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EXPERIMENT #2 PRELAB

Give the value for the resistors drawn below including the tolerance.
In the last part of lab you will be working with a circuit that consists of a power source delivering a constant voltage, a resistor whose value can be varied, and a motor. The resistor value is varied so that we can control the amount of current that is drawn from the power supply and thus through the motor. By controlling the current through the motor we can control the motor speed. How should we connect these three elements so that the variable resistor controls the motor speed? Lets experiment with the two possible connections - a series connection and a parallel connection.
1. SERIES CONNECTION: For this exercise we are going to pretend that one of the resistors (labeled R_m) is one of the car's motors. The series circuit is shown below.
  1. Write KVL loop equation that constrains all of the voltages within this circuit.
  2. Write the expression for the current in terms of V, R_m, and R_c.
  3. Write the expression for the voltage across R_c.
  4. Write the expression for the voltage across R_m.
  5. Write expressions for the power flowing through each component.
  6. As R_c increases what happens to the voltage and current across R_m which is our model for the motor?
2. PARALLEL CONNECTION: The circuit below has a voltage supplied by a power supply connected to two resistors in parallel. Again pretend that one of the resistors (labeled R_m) is one of the car's motors.
  1. Write the expression for the currents flowing through the two resistors in terms of V, R_m, and R_c.
  2. Write the expression for the voltage across R_c.
  3. Write the expression for the voltage across R_m.
  4. Write expressions for the power flowing through each component.
  5. As R_c increases does what happens to the voltage and current across the motor?
COMPARISON - which design do you think would be best for motor speed control?

EXPERIMENT #2

RESISTANCE MEASUREMENTS

We are going to start by looking at some simple resistors. First let's learn what they look like and how to measure their resistance. In your red toolbox you should find several different types of resistors, 1 100 Ω resistors, 1 1k Ω, 1 100k Ω,and 1 M Ω resistors.

Put the multimeter in the mode to measure resistance. If you use the cables that have banana plugs at each end, attach an alligator clip to each then you can connect the clips to either side of the resistor. You should be able to read the resistance on the multimeter display by connecting the multimeter in the same configuration you use to measure voltage EXCEPT that you push the Ω button instead of the DC V button (see figure).

Fill in the table below in your lab book.
Compute the percent error as 100*(labeled resistance - measured resistance)/labeled resistance). Are all of these resistors within the 5% error limit?
How does the multimeter know the value of the resistance?

Touch the ends of the two alligator clips together.
What does the display read now? Why?

Now put the multimeter into a special mode that is used to determine if two points in a circuit are connected together – this is done by pushing the CONT (continuity) button. Now touch your alligator clips together, what happens? You get an audible tone saying that you have detected a short circuit – or that these two points are indeed connected together. Try touching the ends of the alligator clip to the ends of the different resistors. What happens? You should hear nothing because the resistance is large enough that the device does not consider them shorts. This technique is an excellent debugging tool. It helps you determine if two parts of your circuit that you thought were connected are in fact connected or if there is something broken or faulty in your wiring.

Lets practice by determining how your protoboard is connected. We will be using the protoboard all semester to build circuits, so it is good to understand its layout. Below is a picture of a protoboard and some of its connections. Included is an example of how you will be inserting chips and a common connection to power and ground. In this configuration the holes at the very top are 'buses' that carry power - the red holes, and the ground - the black holes. All of the holes connected by the superimposed red line are connected together and all of the black ones are connected together (but the red ones are not connected to the black ones - that would be bad).

Check that this is true with your multimeter using the cables with the banana plug on one end and a simple wire end on the other. Stick the black wire from your multimeter into one of the holes connected by the black line as indicated below. Now stick the red one in any of the other holes along the black line. You should hear a beep, if not you have a bad protoboard. Randomly check some of the other holes along this line. Now stick the red wire from your multimeter into one of the holes along the red line (without removing the black one - it should still be in one of the holes connected by the black line). You should hear no beep - if you do, again, your board is faulty. Check the holes connected by the red line in the same way.
Map the rest of the protoboard using your multimeter on a picture of the protoboard that YOU print out and include it in your notebook. Indicate which holes are connected together by drawing a line as in the figure below connecting the power and ground. You don't actually need to draw lines on the whole board. Once you begin you will quickly see the pattern. Just draw enough lines to demonstrate the pattern.

