When the leads of a hand generator are connected to different objects the crank is sometimes easy to turn and sometimes difficult.  The relationship between the force exerted and expected current flow, and therefore between energy and current flow, are examined.  This examination is extended to series and parallel combinations of flashlight bulbs.

In this experiment you will investigate the relationship between current flow and energy. Two other concepts, those a voltage and resistance, will be required to understand this relationship.

Your hand-cranked generator provides the 'push' necessary to create a flow of electrical current. The push is determined by the rate at which the handle is turned.

Clamp the ends of the leads coming from the generator to a piece of wood or plastic and turn the crank at about 2 complete turns per second. Then clamp the ends together and turn the crank again at the same rate.

• In which case was the crank easier to turn? In which case did you do more work per second (remember that work is the product of force and distance)?
• If which case do you think more electrical current flowed through the wires attached to the generator?
• How would you characterize the relationship between the current flowing and the difficulty of crank in the generator?
• Does current flow more easily through the wires when they are attached to the wood or when they are clamped together?
• Would you say that the circuit resists the flow of electricity more with the wood between the clamps or when the clamps are directly attached to one another?
• In which case is there more electrical resistance, the case when the generator is easy to crank or when it is more difficult crank?

Go around testing different objects in your house to see which ones have high resistance and which ones have low resistance to the flow of electrical current. Try to find at least three different materials that have low resistance and it least three to have high resistance.

Now insert a light bulb into a bulb holder and clamp the leads of the generator to the two tabs on the holder. Starting slowly at first, crank the generator faster and faster until the bulb glows, but not too bright so you don't burn it out.

• Count the number of times you crank the generator in 10 seconds while the bulb glows, and record this data. Note also the numbers marked on the bulb, and record them.
• Repeat for the other bulbs in your kit.   Some bulbs may require faster cranking than others.  Some may crank at the same rate or easier.  Find a way to mark the bulbs and record which is which.

Now place two different types of bulbs in holders. Bulbs are of the same type if they require the same force and the same cranking rate.  Connect a tab on the holder of one bulb to a tab on the holder of the other using a wire lead (one of the colored wires with alligator clips on the ends).

Connect the leads of the generator so that current will flow through the first bulb but not the second.  Describe how you made the connection.

• Crank the generator to make the bulb burn, and note how much force is required to crank the generator and how fast it has to be cranked.

Now connect the leads of the generator so that the current will flow first through the first bulb then through the wire lead connecting the two bulbs and finally through the second bulb and back to the generator.  You will have a lead from the generator to the first bulb, another from the first bulb to the second and a third lead from the second bulb back to the generator.

• Crank the generator as before and note whether it requires more or less force to crank the generator, and whether the generator needs to be cranked faster or slower in order for the first bulb to burn as brightly as before.
• Do both bulbs burn with the same brightness?  If not describe in terms of the previous observation of force and cranking rate the difference between the bulb that burns brighter and the bulb that burns more dimly.

Finally connect the leads of the generator to the first bulb, as before, then complete a parallel circuit to the second in the following manner:

• Connect a lead from the tab of the first bulb to one tab of the second.  It might not be possible to actually connect the second lead to the tab of the first bulb since there is already one lead connected to that tab; it can be connected to the first clip, which is already attached to the tab.
• Connect a second lead from the other tab of the first bulb to the remaining tab of the second.

• The bulbs should be connected so that when the current flows into the out of the first generator lead it branches, with some current flowing into the first bulb and some branching off through the wire lead to the second bulb. The current passing through the second bulb will then travel through the second wire lead back to the second generator lead, where it will rejoin the current that has come through the first bulb.

• Crank the generator so that neither bulb burns too brightly and observe whether the generator requires more or less force to crank, compared to when the leads were attached to a single bulb. Note also whether the generator has to be cranked at the same rate, at a faster rate or at a slower rate in order for the first bulb to burn is brightly as before.

You have experimented with bulbs connected in series and in parallel.   The meaning of these terms is as follows:

• When the bulbs were connected so that current had to flow through the first bulb before flowing through the second, the bulbs were said to be connected in series.
• When the bulbs were connected so that the current branched, with one part going through the first bulb and the other through the second, the bulbs were said to be connected in parallel.

