) Two parallel plates are separated by a distance of 0.05 m and connected to

a voltage source that has a potential difference of 50 V. A) Calculate the electric field between the plates. (magnitude and direction) B) An electron is placed at point A. Calculate the force on the electron (magnitude and direction). C) Calculate the work required to move the electron from point A to point B. D) The electron is now released from point B. Determine the speed of the electron when it hits plate A. E) How much time does it take the electron to go from plate B to plate A? (use Fat Mav)

#19) An ion with charge q and mass m is accelerated through an electric field of magnitude E. What is the magnitude of the acceleration in terms of q, m, and E?

Now go home and do HW chapter 17 - #1,4,10,11

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17.2 Electric Potential Energy between 2 point Charges

If the two charges above start from rest, they initially have KE = ____. As they move farther apart, their KE _______ while their electrostatic PE ________. How do we determine the initial PE in terms of q1, q2 and r? To derive the equation, assume one point charge is fixed and the other is moved from infinity to a distance r apart. 1) Determine work required to move q2 from infinity to a distance r (where PE and Electric potential is set at zero). NOTE: Calculus needed here.

So from this derivation we get a couple of equations: and: More on this one later…

Remember: PE is a ________quantity. But, we need to put in the sign of the charge now because: If the reference level PE= zero @ ∞, then:

1) If like charges then PE is + at a distance r apart

(work needed to move them from ∞ to r distance apart) 2) If opposite charges then PE is – (PE lower relative to infinity as the opposite charges fall towards each other).

r

qkqr

r

qkqdFVqW e

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2

2112

r

qkqPE 21

r

kqV 1

1

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#20) Find the potential energy between two protons separated by a distance of 2 µm.

#22) Find the potential energy between two electrons separated by a distance of 2 µm.

#23) Find the potential energy between a proton and an electron separated by a distance of 2 µm.

#24) Calculate the Electric Potential Energy of the system if:

q1 = 6µC, q2 = 8µC, q3 = -2µC

#25) Calculate the amount of external work done to move the system of charges (from #24) from infinity to the positions shown above.

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#26) Two protons an infinite distance away are moving at 3 x 107 m/s towards each other. What is the distance between the charges when they stop, before they begin to move away from each other due to their repulsion?

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17.2 Electric Potential around a point charge

There exists a potential difference between points A and B since by definition, it requires work to move a positive charge from a point of low potential energy to a point of higher potential energy. Therefore there exists a “potential” at each individual point.

Remember that equation from before?

Potential is a SCALAR quantity, but as we did with Electrical PE, the sign is included, thus: potentials near + charges are __________, and potentials near – charges are __________

Unit of electric potential: Sign convention explained: If the two charges above have the same magnitude of charge, and pt A and pt B are the same distance apart from their respective charges, then magnitude of the voltage at point A and B is the same. But we know that a positive test charge would “fall” from high potential to low potential. That can only happen if we make one of the potentials negative.

r

kqV 1

1

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#27) Calculate the electric potential at:

(A) point A (B) point B (C) What is the potential difference between points A and B? (Vab) D) If a 2-nC charge is moved from B to A, how much work is needed? #28) Calculate the potential 4m from a proton. #29)Calculate the potential 4m from an electron.

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Electric potential due to 2 or more charges #30)

Given: q1 = 5 nC q2 = -2 nC (A) Find the electric potential at point P. Remember, potential is a SCALAR quantity, so there are no components to worry about. To find total electric potential, simply find the algebraic sum of the potentials due to each charge at that point. Just remember the signs! (B) How much work is to needed to bring a third charge (4 nC) to point P from infinity?

