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1 Name Partner Date Class Ohm's Law Equipment: Resistors, multimeters, VOM, alligator clips, wires, breadboard, batteries, 1/4 or 1/2 Amp fuse, low voltage power supply. Object: The object of this exercise is to learn how to set up simple circuits, use electrical meters, calculate the effective resistance of resistors connected in series and/or parallel, and examine the electrical properties of some devices and to obtain Ohm's law. Ammeter Light Bulb Ohmmeter + Power Supply Resistor Voltmeter Figure 1 Symbols for Electrical Components. Kilo (K) 1000 (10 3 ) thousand Mega (M) (10 6 ) million mlli (m) (103 ) thousandth micro (µ) (106 ) millionth nano (n) (109 ) billionth Table 1. Common prefixes for the metric system and electronics V Exercise one: Measuring resistance Find a 220 ohm resistor. The resistors get there name because they resist or impede the flow of electricity (electric current) (See appendix of this lab for color code and resistor information and for a visual resistance calculator. Using a digital multimeter select the proper resistance scale (ohms or Ω). Make sure that two leads are properly plugged into the meter. One should be connected to the point which on most meters is marked with common or () or is colored black, the other should be connected to the meter where it is called volt ohms, (VΩ), (+) or sometimes with a red color. Measure the resistance of the resistor by placing the other sides of the leads on opposite sides of the resistor. It is OK to measure the resistance of this resistor using your fingers to hold the leads. This is because its value is relatively low. Record. 1
2 Now reverse the direction of the leads on the resistor and remeasure. Record. Do resistors have about the same resistance in each direction? What is the percent difference between the color code value and the measured resistance? Is this within the tolerance limits of the resistor (four color)? Repeat the measurement using an analog VOM meter, (one with a needle). VOM stands for VoltOhmMilliamp Meter. You must first zero the meter by placing the two leads together,(shortcircuit) and zero with the zero adjust control. You must repeat this procedure whenever you change resistance scales but not for any other types of measurements. Make sure that you use a resistance scale which places the needle closest to the center of the scale for the most accuracy. Record Measure a 1 Megohm ( 1x10 6 ohm) resistor by holding the two leads of the VOM to the two leads of the resistor with your fingers. Record You will probably find the measured resistance to be much lower than the value indicated on the resistor. You may have found a large error in measuring this way. Repeat but this time hold at least one of the leads using an alligator clip (looks like tiny alligator jaws) so that your fingers are not touching any metal. Record Now hold the ohmmeter leads between your thumb and index fingers so that you may measure your resistance (the analog ohmmeter works best for this). Your resistance Why do you think that the measurement was so much in error when you held both ends of the resistor? Hint: people conduct electricity. You may use either the digital or the analog meters in the rest of this lab. Exercise two: The bread board The breadboard is a device with lots of holes, some connected together, which is used by experimenters for making temporary circuits. You "plug things" into the holes to connect them, but first it's important to know how the holes are connected. If two holes are connected there will be nearly zero resistance between them, if they aren't connected there will be nearly an infinite amount of resistance between them. Holes that are connected act as a single point electrically thus items plugged into connected holes are connected together. 2
3 Using an ohmmeter determine which holes are connected and which are not in your breadboard. Make a sketch of the layout showing how the holes are connected. BreadBoard Sketch Exercise three: Resistors in series Place a 220 ohm and a 390 ohm resistor in the breadboard so that they are joined on one end as shown in figure 1. The upper part of the picture shows how they look on the breadboard, the bottom one shows the schematic diagram of the situation. We will use schematic diagrams from now on. figure 1 Prediction: What do you predict for the combined resistance of these two resistors? Measure the total resistance of the two resistors in series. Record Did your prediction agree with the measurement? Connect three 100 Ω resistors in series as shown below. a 100 Ω 100 Ω 100 Ω b Prediction: What do you predict for the combined resistance of these three resistors? Measure the total resistance of the three resistors in series. Record Did your prediction agree with the measurement? Question: What is the rule for finding the equivalent resistance of resistors in series? Is this a true statement? The equivalent resistance of resistors in series is always greater than the largest value for any resistor in that group. YES / NO 3