Answer the following questions:

• Which required more force to crank, the parallel or the series combination?
• Which required greater cranking speed to achieve the same bulb brightness, the parallel or the series combination?
• Did both bulbs have the samerelative brightness when they were connected in parallel as when they were connected in series?
• In which case do you think work was being done at the greater rate?

It turns out that the amount of force necessary to turn the crank is an indication of the amount of electrical current flowing in the circuit, while the rate at which the crank is turned, in revolutions/second, is an indication of the amount of electrical 'push', or voltage, in the circuit.

More specifically:

• It is pretty much the case for this generator that the force F necessary to turn the crank is directly proportional to the current I flowing in the circuit: F = k1 * I, where k1 is a proportionality constant.
• It is also pretty much the case that the rate `omega at which the crank is turn is directly proportional to the voltage V pushing the current through the circuit: V = k2 * omega, where k2 is a proportionality constant.

In light of this information:

• Which circuit would you therefore say required the greater voltage, the series circuit or the parallel circuit?
• Which circuit would you say required the greater current, the series circuit or the parallel circuit?

Recall that power is the rate at which work is done:  power = force * distance / `dt.

• As determined from the force necessary to crank the generator and from the rates at which the generator was cranked, which circuit seemed to require the greater power?
• As determined from the brightness of the bulbs, which circuit seemed to require the greater power?

The hand-cranked generator is connected to a large-capacity capacitor and the difficulty of cranking changes as time passes.  This cranking difficulty vs. elapsed time is noted.  The general nature of the current flow vs. time (i.e., increasing or decreasing) is inferred.  The capacitor is connected in series and in parallel with a light bulb and the behavior of current vs. elapsed time inferred in each case; the effect of the light bulb is noted.  The charged capacitor is allowed to discharge through the generator, then after recharging it is allowed to discharge through the light bulb; the nature of the capacitor is speculated upon.

Now connect the leads of the generator to the large capacitor, as shown on the video clip.

• Crank the handle of the generator at a constant rate of approximately two revolutions per second and keep cranking. After about a minute release the handle and see what happens.
• What happened to the amount of force necessary to crank the handle? What do you think was therefore happening to the amount of current flowing in the circuit?
• What happened after the handle was released and how could you possibly explain this?
• What evidence do you have that the capacitor in some way stored at least part of the energy you produced when you turned the crank?

Take one of the thin wire leads and clamp each end to a different post of the capacitor so that current can flow from one capacitor terminal to the other.   After about 10 seconds remove the lead.

Now place a bulb in the holder and connect one of the tabs on the holder to one post of the capacitor using a thin wire lead. Connect one of the leads of the generator to the remaining tab of the bulb holder and the other to the remaining post of the capacitor, so that current must pass through the bulb to get to the capacitor.

This circuit is a series circuit consisting of the generator, the bulb and the capacitor.

• Crank the handle of the generator at a rate that causes the bulb to burn, but neither very brightly or very dimly. Continue cranking the handle at the same rate regardless of what happens. After about a minute, release the crank and see what happens.
• As you continue cranking, what do you notice about the force you have to exert, and what do you notice about the bulb?
• After you stop cranking, what happens to the generator and what happens to the bulb?
• What happens to the voltage produced by the generator as you continue cranking?

• Does the voltage increase, decrease, or remain the same? How can you tell?

• What happens to the current passing through the circuit as you continue cranking?

• Does the current increase, decrease, or remain the same? How could you tell if you weren't looking at the light? How can you tell by looking at the light?

• Sketch an approximate graph showing how the current through a capacitor behaves at a constant voltage.

You have directly experienced the fact that the brightness of the light bulb depends on the voltage across the bulb (i.e., the faster you crank the generator when it is connected to a single bulb the brighter the bulb burns).

• What therefore do you conclude happens to the voltage across the bulb as you continue cranking the capacitor-and-bulb circuit?
• Based on the force required to crank the generator, what happens to the current through the light bulb? Is this consistent with your answer to the preceding question?

Position the magnet next to the aluminum strips, as indicated on the video clip.

Attach the leads of the generator as shown, and turn the crank fast.  It should require some force to crank the generator; otherwise the aluminum strip is probably not making good contact with the leads.