Check with your T.A. to demonstrate knowledge of the protoboard
I-V characteristics of different LOADS

For the next three parts of the lab we will be building the very simple circuit shown below consisting of the power supply that we used last lab and another component which when connected to the power supply draws power. We commonly call this component the ‘load.’ Since our power supply regulates the voltage, i. e. keeps the voltage constant across the load no matter what load we attach to it, the value of the load will determine the current drawn from the power supply for each voltage setting. For each type of load we will be plotting current (I) vs. voltage (V). This type of plot is a typical way of conveying the characteristics of any load and one you commonly see in specification sheets. With this information you know pretty much all you need to know about how the device will behave in a circuit.

a. Simple resistance

Connect the 100Ω resistor to the alligator clips inside one of the test boxes. Now connect the outputs of the box using the cables with the banana plugs at both ends to the power supply . This is your first circuit in this class, a simple resistor circuit. In the diagram above the load is the 100Ω resistor.
Draw the resistor circuit in your notebook.

Vary the voltage between 0 and 6V. The power supply will display reading from the power supply’s display the amount of current that the load (resistor) is drawing.
Make a table showing each of your measurements of both the voltage and current off of the power supply display. Include at least 5 values.
A good way of visualizing this data is to make a plot; use the values recorded above to make an I-V plot of the resistor (the x-axis will be the voltage and the y-axis will be the current). You may use Excel if you wish and print out a plot from using the printer - you still must label you plots properly in Excel.

b. Incandescent Bulb (temperature dependent resistance)

Some loads look to the power supply like a simple resistor - a diode once it has been turned on is one such device. The incandescent bulb used in this part of the lab is a resistive device whose resistance changes as the device heats up. Since the bulb is designed to heat up to a white hot state - this is how we get light - the resistance will vary as the filament in the bulb heats up.

Disconnect the test box containing the resistor and hook up the test box containing the lamp.
Again you will be varying the voltage output by the power supply and reading from the power supply’s display the amount of current that the bulb is drawing for a particular voltage setting. Make a table and plot the values to make an I-V plot of the bulb using the following voltages - .1, .3, .5, .7, .9, 1, 1.1,1.2,1.3,1.5,1.7, 2, 2.5, 3, 3.5, 4, 4.5, 5V. These points were chosen so that you obtain a decent plot of I-V curve - if you can obtain a decent plot with fewer points that is fine.
Does the I-V curve of the lamp look like that of a resistor?
Speculate how the temperature is affecting the apparent resistance [1 /(the slope of the curve at any interval) is the apparent resistance] using your I-V plot as evidence.

c. Motor (hysteresis)

Some devices behave differently at different times when the same voltage is applied across its terminals. A motor, such as the ones on your vehicles, is one such device. As the voltage is initially increased the motor does not move because you must supply enough power to overcome the internal friction. After the motor starts running, throughout a range of voltages, the motor will behave as a resitive device. When the voltage is now decreased the motor will continue to run at a much lower voltage than that needed to start the motor running. This is called hysteresis. Do you think the bulb you used might exhibit hysteresis as you decrease the voltage after the bulb has been on for a while?
Repeat the procedure for plotting the I-V curve for the test box containing the motor. If you need additional points to get a good plot add some especially where a small voltage is being supplied and some current being drawn but the motor is not moving - the voltages used to measure the I-V curve of the bulb are probably pretty good ones - you may need more measurements at the .1V interval until the motor turns on.
At what voltage could you detect that the motor STARTS moving?
For which range of voltages does the I-V curve of the motor look like that of a resistor? Include all regions if there are more than one.
Now turn the voltage up to 5V and at the same voltage points redraw the I-V curve - only going backwards (from 5V to 0V). Are the curves the same? At what voltage could you detect that the motor STOPS moving?
You will notice that the motor draws current even though it is not turning. If you touch the little knob you can feel it try to turn. Why is it not turning?

