ohm lab worksheet

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Electrical Engineering

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May 23, 2024

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Student name: Lab 4: Ohm’s “Law” This is the first of three circuit labs. At the end of this lab, you should be able to construct a simple circuit and make measurements of current and voltage in that circuit. You should also be able to decide whether data are consistent with theory or expectations and support that decision with evidence. Introduction: Circuit elements and functions Electronic circuits are part of our everyday lives, but you likely haven’t had much introduction to them in lecture yet, so let’s go over some of the basics. A circuit is a path (or paths) of wire and other elements that electrons travel through and around. In order for electrons to travel and electricity to flow, the circuit must be a closed loop . If you have a closed loop and then another wire attached to that loop on one end, but dangling on the other end, electricity won’t flow through that dangling wire. Electrons flow because an electric potential is set up within the wires of the circuit. This potential is often created by a battery or a voltage supply – it’s no coincidence that electric potential has units of volts (V) and the batteries you can buy at the store are described as 12 V batteries. A voltmeter measures the potential difference between two different points in the circuit. If you hook a voltmeter up across a 5 V power supply, it should read 5 V because the power supply is applying a potential difference of 5 V. If you want to compare the flow of electrons with the flow of water, the battery is like the water pump raising water to a higher level so that it has more potential energy. Current describes how quickly and in which direction the electrons are flowing. Confusingly, current is described as the motion of positive charge, so it flows in one direction while the electrons flow in the exact opposite direction. Current flows from high electric potential to low electric potential. We measure current with a device called an ammeter and the units of current are amperes (A). The battery provides potential energy to the flowing charges and resistors dissipate that energy. Resistors that dissipate more energy have a higher resistance . A circuit diagram is a drawing that shows how different circuit elements are connected – it’s an instruction manual for how to construct a circuit. Every circuit element has a symbol. Those symbols are connected with lines that represent the connecting wires between the physics circuit elements. Here’s a circuit diagram Page | 1

that has a resistor and a battery connected together. The resistor symbol is the zig-zag and the battery is represented by the double line. This next diagram has the same circuit, but now with a tool measuring the current through the circuit and another tool measuring the potential difference across the resistor. Two of the circuit elements are the same as in the previous circuit diagram – make sure you can identify those. You should also be able to identify the two measurement tools in the circuit – both of them are represented as a circle with a letter in it. When these tools are used correctly, they don’t disturb the circuit’s behavior, so you’re effectively measuring the properties of the circuit as well. Introduction: Ohm’s Law German physicist Georg Simon Ohm was the first to publish his observation that the electric current I that flows through an object is proportional to the difference in electric potential V between the object’s ends. Mathematically, Ohm’s Law is: V = IR . (1) The constant of proportionality R is the resistance of the object, and it depends on that object’s physical properties. Resistance is measured in units of ohms. The abbreviation for the unit is the Greek capital letter omega ( Ω ). In fact, Ohm’s “law” has exceptions and therefore is not a universal physical law. It doesn’t apply to all materials or all circuit elements. Semiconductor diodes and transistors, for example, do not obey Ohm’s Law, and this ‘nonlinear’ behavior is key to their use in modern electronics. Most conductive plastics do not obey Ohm’s Law either. However, most metallic conductors and simple circuit elements do follow Ohm’s Law, so it is very useful in practice for controlling electric current precisely even if it is not universally applicable. When a circuit element is called a resistor, that indicates that it obeys Ohm’s Law. Additionally, sufficiently small signals approximately obey Ohm’s law in non-linear devices. Familiarization and Setup First, download the “Ohm’s Law.cap” Capstone file and execute it. This will allow you to control the potential difference across the test resistance and to observe the potential difference that exists and the electric current that flows. Page | 2

Figure 1 below shows the same circuit as a circuit diagram (a) and a pictorial (b). Compare the two figures and be sure you can identify the following circuit elements in both the circuit diagram and the pictorial: resistor, battery/power supply voltage, ammeter, and voltmeter (in the circuit diagram, this is just indicated by where the voltmeter would measure the potential difference, not by an element exactly). If you can’t do this, confer with your lab partner or your TA until you are confident. Select one of the three resistors and construct the circuit in Figure 1. Before continuing, ask your TA to check your circuit. a) The electric current, I , is measured by the ammeter and the potential difference across the device, V , is measured by the voltmeter. b) Pasco’s “High Current Sensor” is the ammeter (A), that Pasco’s “Voltage Sensor” is the voltmeter ( V ), and that Pasco’s “Output 1” supplies the battery voltage ( V B ). All of these are controlled by Pasco’s 850 Universal (computer) Interface. c) The ‘Record’ button at the bottom left allows you to apply the potential difference (“voltage”) and to begin recording data. d) Note the units: Current is in mA=0.001A and potential difference is in V. The Ampere is a very large current and would burn up our devices. e) The “Signal Generator” at the left contains the battery voltage controls ( V B ). You will need to vary “Output 1’s” values. Figure 1: A schematic diagram of a simple circuit (a) and an instructional aid (b) for constructing the circuit. We will use this circuit to study Ohm’s law and to study the electrical properties of five devices. Page | 3