• What happens to positions of the aluminum strips?
• What happens if the direction of the crank is reversed?
• What happens if the direction of the magnet is reversed?

Now position the ceramic magnet beneath the loop, making sure that the bottom of the loop is horizontal and that the magnet is lying on a horizontal surface as close as possible to the bottom.

• Measure the length of the aluminum strips, from the tabletop to the wire segment.
• Slowly crank the generator and see if the wire segment changes position.
• Now crank the generator, slowly at first, then more and more quickly, and see what happens to the position of the wire segment.

Add the wooden dowel weight to the system as shown the video clip, and place a thin ruler over the magnet in order to measure the position of the wire strip.

• The system will probably tend to oscillate about some equilibrium position.   Try to determine the central point of its oscillations; this central point is the equilibrium position.

Using the BEEPS program to set your 'beat', turn the crank of the generator at 1 revolution / sec and see how far the equilibrium position of the wire strip is displaced.

• Repeat for 2 revolutions / sec and for 3 revolutions / sec.

Answer the following questions:

• The field of the magnet is perpendicular to the plane of the magnet, as if it is coming through the hole in the middle of the magnet and out the ends. The current in the aluminum strips goes down one strip, through the wire segment, then up the other strip.

• How does the apparent direction of the force exerted on the aluminum strips depend on the direction of the current and the direction of the magnetic field?

• How does the apparent direction of the force exerted on the wire strip depend on the direction of the current and the direction of the magnetic field?

• Assume that the mass of the loop is 6 grams.  The system consisting of the aluminum strips and the loop is pretty nearly a simple pendulum whose length is that of the aluminum strips, and its mass is that of the loop.
• Using the length and mass of the pendulum, for small displacements from equilibrium you will recall that we can determine the force necessary for the displacement from the fact that the ratio of the displacement from equilibrium to the length of the pendulum is the same as the ratio of the force to the weight of the pendulum.
• Use this principle to determine the force exerted by the magnetic field for the cranking rates 1 rev / sec, 2 rev / sec and 3 rev / sec.

Save your force vs. cranking rate information-- you will use it again in experiment 20.

Now suspend the wire coil from the aluminum strips, as indicated on the videoclip. Be sure that the straw in which the central dowel is inserted is vertical and held securely.

You will position the magnet in three orientations:

• Orientation 1: Magnet positioned so that its field passes through the plane of the loop in a direction perpendicular to the loop.
• Orientation 2: Magnet positioned so that its field passes through the plane of the loop horizontally and parallel to the loop.
• Orientation 3: Magnet positioned so that its field passes through the plane of the loop vertically and parallel to the loop.

Before you conduct the experiment, make the following predictions:

• When current passes through the loop in Orientation 1, in what direction will the force on each of the four segments of the loop act?
• Make the same prediction for the other to orientations of the magnetic field.
• For each orientation of the magnetic field, what the you expect will happen to the loop when a current is run through the loop?

Now conduct the experiment by positioning the magnet in each of the three orientations, as indicated on the video clip, and carefully note what happens when current is passed through the coil.

Finally, make a crude meter out of the loop.

• Attach the horizontal 'pointer dowel' to the loop, as indicated on the video clip, and position a light pendulum as shown.
• Position a ruler in order to measure the horizontal position of the pendulum.
• Position the magnet so that the loop will tend to rotate in such a way that the pointer turns in the horizontal plane.

Using cranking rates of 1, 2, and 3 revolutions/second, send a current through the loop and for each rate determine how far the pointer displaces the pendulum bob.

Answer the following:

• Explain in terms of the forces on the individual segments of the loop why the magnet must be oriented as it is in order to produce a rotation of the loop.
• Explain how the position of the pointer indicates the current through the loop.
• If you were to use the principle illustrated by this experiment to create a meter to measure current, how would you design the meter?

Using a basic multimeter the relationship between voltage and the cranking rate for a hand-held generator is quantified and modeled.  Measurement of current vs. cranking rate indicates the internal resistance of the generator.  Current and voltage relationships for various flashlight bulbs are quantified and resistances inferred.   Current and voltage relationships for parallel and series circuits of flashlight bulbs are then investigated.