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#31) (A) The net electric field could be zero ____left of q1 ____right of q2 ____between q1 and q2 (B) Find the exact location(s) on the line where the electrostatic potential is zero. #32) (A) The net electric field could be zero ____left of q1 ____right of q2 ____between q1 and q2 (B) Find the exact location(s) on the line where the electrostatic potential is zero. Now go home and do HW Ch 17 - #15, 16, 21, 22

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17.4 Equipotential Surfaces

All points on an equipotential surface have the same electric potential. #33) (A) Draw the electric field around an isolated positive charge. (B) Relative to the potential at point A above, where is the potential the same around this charge? Draw the equipotential surface.

Note: electric field lines and the equipotential surfaces are always drawn _______________________________. PHYSICS APPLET

(C) repeat for an isolated negative charge

(D) repeat for two positive charges, equal in magnitude.

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(E) repeat for a positive and negative charge of equal magnitude.

(F)What happens when the magnitude of each charge is not equal? PHYSICS APPLET

(G) Draw the electric field and the equipotential surfaces for two parallel plates.

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#34) Charge q = 6 nC. The dotted lines represent equipotential surfaces. (A) Find the electric potential at pts A, B and C. B) How much work is required to move a -3 C charge from infinity to point B? C) How much work is required to move a -3 C charge from pt. A to pt. B? #35) (A) Graph the Electric Potential vs. distance from center of a solid sphere for a charged sphere of radius r.

Remember, since the electric field is zero inside a conductor, no work is required to move a charge between two points inside a conductor. The electric potential is constant everywhere inside a conductor and equal to its value at the surface! (it’s like an equipotential blob)

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(B) repeat for a hollow sphere.

Back to Chapter 16: Millikan’s Oil Drop Experiment (1923)

Millikan Oil Drop Simulation Millikan Oil Drop Actual microscopic view

What did Robert Millikan do? Millikan varied the voltage between the plates so that the upward electrostatic force on a charged oil drop that was shot from the perfume bottle would balance the force of gravity on the drop. See actual equation

Conclusion: Millikan’s data showed that and was always a multiple of _______________. Hence, the charge on a body is quanticized. Bye-bye, Fluid theory!

E

mgq

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Remember the two charged spheres brought together and separated? #36) (A) Two metal spheres of the same size, q1 = 4C and q2 = 8 C are brought together and separated by an external force. What is the charge on each after they are separated? (B)What is the direction of the electron flow? #37) Same problem, different radii. Is the outcome the same?

(A) If a conducting wire is placed between the two charges, what will the charge be on each after they are connected? (B) What’s the direction of the electron flow?

Electrons will flow from one object to another until their ___________ are the same!!!

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#38)

A) If a conducting wire is placed between the two wires, what will the charge be on each after they are connected? B) What’s the direction of the electron flow? #39) A) If a conducting wire is placed between the two wires, what will the charge be on each after they are connected? B) What’s the direction of the electron flow?

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#40)

A) If a conducting wire is placed between the two wires, what will the charge be on each after they are connected? B) What’s the direction of the electron flow? Hand out problem 50 – T Hand out Chp 17 (additional Problem sheet) (Harder) Hand out Electrostatics Extra Problems (Chapter 16 & 17)

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17.5-6 Capacitance and the Parallel Plate Capacitor Recall: two neutral parallel plates, separated by a distance d, are connected to a battery as shown: (A) Draw the flow of electrons.

(B) When does electron flow stop? When the potential difference between the plates is equal to the voltage of the battery. (C) What happens if the power supply is now removed?

The charged parallel plates are now a capacitor – two parallel plates that store electric charge DEMO: GENECON with 1F capacitor/light bulb (redo for series/parallel later) DEMO: 1st Capacitor – The Leyden Jar (1744)