KVL and KCL (Conservation of energy and charge)

So far we have investigated three circuit elements which will be used to run the motors on our vehicles - a motor (the car motors behave in a very similar fashion to these small motors as we will see next week), a voltage source (we will be using batteries as the source on the vehicles), and resistors. Now we will experiment with a simple circuit combining these three components that is similar to the circuit used to vary the motor speed on your vehicle. The motors on the car body are connected to a battery source whose value is fixed so there is no way to control the speed of the motor (like we did above when we could vary the voltage from the power supply at will) - therefore additional circuitry - well one resistor - is added to modify the voltage and current delivered to the motor. In the prelab we found that connecting the variabel resistor in series was the only way to control the motor speed. Lets construct such a circuit and experiment with Kirchoff's laws at the same time. By computing the power dissipated in each component you should find that - although you do indeed change the speed of the motor this way - it is costly in terms of power consumption. This method also has another drawback - at slower speeds the motor delivers less torque than at higher speeds. We will learn a more efficient way to drive the motors that provides better torque at the same time in subsequent labs.

For this part of the lab you will be constructing a series circuit and then verifying KVL, KCL, and conservation of energy for several settings of the power supply.

Set the power supply to 5V. The power supply in this circuit simulates the battery that is used in the vehicles so we will not be changing the voltage at all during this test. Connect up the circuit above using the small motor, a variable resistor (R_c) and the power supply.

You will investigate how each component in the circuit behaves as the resistance of R_c is changed from its maximum value to its minimum. Start with the resistance set as high as possible (knob turned all the way to the left where the label says OPEN - it is not really an open circuit as you will verify with the multimeter).

Now hook up your test equipment. First set up one of the multimeters to measure alternately the DC voltage and resistance across the variable resistor. This can be done fairly easily since both modes use the same output ports. You will simply toggle between the voltage measuring mode and the resistance measuring mode using the buttons on the front panel of the multimeter. Next set the other multimeter to measure DC voltage of the motor.

We will be filling in and plotting the data specified in the table below - you may copy this table into your lab books or you can enter it into EXCEL. You must include the table in your notebook in either case. Suggested method for making measurements: 1) Unplug one of the cables going to the power supply - measure resistance across variable resistor. 2) turn ON power to circuit. 3) change mode of multimeter and measure voltage across variable resistor. 4) measure voltage across motor. 5) Record the value of the current - reading the value from the power supply. 6) Change setting on variable resistor a little. 7) Unplug one of the cables going to the power supply
REPEAT steps at least 10 times to get good measurements across the range of resistance. Indicate where the motor turns on with a star beside the resistance. NOTE: 1) you CANNOT read the resistance with the circuit powered up. 2) the interesting range of the resistance is toward the lower end, so taking measurements with bigger steps at first will save time because you want to have smaller steps towards the end where the motor starts running.
1. Fill in the above table with the current and voltages first.
2. Compute the power columns.
3. Plot the two voltages against the resistance together on the same graph.
4. Plot the two powers, again against the resistance together on a seperate plot. Explain the shapes of the curves.
5. Add up the voltages V_m and V_R. Is KVL satisfied for all entries? Why or why not? There might be other sinks in the system.
6. Add up the powers. Do the resistors dissipate all the power delivered? Why or why not?
7. Look back at your plot of the I-V curve for the motor (in part c) - a circuit where the power supply is connected directly to the motor and the voltage and current flowing through the motor is controlled directly from the power supply WITHOUT a variable resistor. How much current and voltage was used when the motor first turned on? How much power was needed?
8. Now compare this value to the amount of power needed to be supplied by the supply to turn on the motor with the variable resistor in place. Is it more or less?

Experiment 2 - Ohm's law and Kirchoff's Laws

EXPERIMENT #2

Check with your T.A. to demonstrate knowledge of the protoboard