You will need the a basic multimeter, as mentioned under Sup Study ... > Course Information and specified at http://www.vhcc.edu/dsmith/genInfo/computer_interface_and_probes_cost_etc.htm. Watch the video clip before you attempt to use the meter; if you use the meter incorrectly you can burn out the fuse, which you will be responsible for replacing.

The main rule to avoid burning out the fuse in the meter or otherwise damaging the meter is this:

• Never, never, never connect the meter in parallel when it is set to measure current (the 150 milliamp setting).

Other than this caution, you will not the dealing with voltages and currents capable of damaging the meter.

• Also, when the meter is not in use it should be turned to the OFF position to avoid running down the battery.

Begin by observing how the cranking rate of the generator affects the voltage it produces:

Plug the probes into the meter, with the red plug in the + hole and the black plug in the - hole.

Turn the dial to the DC 15 volt setting and attach the leads of the generator to the probes.

• Crank the meter in the most comfortable direction, not too fast, until the needle on the meter moves. If the needle moves in the correct direction, you may continue. Otherwise either reverse the direction of your cranking or reverse the attachment of the leads so that the meter deflect in the correct direction.
• Using the BEEPS program, determine the voltage obtained by cranking the generator at 1, 2, 3 and 4 complete cycles per second.
• Plot the voltage vs. the number of cycles per second.

Now switch the meter to the 150 mA scale to measure the current created by the generator.

• Crank the meter very slowly, and gradually speed up until the meter indicates that the current is 100 mA. Using a clock or another timing device, count the number of complete cycles of the generator crank in 10 seconds and determine the cranking rate in cycles/second.
• Set the BEEPS program for this cranking rate and observe the current obtained, as accurately as possible.

Nearly all of the resistance in this circuit is in the generator itself. Determine this resistance is follows:

• From the cranking rate determine the voltage (as your graph of voltage vs. cranking rate should have showed you, voltage is proportional to cranking rate).
• Using the current (in amps) and the voltage (in volts) determine the resistance of the circuit in Ohms (you will either divide current by voltage or voltage by current; recalling that a smaller current implies a greater resistance, you should be able to reason out which way to divide without having to resort to a formula).

Now construct a circuit consisting of the bulb marked 6.3, .25 and the bulb marked 6.3, .15, connected in series to the generator (recall that in a series circuit the current does not branch but flows straight from one circuit element to the other).

• Set the meter to the DC 15 volt setting. BE SURE THE METER IS NOT ON THE 150 mA SETTING OR YOU WILL BURN OUT THE METER. Connect the voltmeter in parallel across the two bulbs and crank the generator, starting slowly and watching to be sure you aren't going to blow the meter up, then increasing the rate until the bulbs both glow, but not too brightly. Estimate your cranking rate then set the BEEPS program to give you approximately this rate.

• Crank at this rate, with the bulbs glowing as before, and read the meter to determine the voltage across the bulbs.

• Reposition the probes from the meter to measure the voltage across only one of the bulbs. That is, the meter should be connected in parallel to one of the bulbs. Crank at the same rate as before and measure the voltage across this bulb.

• Repeat for the other bulb.

Answer the following questions:

• How do the voltages across the two bulbs compare to the voltage across both bulbs?
• How much voltage was produced by the generator, according to the beeping rate?

How much of this voltage would you therefore conclude was associated with the current through the generator itself?

Compute the resistance of each bulb:

• The numbers on each bulb are the voltage (in volts) at which the bulb is designed to operate, and the current (in amps) that should flow through the bulb at this voltage.
• From the voltage and current you should be able to determine the resistance of each bulb, in Ohms.
• For each bulb, use the measured voltage across the bulb and the resistance to determine how much current should have been flowing through the bulb.

Are the currents you calculated approximately equal? Should the currents through the two bulbs be equal?

Connect the meter in series with the two bulbs and turn it to the 150 mA setting.

Crank at the same rate as before and determine the current through the circuit.

• How does this current compare with the current you predicted from the computed resistances of the bulbs?

Using the measured current and the resistance you computed for each bulb, determine the voltage change across each bulb.

Using the measured current and the resistance of the generator, as previously calculated, determine the voltage change across the generator.