4 Exercise four: Measuring potential difference Caution: It is very important that any meter used to measure potential difference (voltage) is set to the correct scale and the wires plugged into the right holes. If the meter is incorrectly set on current (amps) It will almost certainly blow a fuse or become damaged if you try to measure voltage with it. If you didn't read the caution above do it now! Measure the potential difference of one of the 1.5 Volt flashlight batteries to four significant digits using a digital multimeter (DMM). Place the positive probe on the positive end of the battery and the negative one on the negative (nonpointy) side Reverse the leads and re measure what do you observe? Is there a difference when you reverse the leads in magnitude? Sign?. Carefully hook up two 1.5 V batteries in series (+ connected to ) as shown in figure 2, the longer, vertical, line represents the positive side of the battery. You should end up with a wire with one free end(a) and the other end connected to the negative of one battery. A wire which goes between the batteries from the positive of the first to the negative of the second. Finally a wire from the positive end of the second battery to a free end(b) Measure the Voltage from A to B by placing the free ends into a voltmeter. Record Figure 2 What is the rule regarding the voltage of batteries in series? Now carefully connect the batteries in parallel (+ to + and  to ) as shown in figure 3. Measure the potential difference between A and B. Record Figure 3 What is the rule regarding the voltage of batteries in parallel? 4
5 Exercise five: Ohm's Law Ohm's law is a relationship between resistance, voltage, and electric current in a circuit. The electric current is a measure of the rate of charge flow in a circuit. It is analogous to the rate of water flow in a pipe. The water flow might be measured in gallons per minute, the electric current is measured in coulombs per second or amperes (Amps). You will be using a power supply to produce a known direct (steady) current (DC) voltage on the circuit in figure 4. Make sure that the voltmeter and ammeter are set to the correct DC settings, start with the ammeter at its highest scale and reduce until you get a reading. Begin with the power supply DC voltage control at its lowest CCW (counter clockwise) setting and the current control at its highest CW (clockwise) setting. ALWAYS adjust the voltage control and leave the current control (limiter) at its highest position. The fuse should have a value of a quarter amp. Do not turn the power supply on until the circuit is complete and the meters are adjusted to the correct scale. Note: some ammeters have a separate place to plug in the probe, usually labeled with an "A". Do not use any holes labeled "10 A" here. 100 ž Figure 4 Here we use the symbol for a battery to represent the power supply. The fuse is a piece of fine wire protected by glass which melts if the current gets too high, 1/4 or 1/2 amp in our case. Check the fuse by eye to see if it is good before starting. See figure 6. Condition of fuse Figure 5 Caution: It is very important that any meter used to measure potential difference (voltage) is set to the correct scale and the wires plugged into the right holes. If the meter is incorrectly set on current (amps) It will almost certainly blow a fuse or become damaged if you try to measure voltage with it. If you didn't read the caution above do it now! Yes I know you've read this before! Once you're satisfied that everything is wired correctly (It doesn't hurt to check). Turn on the power supply and gradually increase the voltage from 0 to 6 Volts in about one Volt increments, checking and recording the current as you do so in the data table below. Record 5
6 both to the maximum accuracy of the meters that you use ( Does changing a scale perhaps give you more significant digits?) Power Supply  Volts Current (Amps) Now, using a computer graph the voltage vs. the current. Voltage on the vertical axis and current on the horizontal axis. Is it a straight line? Are the voltage and current proportional to each other? NOTE: Use the xy plot for the graph or things may not turn out well. Carefully find the slope of the graph. Show your work on the graph. The slope of the graph is. Is the slope of the graph equal to the resistance of the resistor? Find the per cent difference. CAREFULLY LABEL THIS GRAPH AND STAPLE TO THE BACK OF THIS REPORT. Is the slope constant? What happens to the resistance of the resistor as the voltage is increased? If V is the voltage of the power supply, I is the current through the resistor, and R the resistance of the resistor write an equation involving these three variables which satisfies the data that you obtained. The straight line (linear) relationship between current and applied voltage is known as Ohm's law. Question: If a voltage of 25 V is applied to a 45 ohm (Ω) resistor what current will result? Show your work. If you place a 90Ω resistor in place of the 45 Ω resistor above, what will the current be? If you place a 22.5Ω resistor in place of the 45 Ω resistor above, what will the current be? If you place a 50 V battery in place of the 25 V battery (keeping 45 Ω resistor), what will the current be? 6
7 Exercise six: Resistors in parallel. If all went well in the above section you should have experimentally derived the relationship between the voltage drop across a resistor (V in volts), the resistance R (in ohms Ω ), and the current I (amps): V=IR It can be used for any part of the circuit or the circuit as a whole. Using the breadboard connect two resistors in parallel as shown in figure 2. Figure 6 If a 12 volt battery is connected between A and B: what is the expected current through the 220 Ω resistor? what is the expected current through the 390Ω resistor? Because of the conservation of electric charge, the total current flowing from A to B is the sum of these two individual currents. I tot =I 220 +I 390 I220 Itot I390 Itot what is the expected total current from A to B? What is the expected total effective resistance (remember V=12 volts) R tot = V/ I tot Measure the resistance between points A and B. Record. If two resistors R1 and R2 are connected in parallel (as the 220 Ω and 390 Ω resistors are above) and a voltage V is applied across them. Write and equation (using V and Rs) for the expected current through R1. 7
