Physics II Lab: quiz 1

L =

6.59 miles

Capacitors are widely used in electronic circuits where it is important to store charge and/or energy or to trigger a timed electrical event. For example, circuits with capacitors are designed to do such diverse things as setting the flashing rate of Christmas lights, selecting what station a radio picks up, and storing the electrical energy needed to fire an electronic flash unit. Any pair of conductors that can be charged electrically so that one conductor has excess positive charge and the other conductor has an equal amount of excess negative charge on it is called a capacitor

A capacitor can be made up of 2 differently shaped blobs of metal or it can have any number of regular symmetric shapes, such as one hollow metal sphere inside another, or a metal rod inside a hollow metal cylinder (figure 8-1, page 150).

The actual mathematical expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d (figure 8-3) is derived in your textbook. The result when there is vacuum (or just a low-density gas) between the plates is

C = ε0 A / d where ε0 = 8.85x10^-12 C^2/Nm^2

M3L8

Introduction to capacitors and RC circuits

M3L9

Magnetism

M3L8 homework

VVV

correct image (page 170) is

antiparallel orientation (left)

questions 2-2: How did your equation agree with your prediction? Explain

because both added together measured the same as the total

question 1-7: What difficulties did you encounter in making accurate measurements?

getting the correct number of pages between

question 3-5: Does the actual behavior over time observed on the current graph agree with your sketches in Questions 3-2 and 3-3? DO any features of the graphs surprise you? Explain

yes agrees

question 1-12: Do the poles of an individual disk magnet behave the same way when the disk is in the center of a stack? Explain

yes because it still has a north and south pole

question 1-6: what mathematical relationship best describes the dependence of capacitance on plate separation or plate area. How do the results compare with your prediction based on physical reasoning?

C = ε0A/d as distance (d) increases, capacitance decreases

Investigation 3: charge buildup and decay in capacitors

Capacitors can be connected with other circuit elements. When they are connected in circuits with resistors, some interesting things happen. In this investigation you will explore what happens to the voltage across a capacitor when it is placed in series with a resistor in a direct current circuit. From your observations, you should be able to devise qualitative and quantitative explanations of what is happening

questions 2-1: from your measurements, figure out a general equation for the equivalent capacitance of a parallel network in terms of C1 and C2. Explain how you reached your conclusion

Ceq = C1 + C2

prediction 2-2: Use direct physical reasoning to predict the equivalent capacitance of a pair of capacitors wired in series. Explain your reasoning [Hint: if you connect two capacitors in series, what will happen to the change along the conductor between them? What will the effective separation of the "plates" be? Will the effective area change?]

Ceq in series will be less than Ceq in parallel

For the circuit in Question 3 indicate whether the statement 'the voltages across both capacitors are the same.' is TRUE or FALSE.

False

activity 1-1: permanent Magnet Poles

Fiddle with the two permanent magnets and explore the interactions

Magnetic Orientations

Next, let's explore how a suspended magnet orients itself when it is placed close to another identical magnet. What happens when the suspended magnet is placed far away from any other magnets? For this activity you will need to tie a string tightly around the center of a magnet and put a small piece of tape under the string as shown in the figure on page 170. Set up a rod stand, rods, and clamp to suspend the magnet a few cm above the table note: the stand rods and clamp and table should be non-magnetic

You can construct a parallel plate capacitor out of two rectangular sheets of aluminum foil separated by pieces of paper.

Pages in the UVa directory work quite well as the separator for the foil sheets. You can slip the two foil sheets on either side of paper sheets, and weigh the book down with something heavy like some textbooks. The digital multimeter can be used to measure the capacitance of your capacitor.

magnetic interactions with permanent magnets and other objects

Permanent magnets can interact with each other as well as with other objects. Let's explore the forces exerted by one magnet on another and then make qualitative observations of forces that a magnet can exert on other objects

In Question 7 how would your observations be changed if the capacitor were twice as large?

The bulb would start bright, then gets dimmer and dimmer for a short time and finally goes out.