• Is the total voltage change around the circuit consistent with the voltage that should have been produced by the generator at the cranking rate used? Should it be?

Connect the two bulbs in parallel and determine the voltage across each.

• To connect two bulbs in parallel, begin by connecting the first bulb to the generator so that the current flows through the generator to the bulb and back to the generator. Then, just before the first bulb, allow the circuit from the generator to branch off to the second bulb, where it passes through the bulb and then rejoins the current that has passed through the first bulb before continuing back to the generator.
• Crank the generator at a rate that lights both bulbs, but not too brightly. Use the BEEPS program to keep your cranking rate steady.
• Note whether this circuit requires more or less force then the previous series circuit with these bulbs.
• Connect the voltmeter, set to the 15 volt DC position, in parallel across the second bulb and a determine the voltage across this bulb.
• Connect the voltmeter in parallel across the first bulb and determine the voltage across this bulb.

Answer the following questions:

• How much voltage is there across each bulb?
• What then should be the current across each bulb?
• What should be the total current through the generator?

• Is the measured voltage across the bulbs equal to the voltage produced by the generator, according to the cranking rate?

• Which bulb is clearly brighter? Which bulb carries more current? Which bulb has the greater resistance? For these bulbs, how are brightness, current and resistance related?
• Compared to the series circuit as you investigated it, does this circuit expend more or less energy per unit of time?

• If the two bulbs were replaced by a single bulb whose resistance was such that the same current flows for the same voltage (i.e., for the same cranking rate), what would its resistance have to be, according to the measured voltage and the total current flowing through the generator?
• This resistance is called the equivalent resistance for the parallel circuit. Ideally we should have 1 / R = 1 / R1 + 1 / R2, where R is the equivalent resistance and R1 and R2 are the resistances of the bulbs.

Devise a procedure to test with the ammeter whether the total current through the generator is equal to the sum of the two currents through the bulbs, using a steady cranking rate of 1 cycle per second.

• Note that at this rate, it is possible that neither bulb will dissipate enough energy to light. This does not change the fact that current is flowing through the bulbs; they just aren't getting hot enough to emit electromagnetic radiation.
• Your procedure should measure the total current through the generator as well as the currents through each of the two bulbs.

Conduct your test and describe your procedure and your results.

Using small pieces of charged Scotch tape attached to small known masses and suspended as pendulums, we observe and attempt to quantify the relationship between the proximity of charges and the forces between them.

Coulomb's Law relates the forces on electric point charges to the amount of charge and the distance between the charges.

In this experiment you will use strips of Scotch tape as charges, and you will measure force using the force relationships of a pendulum.

Begin by obtaining two pieces of Scotch tape or the equivalent, each about the length of your index finger.

• Place the sticky side of one piece along the non-sticky side of the other and seal them together, then very quickly strip them apart again, without letting them get close to one another.
• If you bring the two pieces near each other, they will be attracted to one another.

• Hang one piece from the edge of a tabletop, leaving it hanging so that its free end will move toward the other piece of tape when it is brought into proximity.
• Grasp the other piece by both ends and turn it so that its non-sticky side is facing the non-sticky side of the hanging piece. Slowly move it toward the hanging piece and observe what happens.

• Tape the free piece to the wood block as indicated on the video clip. Be careful not to run your hands up and down the tape--you could remove its charge.
• Bring the block with the tape close to the hanging piece and determine whether it still attracts that piece.

• Set the block with the tape aside.

Now obtain another piece of Scotch tape by pulling it off the roll and cutting it. Determine whether this piece of tape attracts or repels the hanging piece.

• Hang this new piece of tape from the edge of the tabletop, not two near the first hanging piece.

• Predict what will happen when you bring the piece of tape on the wood block near the new piece of tape.

• Test your prediction.

• Predict whether another piece of Scotch tape pulled off the roll will attract or retail the first piece pulled off the roll.

• Test your prediction.

Answer the following:

• Do you think the electrostatic charges on the two pieces pulled off the roll are like or unlike? What makes you think so? (Don't quote some rule about light and unlike charges; in terms of how the pieces of tape were obtained determine whether there charges should be like or unlike).
• Do you think that the electrostatic charges on the two back-to-front pieces of tape that were stripped apart are like or unlike?
• Is it possible that in this situation there are three types of charge? Is there a way that you could test whether there are three types of charge?