8 the expected current through R2. The expected total current flowing from A to B. If we want to be able to write I tot = V/R tot, what must (1/R tot ) be? Compare this derived value with that given in your text. Question: Is this a true statement: The equivalent resistance of resistors in parallel is always lower than the value of the lowest resistor? Exercise 7: A light bulb Remove the resistor from the previous circuit and replace it with a 5 to 7 volt light bulb. 100 ž Again increase the applied voltage in about one volt increments until you reach 6.0 volts. Enter the data in the table below and make a graph of Voltage vs. current as you did before. NOTE: Use the xy plot for the graph or things may not turn out well. Use V=IR to compute the resistance of the light bulb at each voltage. 8
9 Power Supply  Volts Current (Amps) Resistance (Ohms) What happens to the slope as the temperature goes up? Is the resistance constant in this case? Resistance can change with temperature changes. From your results and graph what can you conclude about the dependence of resistance in light bulbs vs. temperature. In other words does the resistance increase or decrease with temperature? Big hint: the temperature of the bulb when bright is higher than when it is dim! STAPLE THIS GRAPH TO THE BACK OF THIS REPORT. Based on the experimental evidence thus far, discuss whether Ohm's law is true in all cases, that is, does the current always increase linearly in proportion to voltage? Explain based on what you have observed. Exercise 8: Current Use the same light bulb circuit that you used above with the power supply set at 6.0 volts. Notice that the ammeter measures the current going INTO the light bulb from the battery. Now break the circuit between the light bulb and negative battery terminal and insert the same ammeter in the circuit here so that you can measure the current coming OUT OF the light bulb. Current in =, Current out = How does the current coming out of the light bulb compare to that going into the light bulb? Answer the following: Be careful! Many people miss one or more of these! 9
10 True or False, The light bulb uses up current. True or False, The light bulb uses up electric charge. Hint: I= Q/t True or False, The light bulb uses up electrons. Hint: Electrons have charge. Disconnect the ammeters from the circuit and reconnect the circuit so that the bulb lights. Switch the range switch on both meters to DC Volts and remove the wire in the "A" or amps terminal. (This makes it less likely that someone will hook the meter up incorrectly. Exercise 9 Potential Difference and Power Now using one of the meters set to measure voltage (use a scale of at least 20 VDC) measure the potential difference (voltage) between the negative terminal of the power supply and the terminal on the light bulb closest to the positive terminal on the power supply. (The negative (com) on the meter goes to the negative on the power supply). Result. This is the potential of this side of the light bulb Now measure the potential of the other side of the light bulb by leaving the meter attached to the negative on the power supply but moving the positive lead to the side of the bulb closest to the negative of the power supply. Result. This is the potential of this side of the light bulb Answer this question: What is different between the two sides of the bulb and what is the difference? This is called the potential difference across the bulb or the voltage drop across the bulb. Usually to find the potential difference one places the voltmeter leads on either side of the device being measured (with the common or negative closest to the negative of the power supply) and makes the measurement. Do it and compare with the result above. P.D.= V= Volts The power (in Watts) consumed by a resistor is given by the product of the current (I) and the voltage (V) P=IV. Calculate the power of the light bulb at 6 volts the circuit above. Show your work. Power = 10
11 Home work Resistors in parallel Assume that you have 3 resistors in parallel as shown in figure 9. The power supply is set to 6.0 Volts. Figure 9 Calculate the equivalent resistance of the network of three resistors. Show your work. Re = Use Ohm's law to calculate the current supplied by the power supply. Show your work. I (supply calculated) = What will the voltage across each resistor be? Hint: They are all connected directly to the power supply. V(220 Ω top) = V(220 Ω middle) = V(390 Ω) = What general rule can you make about the voltage of resistors connected in parallel? Compute the current (using Ohm's law) through each resistor. Show your work. I (220 Ω) I (220 Ω) I (390 Ω) Fill in the blanks: In a series circuit all resistors have the same current or voltage In a parallel circuit all resistors have the same current or voltage 11
12 Appendix: Color Codes Color 0 Black Example I 1 Brown OrangeYellowBlueGold 2 Red 34,000, % 3 Orange or 34 M Ω + 5% 4 Yellow 5 Green Example II 6 Blue RedBlackGoldSilver 7 Violet 2 ohms + 10% 8 Gray 9 White Example III 5% Gold or 101 YellowBlackBlackGold 10% Silver or Ω + 5% 12
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