Static Electricity and Grounded Sensors

For this experiment, you will need

Hold the two pith balls together in one hand, hanging from their threads so that the two pith balls are at the same height. Try to avoid tangling the pith balls together.

With your other hand, use the alligator clips to clip together the tops of the threads.

Find a suitable hook or handle from which to hang the pithballs. Thread the alligator clips through the hook and then clip them together.

Forcefully rub the green vinyl sheet over the white nylon rod in order to build up a charge on the rod.

The nylon rod is an insulator, meaning that it does not allow charges to flow freely through it, so if a charged particle is added to the surface of the rod, it cannot flow away, but instead remains "stuck" in the same spot.

It is possible to transfer these trapped charges to another material through direct contact. Touch the nylon rod to the pith balls in order to transfer the charge.

Continue building up charge on the rod and transfer as much charge to the pith balls as you can. When you are finished, the pithballs should hover 1-2 cm away from each other.

Bring the charged nylon rod close to the pith balls and observe their behavior. Are the pith balls attracted or repelled? (Question 1.A)

Forcefully rub the brown wool cloth over the gray PVC rod in order to build up a charge on the rod.

Bring the charged PVC rod close to the pith balls and observe their behavior. Are the pith balls attracted or repelled? (Question 1.B)

Begin transferring charge from the PVC rod to the pith balls, and transfer as much charge as you can. At first, the pith balls should come together as their previous charge is negated, but after enough charge is added, they should begin to repel each other again.

Bring the charged PVC rod close to the pith balls and observe their behavior. Are the pith balls attracted or repelled? (Question 1.C)

Bring the charged nylon rod close to the pith balls and observe their behavior. Are the pith balls attracted or repelled? (Question 1.D)

For this experiment, you will need

To properly use the charge sensor, you must use a computer that is plugged into the wall and connected to earth ground.

Connect the LabQuest to the computer and plug the charge sensor into the LabQuest.

Connect the ground clip (black) of the charge sensor to the Faraday cage. Connect the high voltage clip (red) to the Faraday pail.

Make sure the Faraday pail doesn't tip over as this will affect the readings.

How the Charge Sensor Works

The charge sensor is made up of a capacitor and a voltmeter in parallel as shown below.

In our setup, the high-voltage terminal is connected to a conductive metal cup called a Faraday pail.

When an object with charge \(Q\) is lowered into the pail, like charges are repelled and flow out of the pail, through the capacitor, and into ground.

When the system reaches equilibrium, the charged object and the pail will have equal and opposite charge. Therefore, the total amount of charge that flows out of the pail and gets trapped on the capacitor is equal to the charge \(Q\) of the charged object.

The voltmeter measures the voltage \(V\) across the capacitor, and the charge \(Q\) is calculated using the capacitance equation.

$$Q = CV$$

Measuring the Charge on a Rod

Once again, forcefully rub the white nylon rod with the green vinyl sheet in order to build up a charge.

On your charge sensor, hold down the reset button until the charge sensor reading drops to zero. The reset button shorts the internal capacitor, draining it. The charge sensor will build up charge on its own in a manner of seconds, so you will need to repeat this step before starting each set of measurements.

Dip the white nylon rod into the faraday pail without touching the sides or the bottom.

Record the charge of the nylon rod. (Question 2.A)

Was the charge on the nylon rod positive or negative? (Question 2.B)

When the nylon rod and the vinyl sheet were rubbed together, electrons were transferred from one material to the other. We call the material that loses electrons the electron donor and the material that gained electrons the electron acceptor.

Which material was the electron donor, the nylon rod or the vinyl sheet? (Question 2.C)

Which material was the electron acceptor, the nylon rod or the vinyl sheet? (Question 2.D)

---

We will now repeat the experiment with the gray PVC rod and the brown wool cloth

Forcefully rub the gray PVC rod with the brown wool cloth in order to build up a charge, zero the charge sensor by holding down the reset button, then dip the gray PVC rod into the faraday pail without touching the sides or the bottom.

Record the charge of the PVC rod. (Question 2.E)

Was the charge on the PVC rod positive or negative? (Question 2.F)

Which material was the electron donor, the PVC rod or the wool cloth? (Question 2.G)

Which material was the electron acceptor, the PVC rod or the wool cloth? (Question 2.H)

For this experiment, you will need

While keeping the setup from Experiment 2, clip one side of the alligator clips to the Faraday cage.

Forcefully rub the white nylon rod with the green vinyl sheet in order to build up a charge.

On your charge sensor, hold down the reset button until the charge sensor reading drops to zero. Then, immediately afterward, complete the following steps in no more than 15 seconds total.

---

Dip the white nylon rod into the faraday pail. Record the charge reading. (Question 3.A)

Without removing the rod, connect the other end of the alligator clips to the Faraday pail. Record the charge reading once it has settled. (Question 3.B)

Without removing the rod, disconnect the alligator clips from the Faraday pail. Record the charge reading. (Question 3.C)

Remove the rod from the Faraday pail. Record the charge reading. (Question 3.D)

Charging By Induction Explained

When you first placed the nylon rod in the pail, charge flowed out of the pail, throught the capacitor, and into ground.