For the circuit in Question 3 indicate whether the statement 'the sum of the voltages on the two capacitors equals the voltage of the battery.' is TRUE or FALSE.

True

question 1-2: Can the excess positive charges on one plate of a charged parallel plate capacitor exert forces on the excess negative charges on the other plate? Explain

Yes, electric field can pass through non-conducting material

Note: One of the ends of a bar or cylindrical magnet is usually called the north pole and the other the south pole.

You will explore why shortly.

question 1-6: What does a compass needle probably consist of? Explain

a magnetized material because the orientation of the magnet to the compass affects the position of the needle

Capacitance is defined as

a measure of the amount of net or excess charge on either one of the conductors per unit potential difference. Thus the more charge a capacitor can store at a given voltage, the larger the capacitance. -d = spacing -A = area -V = voltage

question 3-6: Based on the graph of potential difference across the capacitor, explain why the bulb lights when the switch is moved from position 1 to position 2 (when the bulb is connected to the capacitor with no battery in the circuit)? Also, explain the way the brightness of the bulb changes with time

the capacitor isn't taking charge from the battery during this time

Investigation 1: Magnetic Forces and Fields

*permanent magnets* the attraction of iron to a magnet is so familiar that we seldom realize that most of us know little more than the ancients about how the attraction occurs. Let us begin our exploration of magnetism by playing carefully and critically with some permanent magnets and observing what happens

describes the properties of a parallel plate capacitor

-If the area of the plates is increased the capacitance increases. -This is because more electrons can fit on the plates with the same force between them (the same potential is applied). -The capacitance decreses as the separation between the plates increases. -This is because the electric field between the plates decreases (same applied voltage)

question 1-5: If the suspended magnet still appears to orient itself, what might be underneath the room? Does the orientation happen outdoors? if its convenient, take a suspended magnet outside. What might be under the ground?

-a conducting material -no

prediction 1-1: Assuming that two rod-shaped magnets are identical, do you expect the "like" ends of a magnet to attract or repel each other? What do you predict will happen if you bring "unlike" ends together?

-like repel -unlike attract

question 1-1: Do the like ends attract or repel each other? What about the unlike ends? How do the rules of attraction and repulsion compare to those for electrical charges of like sign? Are the rules the same or different?

-like repel -unlike attract -same rules, like charges repel and unlike attract

question 1-1: What type of excess charge will build up on the metal plate that is attached to the negative terminal of the battery? What type of excess charge will build up on the plate that is connected to the positive terminal of the battery? Explain.

-negative charges on the negative terminal -positive charges on the positive terminal

question 1-2: Each pole represents a different type of magnetic charge. Can you find a magnet with just a north pole or just a south pole? Can you find unlike electrical charges separately? Discuss the differences between electrical and magnetic charges.

-no -no -electrical charges deal with electrons

question 1-7: Are the north poles of your large permanent magnets red or blue? Describe how you determine this?

-north pole is the side with the dash in it -compass pointed south to that end

question 1-4: If the battery is then disconnected, what do you think would happen to the potential difference between the plates if the separation, d, were decreased with the excess charge on each plate held constant? Explain. [Hint: What happens to the electric field between the plates as d decreases while the excess charge is kept constant by disconnecting the capacitor form the battery? What happens to the potential difference across the plates as d is made smaller after the capacitor is disconnected from the battery?]

-potential difference will decrease Q = AεV/d

question 1-5: Describe how you measured all of the quantities in table 8-1 (page 153). Explain how you varied the separation or the area

-separation was varied and measured by pages in the book -length and width of the plates were measured and area was found by multiplying them together -capacitance measured with multimeter

question 1-8: Which pole fo your compass is the north pole? Describe how you determined this. (On average, which poles are the north poles?)

-the side with the red tip -south end of the magnet attracted the red end

question 1-10: After making 2 stacks, does it behave like the unbroken rod-shaped magnet? Why or why not? Does it have north and south poles?

-yes, have their own poles -yes

question 1-11: After pulling the magnets apart completely, does it behave like the unbroken rod-shaped magnet? Why or why not? Does it have north and south poles?