Note: Since the electrons are pulled off of one plate and transferred to the other plate, it takes a long time for the capacitor to charge. After this long time we say the capacitor has reached STEADY STATE and will charge no further. Uses for Capacitors – Capacitors are used in circuits where any of the following a required: (1) Energy Storage – Capacitors maintain power supply in electronic devices while the battery is being changed. This is why when pulling the battery to restart your phone, you need to keep it out for 15 seconds or more to allow any capacitors to drain. (2) Pulsed Power – Capacitors are used when a large current is required for a very short time (Tasers, flashbulbs on cameras, high-energy pulsed lasers, detonators in nuclear weapons) This is because DC batteries have fairly large internal resistance and cannot deliver large quantities of charge in a short time. (3) Power Conditioning – Unlike motors, incandescent light bulbs, or heating elements that can run on AC current, electronic devices (laptops, TVs, music systems) required DC current. These devices when not running on DC battery power, require rectifiers, that convert AC to DC current. While AC runs in one direction, it powers the device and charges capacitors. When the AC reverses, the rectifier “shuts off” the AC (through the use of transistors or tubes), and the capacitors release their charge to keep current flowing in one direction.

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(4) Tuned (LC)Circuits – a tuned circuit combines an inductor and a capacitor which is essentially a harmonic oscillator used in radio tuners to tune to a certain frequency. (More on inductors later) (5) RC Circuits – combine a resistor and a capacitor and act as electronic timers. They also act as filters, allowing only certain frequencies to pass through.

Capacitance Equations:

Capacitance is the ratio of the magnitude of charge on the plates to the magnitude of the potential difference between them. To increase the capacitance between two plates we can change several variables. How do these affect capacitance?

(1) __________ the surface area of the plates: (allows for more charge to be held at the same voltage)

(2) __________ the distance between the plates: (increases the attractive force between the plates at a given voltage, allowing for a greater electric field strength and therefore a greater buildup of charge on the plates)

(3) __________ the material between the plates. (by using a better insulating, yet polarizable material, (a.k.a. dielectric material) other than air between the plates, more charge can be put on the plates before arcing occurs)(Stud Finders)

Note: k = dielectric constant (for air: k = 1, for glass: 5-10) εo= electrical permittivity of free space= 8.85 x 10-12 C2/Nm2 A = Area of either plate d = distance between the plates Units of Capacitance: 1 C/V = 1 F (1 coulomb/volt = 1 farad) Circuit Symbol:

V

QC

d

AkC 0

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Also, note that the electrostatic constant Because the dielectric constant is also k, many textbooks write Coulomb’s law as #41) A capacitor is composes of two parallel plates separated by a 0.001 m air gap. The plates are 0.2m long x 0.03 m wide. (A) Calculate the capacitance of the capacitor. (B) Calculate the charge on each plate if the capacitor is connected to a battery with a potential difference of 12 V. (Assume the capacitors has reached steady state.) (C) Determine the number of electrons transferred from one plate to the other to bring it to the charge determined in B. #42) A capacitor with capacitance C0 is charged by voltage source V0, giving it a charge Q0. Determine new values for capacitance, charge and voltage in terms of C0, Q0, and V0 for each of the following:

04

1k

2

21

04

1

r

qqFe

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(A) The distance between the plates is doubled while the voltage source is connected to the circuit.

C1= Q1= V1= E1= B) The voltage source is removed, and the circuit remains open.

C2= Q2= V2= E2=

17.8 Energy stored in a capacitor

Remember: is the work required to move a quantity of charge across a potential difference. Well, when the plates are neutral, the work to move one charge is negligible compared to the work later to move a like charge onto a plate nearing steady state.

and: thus:

#43) A battery is placed across a capacitor as shown in the circuit diagram below.