This left a charge on the pail and opposite charges on either side of the capacitor.

When you connected the pail to ground, this created a path for the charge to flow out of the capacitor.

This left the capacitor drained.

Removing the alligator clips has no effect.

After the rod is removed, charge rushes back into the pail from ground.

This leaves a reverse charge on the capacitor.

Followup

Describe what would happen if we repeated this experiment but instead using the gray PVC rod and the brown wool cloth. (Question 3.E)

When two-like charges are brought close together, the energy required to overcome the repulsion between the two charges is stored as electric potential energy. If the charges are positive, this translates to a very high electric potential, (or energy per unit charge). If the charges are negative, this translates to a very large negative electric potential.

When the charges are released, they will naturally spread out, with the electric potential energy decreasing as it is converted into the kinetic energy of the particles moving away from each other. When the particles get far enough away from each other, the electric potential energy of the system becomes negligible, and so the energy per unit charge also becomes negligible. This is known as zero or ground potential .

A ground is a large, conductive material in which charges are able to spread out evenly. As new charges flow into ground, they have plenty of room to spread out, so the material remains at ground potential. This allows a ground to act as a sort of charge reservoir, or in other words a sink or source for charges.

The ground prong of an appliance plugged into an electrical outlet connects to earth ground, which consists of a metal spike nailed into the actual ground at a location with good soil conductivity.

All electrical outlets in the same room or building will most likely be connected to the same ground.

In the last experiment, we used charge sensors, which was our first example of a grounded sensor.

As this next experiment demonstrates, you must always use caution when dealing with grounded sensors, as they can often behave unexpectedly when not used with care.

For this experiment, you will need

Note: Supplies are limited, so please do not pick up the direct voltage sensors until you are ready to use them, and put them away immediately after you are done with this experiment so the next group of students can use them.

We'll start by powering two lightbulbs in series.

Use the multimeter to set the power supply to 5 volts. Then, use the alligators clips to connect high voltage to the first lightbulb, the first lightbulb to the second, and the second lightbulb to low voltage.

Connect the direct voltage sensors to the LabQuest. The direct voltage sensors are both grounded sensors, meaning their low voltage probes are connected to earth ground.

---

Call over the instructor to ensure you correctly execute the next step.

You will now attempt to measure the voltages across each lightbulb at the same time. Your intuition should tell you that the voltage across each lightbulb should be about half.

Connect the direct voltage sensors exactly as follows.

Connect the high-voltage lead of the first sensor to the high-voltage side of the first bulb, the low-voltage lead to the low-voltage side of the first bulb, the high-voltage lead of the second sensor to the high-voltage side of the second bulb, and finally, the low-voltage lead of the second sensor to the low-voltage side of the second bulb.

(If both lightbulbs go dim, stop immediately. This means you've connected the sensors at the wrong spots and caused a short.)

Describe what happened as soon as you finished connecting the second voltage sensor. (Question 4.A)

What is the voltage reading across the first lightbulb? (Question 4.B)

What is the voltage reading across the second lightbulb? (Question 4.C)

The Paradox Explained

At first glance, the setup seems simple enough, two voltmeters placed across two resistors in series to give two voltage readings. It doesn't seem like there should be any problems.

However, the voltage sensors we used are grounded, so their low voltage leads both have a hidden connection to ground, and therefore, to each other.

This hidden ground connection shorts out the second lightbulb, leaving only the first lightbulb between high and low voltage.

In a previous lab, we designed a half-wave rectifier, a circuit which converts an AC signal to a DC signal by using a diode to let only half of the voltage signal through, (the positive half), and by using a capacitor to smooth the signal.

In the following experiment, you will design a full-wave rectifier. A full-wave rectifier makes use of both halfs of the signal.

Design of the Full-Wave Rectifier

To understand how a full-bridge rectifier works, we begin by looking at the two main components of the circuit: The AC power supply, and the RC load.

The AC power supply, (on the left), alternates between having high voltage on top and low voltage on bottom and having low voltage on top and high voltage on bottom.

However, the RC load (on the right) must always have high voltage on top and low voltage on bottom.

To make a half-wave rectifier, we can add diodes (blue) that only allow current to flow through them when the power supply has high voltage on top.

However, we can just as easily make a half-wave rectifier where the diodes (violet) only allow current to flow through them when the power supply has low voltage on top.

By combining the two half-wave rectifier circuits, we can create a full-wave rectifier, which allows current to flow through one set of diodes (blue) when the power supply has high voltage on top, and the other set of diodes (violet) when the power supply has low voltage on top.

We can visually untangle the diodes in our circuit diagram and rearrange them into a diamond shape, (as shown below). This is the standard way to draw a full-wave rectifier circuit.

For this experiment, you will need

Setting Up the Breadboard

Slot one wire into the top of the left positive column, and one wire into the top of the right negative column.

Slot the first capacitor (101) into h15 and h17. (Avoid bending the legs of the capacitor. The capacitor should go in smoothly if the legs remain straight).