-yes, have their own poles -yes

question 1-9: Does it behave like the unbroken rod-shaped magnet? Why or why not? Does it have North and South poles?

-yes, have their own poles -yes

question 3-9: Use the exponential function to calculate the time constant for your capacitor-resistor combination. [Hint: what time t in the function would make the value for V(t) be just 0.37 V0? (This is just V0/e), where e is the base of natural logarithms.)] Use your values for R and C. Show all work. Does this value agree with your measured value?

0.11/e = 0.0405 yes, ours was at 0.0407

activity 1-4: determining magnetic poles

1.) make observations to determine which poles of your magnets are north-the red poles or the blue poles 2.) make observations to determine which pole of your compasses are north (warning: sometimes cheap little compasses get magnetized in the "wrong" way. Check a group of little compasses)

activity 1-3: Magnet orientation

1.) place identical magnet on the table under the suspended magnet (shown in figure on page 170) 2.) circle which figure accurately represents the suspended magnet 3.) next, suspend both magnets at some distance away from each other so they don't interact 4.) repeat 3 with two small compasses

activity 1-5: Magnetic Disks Together and Apart

1.) place the 4 disks in a stack and compare the behavior of the resulting magnet with that of the rod-shaped magnet 2.) pull the stack apart into 2 stacks with 2 disks in each stack. Compare the behavior of one of the resulting magnets with that of the rod-shaped magnet 3.) Pull the magnets apart completely. Compare the behavior of one of the resulting magnets with that of the rod-shaped magnet

questions 2-3: Are your measurements consistent with the following equation for combining capacitors connected in series into an equivalent capacitance Ceq? 1/Ceq = 1/C1 = 1/C2 Show the calculations you used to reach your conclusion

1/Ceq = 1/0.225 + 1/0.230

The type of capacitor that is the easiest to analyze is the parallel plate capacitor. We will focus exclusively on these.

Although many of the most interesting properties of capacitors come in the operation of AC (alternating current) circuits (where current is first moves in one direction and then in the other), we will limit our present study to the behavior of capacitors in DC (direct current) circuits. The circuit symbol for a capacitor is a simple pair of lines as shown in Figure 1-2. Note that it is similar to the symbol for a battery, except that both parallel lines are the same length for the capacitor.

Activity 1-2: Measuring how capacitance depends on area or on separation

Be sure that you understand how to use the multimeter to measure capacitance and how to connect a capacitor to it. Devise a way to measure how the capacitance depends on either the pool area or the separation between foils. Of course, you must keep the other variable (separation or area) constant. When you measure the capacitance of your "parallel plates" be sure that the aluminum foil pieces are pressed together as uniformly as possible, and that they don't make electrical contact with each other If you hold the separation constant, record its value in table 8-1 (page 153). This may be measured in "pages" or the vernier caliper or micrometer may be used to translate this into meters. The area may be varied by using different size sheets of aluminum foil Alternatively, if you hold the area constant and vary separation, then record the dimensions of the foil so you will be able to calculate the area and enter it in table 8-1 (page 153)

question 1-9: Use one of your actual areas and separations that corresponds to measurements you recorded in table 8-1 (page 153) to calculate a value of C using this equation. Show your calculations. How does the calculated value of C compare with your measured value? What might be wrong with the theoretical model for a capacitor in describing the behavior of your capacitor in this activity?

C = (8.85x10^-12) (0.013) / 0.0026 C = 0.313 slightly off

In general, the amount of charge needed to produce a potential difference equal to that of the battery will depend on the size, shape, location of the conductors relative to each other, and the properties of the material between the conductors. The capacitance, or the ability to store electric charge, of a given capacitor is defined as the ratio of the magnitude of the charge, q (on either one of the conductors) to the voltage (potential difference), V, applied across the two conductors. Thus

