very small Ohm s Law and DC Circuits Purpose: Students will become familiar with DC potentiometers circuits and Ohm s Law. Introduction: P31220 Lab

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1 Ohm s Law and DC Circuits Purpose: Students will become familiar with DC potentiometers circuits and Ohm s Law. Introduction: Ohm s Law for electrical resistance, V = IR, states the relationship between current, voltage, and electrical resistance. If R is constant, V is proportional to I. However, the resistance of a device can t always be assumed to be a constant. If you did the Properties of Resistors lab, you might recall that electrical resistance varies with temperature. Diodes are designed to conduct electricity in only one direction, and thermistors are designed to be especially sensitive to temperature. Batteries have an internal resistance that is a consequence of the internal chemistry of the battery. Chemical reactions in the battery cause the internal resistance to increase. Batteries go dead not because they lose voltage, but because their internal resistance increases to the point where current can no longer flow. In this lab, you will observe how Ohm s Law works, you ll learn about voltage dividers, and you ll learn how to measure the internal resistance of a battery. About Voltmeters, Ammeters, and Ohmmeters: The table below summarizes the important characteristics of meters and how to connect them so that the meter has a minimal effect on the circuit. The resistor in the table could be any circuit element with resistance, such as an actual resistor, a light bulb, a motor, a diode, etc. The DMM can be used as an ammeter, voltmeter, or ohmmeter. It is important to understand that Ammeters have very small resistance, and Voltmeters have very large resistance. Ohmmeters basically are voltmeters that use a known voltage from a battery inside the meter, and therefore should not be used when other voltages are present. Meter Measures Meter s own resistance Connected to circuit element Circuit Diagram Circuit is Voltmeter Voltage across resistor very big In Parallel ON V Ammeter Current through resistor very small In Series ON A Ohmmeter Resistance of resistor Big. Uses its own battery In Parallel Element is disconnected Ω OFF and disconnected 1

3 Experiment 1: Find the internal resistance of a Battery (15 minutes) You have a 9V battery. Use the DMM to measure its voltage. There are two resistors on the board. Measure their actual resistances using the DMM as an ohmmeter. You ll need these numbers later. Record your results on the Data Sheet. You can measure the resistance of the diode if you want to, but you don t have to. Remember, an ammeter s resistance is very small. We can t measure current from a battery by connecting an ammeter directly across its terminals. This would cause a large current to flow, running down the battery very quickly and/or blowing the DMM s internal fuse. We will measure the internal resistance indirectly, by putting a resistor in series with our battery and ammeter. Construct the following circuit: Hint: 240Ω = red-yellow-brown V 9V battery 240Ω A Fig. 2: Circuit for Experiment 1 Record your measurements and answer the Analysis Questions on the data sheet. Experiment 2: Voltage Drops Across Series Resistors (15 minutes) In Experiment 1, you might have observed that the measured voltage across the 240Ω resistor was not exactly 9V. In this part of the lab, you will find out why. You have a plastic block with a wire in it. Points a and e represent the two ends of the wire. Using a DMM as an ohmmeter, measure the resistance between point a and the other four points on the wire, as well as the actual resistance of the 27Ω resistor. Then construct the following circuit. Use the 6V power supply instead of the battery. Measure the voltages between point a and the other four points along the wire. In addition, measure the voltage across the 27Ω resistor and the voltage across the power supply. Complete the data table and answer the Analysis Questions for Experiment 2. Hint: 27Ω = red-violet-black V 6V Power Supply 27Ω a b c d e Long Wire Fig. 2: Circuit for Experiment 2 3

4 Experiment 3: Building the Potentiometer Circuit (5 minutes) If you did the Properties of Resistors lab, you might recall that the longer the wire, the more resistance it has. You can think of a long wire as several short segments of wire that are connected in series. Each segment is a resistor. As you hopefully saw from Experiment 2, the more resistance you have, the greater the voltage across that resistor. A potentiometer is basically a long wire with a sliding contact. We can adjust the voltage between two points in the circuit by moving the slider along the wire. Potentiometers are commonly used for volume and brightness control knobs. Fig 3a: Potentiometer. Fig. 3b: Internal construction Fig. 3c: Circuit symbol Connect the circuit shown in Fig. 4. Use the power supply, not the battery. Points a and b are the outside terminals of the potentiometer as shown in Fig. 3b above. Point w is the middle (wiper) terminal of the potentiometer. If you have connected everything properly, your DMM should read 0V when the knob is turned all the way counterclockwise, and some maximum voltage when the knob is turned all the way clockwise. If this is backwards, simply switch the wires connected to terminals a and b. 6V V w a 25Ω potentiometer b Fig. 4: Basic Potentiometer Circuit Observe that you now have a variable voltage between points a and w. We can now use this circuit as a variable voltage source for the rest of the lab. 4