Now go around stripping tape off of different surfaces and see what sort of charges you get, by bringing them close to the original hanging piece.

You will now attempt to determine the relationship between the force attracting two charged pieces of tape and the distance between the pieces.

Answer:  What have you experienced so far in this experiment that indicates to you that the force of attraction between two charges is greater when the charges are closer together?

In your kit you will find two pieces of tape, back to front, on a piece of wood. On each piece of tape is a piece of wood attached to a piece of paper and a loop of thread attached to another piece of paper. When the two pieces are stripped apart, they can be hung as demonstrated in the videoclip from pieces of thread to form charged pendulums.

• As the suspending threads are moved closer and closer together, the charged pieces of tape will tend to move closer together and attract one another more and more strongly.

The force of attraction is determined from the pendulum parameters, and can be determined as a function of the proximity of the two pieces of tape.

Since the tape pieces will tend to move with moving air, this experiment is best performed in a place where there is not circulating-- away from fans, heating registers, open windows, active pets, heavy breathers, etc..

• Strip the tape apart and suspend the two pieces about 30 cm apart, as shown on the video clip using threads at least a meter long. Be sure you measure the lengths of the strings.
• Place a meter stick so you can measure the separation of the threads just above the pieces of tape.
• Measure the separation of the threads at the top, just below the points from which they are suspended, and just above the pieces of tape.

• Move the tops of the threads a few cm closer and repeat your measurements.

• Continue moving the tops of the threads closer and closer and repeating measurements. As the pieces of tape get closer and closer, you will need to move that tops of the threads less and less between measurements. Eventually the pieces will simply continue attracting one another more and more strongly until the pieces of tape touch, at which point you must end your measurements due to the contamination of the charge on one tape by that on the other.

Analyze your results.

The total mass of each piece of tape plus the wood piece and the glue, in grams, should be marked on the tape.

Several factors make this experiment less than perfect, though it should still be reasonably accurate:

• Note that the system is not a perfect simple pendulum, since the mass of the tape and the stuff stuck to it is spread out over several cm.
• Furthermore the force of attraction is spread out over the length of the tape.
• Finally, you measured the separation of the thread just above the tape and not the average separation of the charged tape that was measured.
• Thus your results there will be approximations of the results that would be obtained if the charge on each tape piece was confined to a point.
• However, since the tape is fairly short compared to the length of the thread and sense for most of the measurements the length of the tape was short compared to the separation, the approximations obtained here should be fairly good approximations of the situation for a point charge.

Graph your data and linearize

• Graph the force of attraction vs. the separation of the threads.
• Linearize your data by either squaring or taking the square root of the force of attraction, or of the reciprocal of the force of attraction, as appropriate.
• How well is your data linearized?

Using Scotch Tape, PVC pipe and aluminum foil we investigate the nature of charges, induced charge and shielding of charges by conductors.

As demonstrated on the video clip, place two pieces of Scotch tape or equivalent back-to-back, then rapidly strip them apart.

• Convince yourself that the two pieces attract one another.
• Hang both pieces from the edge of a table (it might be necessary to extend a book or a board beyond the edge of the table so that the tape can hang freely without being attracted to the body of the table).

Charge the piece of PVC pipe by rubbing it vigorously against your clothing or a cloth.

• Test whether the pipe attracts or repels each piece of tape.
• Keep track of the two pieces of tape so you know how each is affected by the pipe.

Strip two more pieces of tape in the same manner and bring one of them near each of the hanging strips, in turn.

• Pick one of the pieces and determine whether the charged pipe attracts or repels it.
• Predict whether this piece of tape will attract or repel each of the hanging pieces. Then observe, and note your results.
• Predict whether the other piece of tape just stripped will be attracted to or repelled from the charged pipe, and from each of a hanging pieces, then test your prediction and note your results.
• Explain how you can reliably make such predictions.

Now wrap a piece of aluminum foil around one end of the pipe, extending back about a foot from the end. Hold the other end and bring it near one of the pieces of hanging tape.

• Explain what happened in terms of two types of charge.