C = q/V

measure the capacitance of each capacitor with the multimeter. include units

C1: 0.225 nF C2: 0.230 nF

Investigation 2: capacitors in series and parallel

Capacitors come in all sizes, shapes, and colors. take a look at the array of actual capacitors. You can measure their capacitances with the multimeter. you can also connect them in various series an parallel combinations and measure the equivalent capacitances of these combinations The definitions of series and parallel wiring are the same as for other circuit elements such as resists as shown in figure 8-4 (page155) In series connection, there is only one path for the charge. Whatever charge is placed on one of the capacitors must also be transferred to the other(s). In a parallel connection, the 2 terminals of each capacitor are connected directly to the terminals of the other(s). Each capacitor defines a branch, so that the total charge transferred to the capacitor combination is divided among the different capacitors To examine the equivalent capacitance of 2 identical capacitors connected in series or in parallel you'll need the stuff on page 155

Prediction 2-1: Use direct physical reasoning to predict the equivalent capacitance of a pair of capacitors with capacitance C1 and C2 wired in parallel. Explain your reasoning below. [Hint: What is the effective area of 2 parallel-plate capacitors wired in parallel? Does the effective separation between plates change when the capacitors are connected in parallel?]

Ceq = C1 + C2 in parallel, both receive the same amount of split current

connect the same 2 capacitors in series and measure the equivalent capacitance of the series combination

Ceq: 0.1138

connect the 2 capacitors in parallel and measure the equivalent capacitance of the parallel combination

Ceq: 0.455 nF

Activity 1-1: Predicting the dependence pf capacitance on area and separation

Consider two identical metal plates of area A that are separated by a distance d. The space between the plates is filled with a non- conducting material (air, for instance). Suppose each plate is connected to one of the terminals of a battery.

Although electricity and magnetism are not the same thing, the fascinating this is that, from a theoretical perspective, these two phenomena that appear different in many ways are closely related. For example electric currents that are caused by electric fields can cause magnetic effects. Permanent magnets can exert forces on current-carrying wires and vice versa. Electric currents can produce magnetic fields, and changing magnetic fields can, in turn, produce electric fields

In contrast to our earlier study of electrostatics, which focused on the forces between resting charges, the study of magnetism is at heart the study of the forces acting between moving charges.

Magnetic "field" lines around a rod-shaped magnet

In preparation for defining a quantity called magnetic field which is analogous to, but not the same as, an electric field, you should explore the alignments of the small compass at various places nearthe larger cylindrical magnets. This will allow you to postulate the existence of magnetic flux and of a mathematical law for magnetic flux not unlike Gauss' law for electrical flux. The direction of the magnetic field at a point in space is defined as the direction that a small magnet (e.g., compass needle) would point (which way the North pole would point) if it was placed at that point. By determining the orientation of a compass at different points around a rod-shaped magnet, you have effectively determined what the magnetic field around the rod-shaped magnet looks like, Of course, it is difficult to determine the orientation at all points around a rod-shaped magnet by suing something as large as a compass needle. However, there is a very nice method for determining the magnetic field around a rod-shaped magnet that uses the fact that iron becomes magnetized in a magnetic field.

question 1-10: In theory, what length and width in miles would big square foil sheets separated by a distance of 1 mm with wax paper have to be on each side for you to construct a 1-F capacitors? Show your calculations. Assume that wax paper has the same electrical properties as air. [Hint: Miles are not meters! In fact, 1000 m = 1 km = 0.62 mile]

L = 6.59 miles 1 = (8.85x10^-12) A / 0.001

Activity 3-1: Observations with a capacitor, battery, and bulb

Set up the circuit shown in Figure 8-5 (page 157) If you are using a "polar" capacitor with + and - signs on its inputs, be sure that its positive and negative terminals are connected correctly

How would your observations in Question 7 be changed if the bulb had half as much resistance?

The bulb would start brighter, then gets dimmer and turns off in a shorter time

Investigation 1: Capacitance, Area, and Separation

The usual method for transferring equal and opposite charges to the plates of a capacitor is to use a battery or power supply to produce a potential difference between the two conductors. Electrons will then flow from one conductor (leaving a net positive charge) and to the other (making its net charge negative) until the potential difference produced between the two conductors is equal to that of the battery (see figure 8-3, page 151)

comment: If you made careful measurements of V vs t for a capacitor C discharging through a resistor R, you should have obtained what is known as an *exponential decay curve*.