QVW

CVQQVQEddFW2

1

2

1

2

2

1CVW

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(A)Calculate the charge on the capacitor at steady state. (B) Calculate the electrical energy stored in the capacitor. Check out this video summing it all up Now go home and do HW #29, 30, 31

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17.8 Combinations of Capacitors

I. Capacitors in Parallel (not to be confused with resistors in parallel)

#44) (A) The potential across C1 _____ (B) The potential across C2______

Remember: V=V1=V2=V3 in a parallel circuit

(C) The charge on C1____ (D) The charge on C2_______ (E) The total equivalent capacitance.______ (F) The energy stored in C1____ (G) The energy stored in C2_____ (H) The total energy stored_______

RULES (Parallel Capacitors):

Ceq = C1 + C2 + … V=V1=V2=V3 CeqV = C1V + C2V + … or: QT= C1V + C2V + … ET = ½ CeqV2

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#45)

(A) The potential across C1 _____ (B) The potential across C2______ (C) The charge on C1____ (D) The charge on C2_______ (E) The total equivalent capacitance.______ Total charge_____ (F) The energy stored in C1____ (G) The energy stored in C2_____ (H) The total energy stored_______

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II. Capacitors in Series

#46) The circuit above comprised of uncharged capacitors initially,has been hooked up for a long time. (A) Which capacitor has a greater capacitance? Justify your answer. ______ C1 ______C2 ______ C1=C2

Duh. C1 is labeled with a greater capacitance. (B) Which capacitor has a greater charge? Justify your answer. ______ C1 ______C2 ______ C1=C2 Since C1 and C2 are originally neutral, the wire joining C1 and C2 has an equal amount of positive and negative charge. When voltage is applied, the right plate of C1 must have a charge of –Q, and The left plate of C2 must have a charge of +Q. Because of this, both capacitors must have the same charge! RULES (Series Capacitors):

V=V1+V2+V3… Q = Q1 = Q2 = Q3… Q/Ceq = Q/C1 + Q/C2 + … ET = ½ CeqV2

...1111

321 CCCCeq

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Hmmm… Why is the relationship for: (i) capacitors in series the same as resistors in parallel (ii) capacitors in parallel the same as resistors in series

It’s in the equations that derive capacitance and resistance:

Notice: C is proportional to A, R is proportional to 1/A. Putting capacitors and resistors in parallel effectively increases A, which increases Ceq but decreases Req. Moreover, C is proportional to 1/d, R is proportional to L. Putting capacitors and resistors in series increases L or d. Increasing L increases Req but decreases Ceq (it’s like moving the plates farther apart).

d

AkC 0

A

LR

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#47) (A) Equivalent capacitance (B) Draw the equivalent simple circuit (C) Total charge? (D) Charge on C1 (E) Charge on C2 (F) Potential across C1? (G) Potential across C2? (H) Energy stored by C1? (I) Energy stored by C2? (J) Total energy stored?

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Combinations of Parallel and Series Capacitors #48) For each of the following, find the equivalent capacitance Ceq (A)

(B)

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(C) Find the total capacitance when (i) switch S is open (ii) switch S is closed

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#49) Given four capacitors, each of C = 4 F. Using all four, draw a circuit such that the equivalent capacitance is: A) 1 F B) 16 F C) 4 F D) 2.4 F E) 3 F F) 10 F G) 1.6 F (A) All in series (B) All in parallel (C) (2 in series) // (2 in series) (D) [(2 in series) // 1] in series 1 (E) (3 in parallel) in series 1 (F)? (G)??

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#50)

Fill in the chart:

Charge Capacitance Voltage Energy C1 4 pF

C2 3 pF

C3 5 pF Total

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#51)

Fill in the chart: Charge Capacitance Voltage Energy

C1 3 nF

C2 2 nF C3 4 nF

C4 6 nF Total

Now go home and do HW #37,40,46,48,69,70

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#52) Additional Practice Problem

Fill in the chart:

Charge Capacitance Voltage Energy

C1 72.8 C 1 F 72.8 V 2647.7 J C2 72.8 C 2 F 36.4 V 1324.1 J

C3 18.6 C 3 F 6.2 V 57.5 J C4 18.6 C 4 F 4.65 V 43.2 J

C5 54.25C 5 F 10.85V 293.8 J

Total 72.84C 0.607 F 120 V 4366.3 J It’s not the volts that kills you, it’s the amps! Chapter 16-17: Done.