• Hint: the surface of the aluminum foil is densely permeated with freely mobile electric charges, which will move in response to any net electrostatic field.

Bring your finger close to one of the hanging pieces of tape, and determine whether your finger attracts or repels the tape.

• Predict whether your finger will attract or repel the other piece of tape, then test and note your results.

Charge the PVC pipe again and test to be sure it either attracts or repels the hanging pieces of tape. Then place a sheet of aluminum foil near one of the hanging pieces, as close as possible without attracting the tape.

• Bring the PVC pipe (without the foil on the end) closer and closer to the tape, while keeping the foil between the pipe and the tape.
• How is the effect of the pipe on the tape different than if the aluminum foil is removed? Explain what is going on.

Make an aluminum cylinder at least 20 cm in diameter, and carefully surround one of the hanging pieces of tape with the cylinder.

• Bring the charged pipe (without the foil on the end) near the tape while keeping it outside the cylinder. Explain what happens.

Remove the aluminum foil from the end of the pipe, keeping it cylindrical. Place one end of the foil cylinder near the hanging tape which is repelled by the charged pipe, but not so near that it pulls the tape into contact.

Using the hand-held generator, a capacitor and a multimeter we observe the discharge of the capacitor through the volmeter alone, through a series combination of the generator and the voltmeter with the handle on the generator held stationary, and the same with the handle freely turning.  We observe the exponential nature of the discharge in each case.  We also note the effect of the reactance of the generator as current flows through it with the handle free.

Connect the voltmeter in parallel to measure the voltage on the capacitor and place a 10 volt charge on the capacitor. Then, holding the handle of the generator to prevent it from moving, allow the capacitor to discharge through the generator while timing the process.

Now you will repeat the experiment, but this time you will let the handle turn freely as the capacitor discharges.

• First predict whether the capacitor will discharge more or less quickly with the handle turning, and give reasons for your prediction.
• Now repeat the experiment.
• How does the R observed with the handle turning freely compare to the R observed with the handle fixed?
• Can you explain what is going on here?

Now discharge the capacitor completely by clipping the two ends of a lead to its terminals and leaving it there for 10 seconds or so before removing it.

• Place the meter in series with the generator and capacitor and turn it to the ammeter position.
• Very slowly crank the generator to determine in which direction to turn the handle in order to create a small positive current (about 10 mA) in the meter.
• Crank the generator at this rate for a few seconds only, then stop cranking and observe what happens to the current when the capacitor is permitted to discharge through the meter.

Prepare to interrupt the circuit by pulling one of the leads out of the meter (they come out very easily, as you have probably noticed).

Once you start cranking, do not stop until the circuit has been interrupted in this matter. Otherwise the 'backwards' flow of current could damage the meter.

Determine approximately how fast the generator should be cranked to create a 100 mA current and use the BEEPS program to set the appropriate rhythm. Remember to interrupt the circuit before you stop cranking.

Discharge the capacitor once more and remove the leads.

Crank the generator at the appropriate rate and observe the current as a function of time.

• If you cannot write down the times as you crank, determine at least the time required for the current to fall a half its original value, then if possible to 1/4 its original value.
• Continue cranking until the current has fallen below 5 mA.
• Then, while still cranking, interrupt the circuit.

For the moment place the meter lead remaining in the meter in the jack from which the other lead has been removed.

• You will shortly place the other lead in the vacated jack, reversing the leads in the meter and, while timing the changes in current, allow the capacitor to discharge through the meter and the generator, with the crank held stationary.
• You must be very sure that the generator is still connected. The only thing that should change in the circuit is the reversing of the meter leads.

When you are ready, place the remaining lead in the vacant jack and begin timing at this instant.

• Immediately observe the initial current (if the indicator on the meter goes all the way to one side or the other, immediately remove one of the leads from the meter to prevent damage).
• Observe the time required for the current to fall to half its original value, then to half this value, then to half this value.

Sketch a graph of current vs. clock time.

• The current should be I(t) = I0 * e^(-t / (RC) ), where I0 is the initial current.
• As you did before, determine from your graph the value of RC.
• From RC and C, determine the resistance R.

Repeat this procedure with the crank allowed to rotate freely.

• Compare the resistance with the freely rotating crank to that with the fixed crank.