This curve has exactly the same mathematical form as the cooling curve you may have encountered in the study of heat and temperature. Mathematical reasoning based on Ohm's law as well as the definitions of current and capacitance can be used to show that the following equation represents the voltage V(t) across the capacitor as a function of time V(t) = V0 e^-t/RC In this equation, V0 s the initial potential difference across the capacitor. (Note that V0 is not necessarily the voltage of the battery)

There are several types of capacitors typically used in electronic circuits including disk capacitors, foil capacitors, electrolytic capacitors and so on. You should examine some typical capacitors that should be on your table.

To complete the next few activities you will need to construct a parallel plate capacitor and use a multimeter to measure capacitance.

3.) For the circuit below, two capacitors of different capacitance are connected in series. Indicate whether the statement 'Both capacitors have the same amount of charge on their plates.' is TRUE or FALSE

True

activity 2-1: Equivalent Capacitance for Parallel Connection of Capacitors

VVVVV

By now, you should have discovered that the Earth behaves as if it has a rod-shaped magnet embedded in it. The Earth's magnet also has 2 poles- a north and south pole, just like any other magnet

Want to know something crazy?! The north pole on the earth attracts the north pole on the magnet. So magnetically, the earth's north pole is actually a south pole. This is just as bad as the way Ben Franklin defined the signs of charges so that, once they were discovered, electrons turned out to be negative.

For each of the following combinations of capacitors match the equivalent capacitance. (All capacitances are in μF. a.) in series: 20, 30, 30 b.) 20 and 30 in series and two 15s in parallel c.) 10, 20, 30, 40 in parallel

a.) 1/20 + 1/30 + 1/30 = 1/Ceq Ceq = 2. 8.6μF b.) 1/20 + 1/30 + 1/(15+15) = 1/Ceq Ceq = 2. 8.6μF c.) 10 + 20 + 30 + 40 = C C = 100 μF

prediction 1-3: based on your previous observations, do you expect the suspended magnet to align itself parallel or antiparallel to a stationary magnet? why?

anti-parallel because unlike attract

prediction 1-4: How do you predict the pieces will behave if you break them into 2 pieces, and so on?

any way you break it up, the magnet will create new north and south poles on each piece

prediction 3-1: What do you predict will happen to the brightness of the bulb when you move the switch to position 1 for a while?

decrease brightness over time because the capacitor will collect charges

In the circuit below, the capacitor is initially charged. It has capacitance of 0.023F, while the resistor has resistance 47Ω. How long after the switch is closed does the voltage on the capacitor fall to 37% of its initial value? Circuit: capacitor, resister, and switch in series

e^(0.023)(47) x .37 = *1.1s*

question 1-3: Consider two identical metal plates of area A that are separated by a distance d shown in figure 8-3 (page 151). If the area, A, of the plates were increased (with the spacing and potential difference between the plates held constant) what do you think would happen to the amount of excess charge on each of the plates? Explain your reasoning. How will this affect the capacitance of the capacitor? [Hint: Do the electric field and potential difference between the plates depend on the total charge one each plate, or on the charge permit area?]

excess charge should decrease as well as capacitance too because capacitance and area are directly proportional

data recorded:

initial voltage: 0.11 37% of initial voltage: 0.0407 time: 0 time: 2.48 time constant: 2.48

As you have seen before, a bulb does not have a constant resistance. Instead

its resistance is temperature-dependent and goes up when it is heated by the current through it. For more quantitative studies of the behavior of a circuit with resistance and capacitance. you should replace the bulb with a 22 ohm resistor

The unit of capacitance is the farad, F, named after Michael Faraday. One farad is equal to one coulomb/volt. As you should be able to demonstrate to yourself shortly, the farad is a very large capacitance. Thus, actual capacitances are often expressed in smaller units with alternate notation as shown below:

microfarad: 1mF = 1μF = 1UF = 10^-6 F nano farad: 1 nF = 1000 mmF = 1000 μμF = 1000 UUF = 10^-9 F pico farad: 1pF = 1mmF = 1μμF = 1UUF = 10^-12 F (Note that m, μ, and U when written on a capacitor all stand for a multiplier of 10^-6.)