Slot the resistor into c15 and c22. Record the resistor code (Question 5.A) and calculate the resistance (Question 5.B).

Connect one wire from e15 to f15 and the last wire from e22 to f17.

Connect one diode from near the top of the left positive column into a15.

Connect one diode from near the top of the right negative column into j15.

Connect one diode from a22 into near the bottom of the left positive column.

Connect one diode from j17 into near the bottom of the right negative column

Pass off your breadboard design with the instructor.

The wires at the top of your circuit will be connected to your transformer which provides an AC signal. When the voltage on the left side is positive (left), current will flow from top to bottom through the first set of diodes. When the voltage on the left side is negative (right), current will flow from top to bottom through the second set of diodes.

Powering the Circuit and Setting Up the Oscilloscope

Plug in the transformer.

Using the alligator clips, connect the positive column wire to the yellow terminal of the transformer. Connect the negative column wire to one of the white terminals.

Plug in the Oscilloscope and turn it on.

Plug the oscilloscope leads into the CH 1 port on your oscilloscope. To do so, properly line up the holes in the cable, push the cable in, then turn clockwise to lock in place.

Connect the ground clip (black) of the oscilloscope leads to the diode leg at a22.

Hook the high-voltage probe (gray) of the oscilloscope leads to the diode leg at 15.

Your oscilloscope should now measure the voltage across the resistor/capacitor.

We will now adjust the graph settings on the oscilloscope.

Turn the VOLTS/DIV knob above the CH 1 port and set the voltage axis scale to 5 V per grid square.

Turn the SEC/DIV knob above the EXT TRIG port and set the time axis scale to 2.5 ms per grid square.

Turn the POSITION knob above the CH 1 port to set the voltage offset to 0 divs.

Press the SET TO 50% button in the bottom right corner to stabilize the signal.

Your graph should look something like this.

As you can see from the graph, the diodes have flipped the negative peaks of the sign wave to positive, but the capacitor has not done a very good job of smoothing the signal.

To quantify how well our capacitor has smoothed the signal, we can compare the minimum voltage to the maximum voltage of our signal. The closer the minimum voltage is to the maximum voltage, the flatter our graph and the smoother our signal.

Press the MEASURE in the top-left corner of the oscilloscope to bring up the measure menu.

Press the F1 button to toggle between changing the source or type of measurement.

Press the F2-F5 buttons to cycle between sources or types of measurement for up to four measurements total.

Set one of the measurement boxes to measure \(V_{\max}\) from Channel 1.

Set one of the measurement boxes to measure \(V_{\min}\) from Channel 1.

In the first row of Table 5.C, record \(V_{\max}\), \(V_{\min}\), and calculate \(V_{\min}/V_{\max}\).

Predicting the Smoothness of the Signal

If we think about our circuit carefully, we can divide up the behavior of our signal into three main phases per cycle.

The first phase starts at peak voltage, when the voltage signal from the AC source (as filtered through the diodes) begins to decrease. As the AC voltage decreases, the capacitor voltage decreases in tandem by releasing charge through the resistor.

However, at some point, the AC signal voltage begins to decrease faster than the capacitor can release charge, and the second phase begins. In the second phase (shown in white), the capacitor is isolated from the AC signal and leaks current through the resistor following an RC decay curve.

Eventually, though, the AC voltage signal rebounds, increases again, catches up with the capacitor voltage, and the third phase begins. In the third phase, the AC voltage increases, and the capacitor voltage increases in tandem as it receives current from the AC source.

The point where our output signal transition from Phase 1 to Phase 2 is represented by an inflection point on our graph, where the graph transitions from a sinusoidal curve (concave down) to an exponential curve (concave up).

Given an AC input signal of

$$ V_s = V_0 \cos{\omega t} $$

where \(\omega\) is the angular frequency of the wave, and given resistance \(R\) and capacitance \(C\), we can find the voltage at which the inflection point occurs as

$$ V_{in} = V_0 \frac{\omega RC}{\sqrt{1+(\omega RC)^2}} $$

(The proof is left as an exercise for the reader.)

Finding the point at which the phase 3 begins, (the minimum voltage), is less straightforward, but can be calculated numerically. We can tell from the previous equation, that the behavior of our graph probably depends on the parameter \(\omega RC\) (angular frequency multiplied by time constant). A log-graph of \(V_{\min}/V_{\max}\) vs \(\omega RC\) is shown below.

The AC signal from the wall has a frequency \(f\) of 60 Hz, which corresponds to an angular frequency \(\omega = 2\pi f \approx 377\) rad/s.

In the first row of Table 1.D calculate the RC time constant, and the parameter \(\omega RC\).

Find the value of \(V_{\min}/V_{\max}\) on the graph that corresponds to your value \(\omega RC\). Is it close to your measured value.

Increasing Capacitance

Repeat the experiment 5 more times by replacing the 101 capacitor with the remaining capacitors (102, 103, 104, 105, and 106).

Downloads

Answer Sheets:

static_answer_sheet.pdf