5 Experiment 4: Measuring Resistance as a Function of Voltage Now, things get a little more interesting. Carbon resistors, light bulbs, and semiconductors behave very differently. While V=IR is always true for fixed values of V, I, and R, the graph of V vs. I is not necessarily linear. This is because R cannot be assumed to be a constant. We will plot V vs. I for several different devices so that you can observe this. Basic setup: Modify your potentiometer circuit by adding an ammeter, as shown in Fig. 5. The resistor marked X is whatever device we are measuring either a resistor, light bulb, or diode. We will measure the current through X and the voltage across X at the same time. For starters, use the 27Ω resistor as X. V 6V a A X w 25Ω potentiometer b What to do: Fig. 5: Potentiometer Circuit for Measuring Resistor X 1. Measure and graph V vs. I for the 27 Ω resistor. Measure and graph the V vs. I curve for both positive and negative voltages. The easiest way to get the negative voltages is to switch the wires from the power supply. You can expect this first graph to be linear. Remove the connect the dots and do a linear fit to your data. The slope of this line should be the resistance of X. This is the classic Ohm s Law measurement. IMPORTANT: Complete each graph before changing to the next element. You may want to fill in some more data points after you see the graph. 2. Next, remove the 27Ω resistor and replace it with the light bulb. Make a graph of V vs. I, using both polarities and taking care to obtain more data points in the regions of the graph that are changing more rapidly. Notice how the resistance is changing and observe whether reversing polarity makes a difference. Forget the linear fit. Tell this graph to connect the dots to guide the eye. 3. Finally, replace the light bulb with the diode. Measure and graph both the positive and negative voltages as before, even if it looks like nothing is happening. Take more data points where things are happening fast. Tell this graph to connect the dots also. 5

7 Name: Lab Section: T.A. s Today s Lab Partners: Ohm s Law and DC Circuits Data Sheets and Analysis Questions Data and Analysis Questions for Experiment 1: Actual resistance of the 240Ω resistor, measured with the DMM as an Ohmmeter: Actual resistance of the 27Ω resistor, measured with the DMM as an Ohmmeter: Actual voltage of the 9V battery: ± Voltage across the 240Ω resistor: V±δV: ± Current passing through the 240Ω resistor: A±δA: ± (To figure δv and δa, use 2% of the meter s reading.) 1. The error in R is given by the resistor color code (silver = 10%, gold = 5%). Does V=IR, within error? (Hint: You may need to do a propagation of error calculation.) Please justify your answer with an explanation, in addition to answering yes or no. 2. Although a battery is really one device, the circuit analysis is simplified if you treat it as a pure voltage source in series with a pure resistance, called the internal resistance. The new circuit is shown below. Everything inside the dashed line is inside the battery. 9V r V 240Ω A Recall that the voltmeter has nearly infinite resistance compared to the other resistors in the circuit, and that the ammeter s resistance is so small that you can ignore it. The resistance of this circuit is therefore (240Ω + r). Calculate r, using Ohm s Law (V=IR) and V = 9V. Fig. 5: Circuit for measuring the internal resistance of a battery. Answer: 7

8 Name: Lab Section: T.A. s Today s Lab Partners: 3. (circle one) Using the circuit in the previous question, would you expect the measured voltage across the 240Ω resistor to be LARGER, SMALLER, or the SAME as 9V? Explain your thinking: 4. Typically, r gradually increases as electrical energy is drawn out of the battery. a. Assume that r = 20Ω. Calculate the current in the circuit. Answer: b. Assume that r = 60Ω. What is the new current in the circuit? Answer: 5. Why won t measuring battery terminals with a voltmeter always tell you whether a battery is weak? If weak and dead batteries are available, you might try testing them with your DMM. Report what you did and what you found out below. MAKE SURE THAT THE DMM IS ON VOLTS! 8

9 Name: Lab Section: T.A. s Today s Lab Partners: Data and Analysis Questions for Experiment 2: Voltage measured across Power supply Length (cm) Nominal resistance (ohms) Measured resistance (ohms) Measured voltage (Volts) Resistor 27Ω a to b a to c a to d a to e 6. Examine your data. Compare the measured voltage across the power supply with the sum of the measured voltages across the resistor and the entire length of the wire (points a to e). What can you conclude? 7. Consider your data for the wire only. Graph the voltage vs. length of the wire. Include 2% error bars for the voltages, and 2 mm error bars for the lengths. Do a linear fit to your data. What can you conclude about the relationships between the measured resistances, the length of the wire, and the measured voltages along the wire? 9

10 Name: Lab Section: T.A. s Today s Lab Partners: 8. Predict, then test: What voltage would you expect to measure from point b to point e? Prediction: Reason for this prediction: (do NOT change this if it was wrong!) Test: Correction to your thinking, if your prediction was wrong: 9. Repeat question 8, this time measuring the voltage from point c to point e. Prediction: Reason for this prediction: (do NOT change this if it was wrong!) Test: Correction to your thinking, if your prediction was wrong: Data and Analysis Questions for Experiment 3: 10. Just get your circuit working. Is it working? YES NO CAN T TELL If it isn t working or if you can t tell, ask your TA for help. 10

11 Name: Lab Section: T.A. s Today s Lab Partners: Data and Analysis Questions for Experiment 4: Warning! Do NOT exceed 200 ma of current! Doing so can damage the DMM. Carbon Resistor Light Bulb Diode V I V I V I Hints: Take more data points where the graphs are changing rapidly. The most interesting part of the light bulb s graph happens when the bulb is not yet glowing. There IS current, but not enough to make a glow. You ll also want to take data points more often where the diode s graph is changing rapidly. Feel free to add pages, use the margins, or use the back of the page if there aren t enough blanks in this table. 11

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