question 1-4: Do the non-interacting suspended magnets appear to be oriented relative to each other? If yes, what is the direction of their orientations? Cite evidence for or against orientation

no

question 1-13: What do you think would happen is you cut one of the individual magnets in half along its axis? Does it seem possible to split a magnet into one with just a north pole and another with just a south pole?

no, the magnets will just create new poles

question 3-1: Sketch the complete circuit for current when the switch is in position 1 and in position 2

page 157

question 3-2: Draw a sketch on the axes below of the approximate brightness of the bulb as a function of time for the above case where you move the switch to position 1 after it has been in position 2 for a long time. Let t = 0 be the time when the switch was moved to position 1

page 158

question 3-3: Draw a sketch on the axes below (page 158) of the approximate brightness of the bulb as a function of time when it is placed across a charged capacitor without the battery present, i.e., when the switch is moved to position 2 after being in position 1 for a long time. Let t = 0 when the switch is moved to position 2

page 158

For a fixed voltage from a battery, the net charge found on either plate is proportional to the capacitance of the pair of conductors and the applied voltage

q = CV

A 1.5V battery is connected to a 250μF capacitor. The charge stored on the capacitor is

q = VC q = (1.5) (250x10^-6) *q = 375x10^-6 C*

activity 3-2: The Rise and Decay of Voltage in an RC Circuit

replace the light bulb with a 22 ohm resistor

question 1-3: How do your predictions and observations compare? Be specific

same

Prediction 3-2: What do you predict will happen to the brightness of the bulb after you move the switch back to position 2?

same thing, brightness will decrease over time

activity 1-6: Field Directions Around a Rod-Shaped Magnet and Gauss' Law for Magnetic Fields

sprinkling the iron fillings to show magnetic field

7.) In the circuit below, the capacitor is initially uncharged. When the switch is closed, the bulb Circuit: battery, capacitor, and resistor in series

starts bright, then gets dimmer and dimmer slowly until it goes out.

suppose you have a magnet made up of several small disks stuck together. How does its behavior compare to that of the rod magnets you have been using?

stronger magnetic force

prediction 1-2: List at least four objects, one fo which is an aluminum rod. Predict what will happen if you bring each object near one pole of a magnet and then near the other pole of that magnet (first table on 169)

table 1 on page 169

activity 1-2: Permanent Magnet Interactions with Objects observe what happens when you bring the various objects close to each of the poles of the magnet and summarize your results in the second table on 169

table 2 on page 169

question 1-15: Try to explain what was happening to the iron filings to cause the pattern you saw

they were becoming magnetized and following the magnetic field

question 1-8: Do your predictions and/or observations on the variation of capacitance with plate area and separation seem to agree qualitatively with this result? Explain

yes, because d and c are inversely proportional

questions 2-4: Is the equation given in questions 2-3 consistent with your prediction? Explain

yes, consistent with predictions -used equation to predict Ceq

question 3-8: Do the curves you measured for the decay of the potential difference across the capacitor in series with a resistor have the shape described by an exponential decay? How do you know?

yes, see page 161

question 3-7: Do the graphs for the resistor appear similar to those for the bulbs? Are there any significant differences?

yes, similar

question 3-4: Can you explain why the bulb behaves in this way? Is there charge on the capacitor after the switch is in position 1 for a while? What happens to this charge when the switch is moved back to position 2?

yes, the capacitor collects charges, releases them when the switch is open, then collects them again once it's closed

question 1-14: were the patterns observed with the compass needle and with the iron filings consistent with each other?

yes, the fillings moved towards the poles

question 1-16: Note the direction of the arrows you drew around the bar magnet shown above. Assuming that each line coming into a loop is negative and each line coming out is positive, what is the net number of magnetic field lines coming in and out of the loop in each case?

zero