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Observing Potential Difference vs. Current 1.1 (15 points) Record the labeled resistance of whatever resistor is in your circuit in the box above the table. Using that resistor, set the Signal Generator voltages as indicated in Table 1 and record the voltage across the resistor and current for each battery voltage. Be sure your current units match the values in your table. Resistor value: 100 ohms Table 1: Potential difference vs. electric current observed for an electric resistor. Battery voltage (V) Voltage across resistor (V) Current (A) -5.00 -4.439 -0.0445 -4.00 -3.558 -0.0357 -3.00 -2.666 -0.0268 -2.00 -1.784 -0.0179 -1.00 -0.895 -0.00897 1.00 0.885 0.00887 2.00 1.775 0.0178 3.00 2.659 0.0267 4.00 3.549 0.0356 5.00 4.430 0.0444 Page | 4

1.2 (15 points): Plot the voltage across the resistor ( y -axis) vs. the resulting current ( x -axis). Using the “LineFit.xslx” file available on Canvas, fit the data to a proportional relationship (zero intercept). Show the plot here, and record the fitted slope and its uncertainty in the boxes below. (No need to give the y -intercept of your fit since it should be set to zero.) Fitted slope: 99.71 ± 0.05 in units of V/A 1.3 (10 points): Do your data fit this line? Is the shape of your graphed data consistent with Ohm’s Law being correct? Give some sort of explanation to justify your conclusion. Page | 5 My data fits this line, and it is consistent with Ohm’s law. Ohm’s law defines a linear relationship between voltage and current, which is seen in this graph.

1.4 (10 points): Is your observed slope consistent with Ohm’s Law being correct? As part of your answer, calculate a Z-score. The manufacturer specified the resistance to 5% tolerance, so the uncertainty in the labeled resistance will be 0.05 R , where R is the resistance of your resistor. Note: use whichever uncertainty is larger in your Z-score calculation. There are more complex ways to combine uncertainties, but we will not deal with them until later a later course. For now, a safe procedure is to always use the dominating uncertainty, which is to say the larger one. Properties of Electric Meters 2.1 (10 points): Remove your resistor and record the ammeter and voltmeter readouts. Use this information to deduce the resistance of the voltmeter, and explain your reasoning. (Hint: What path is available for the current now? See Figure 1(a).) 2.2 (10 points): Re-install your resistor and connect the voltmeter across the ammeter instead of the resistor (for best results, connect directly to the ammeter instead of to the breadboard). Connect red to red and black to black. Record the voltage across the ammeter and the current through the ammeter. Using Ohm’s Law, what is the resistance of the ammeter? Page | 6 This slope is consistent with Ohm’s law. The slope is 99.71, which makes sense because voltage/current should be equal to resistance according to Ohm’s law, and the resistance is 100 ohms. The Z value is very low, which shows this is significant. Z = X − X σ = 100 − 99.71 5 = 0.058 Voltmeter reading (for 3 V): 2.992 V, Current: 0.00 A V = IR  2.992 = 0.00(R) The resistance of the voltmeter is effectively infinite. This makes sense physically because you don’t want any current flowing through the voltmeter when it is used to measure the current through another element. Voltmeter reading (for 3 V): 0.316 V, Current: 0.0267 A V = IR  0.316 = 0.0267(R)  R = 11.84 ohms

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Some additional notes about instrumentation In the real world, we cannot build ammeters with zero input resistance. The ammeter needs some mechanism to interact with the current in order to measure it, and this interaction will always produce a slight resistance and thus a slight potential difference. Similarly, it is impossible to build a voltmeter with infinite input resistance, since it needs a trickle of current in order to measure the electric potential difference. Luckily, it is possible to make instruments which are nearly ideal, at least under normal operating conditions. Modern ammeters have input resistance ~1  -10 m  which is negligible compared to typical resistances of other components. Modern voltmeters have input resistance 10 M  -1000 G  , which is close enough to infinite that the current drawn by a voltmeter is negligible in typical circuits. However, it is very important that we never connect an ammeter across a voltage source . Because the ammeter resistance is so low, doing so will definitely blow the ammeter’s fuse and might destroy the ammeter and/or the voltage source. Please confine your explosions to the simulated lab equipment where injury is less likely. Exceptions to Ohm’s Law 3.1 (10 points): Restore your circuit to Figure 1. Replace your resistor with an incandescent lamp or a light emitting diode (LED). Record which device you’re observing (lamp or LED) in the box below. Set the battery voltages, V B , to the values shown in Table 2 and record the observed potential differences and currents. Be sure your current units match the values in your table Device: Incandescent lamp Table 2: Potential difference vs. electric current observed for an electric resistor. Battery voltage (V) Voltage across resistor (V) Current (A) -5.00 -3.516 -0.10855 -4.00 -2.746 -0.09442 -3.00 -1.224 -0.07866 -2.00 -1.224 -0.06088 -1.00 -0.503 -0.03921 1.00 0.508 0.03912 2.00 1.228 0.06103 3.00 1.969 0.07888 4.00 2.742 0.09460 Page | 7

5.00 3.491 0.10845 3.2 (10 points): Plot the potential difference observed by the voltmeter ( y -axis) vs. the resulting current ( x -axis). Show the plot here. 3.3 (10 points): Describe the relationship between this data and Ohm’s law. Do the data seem to obey Ohm’s law? All the time? Some of the time? Don’t worry about fitting here, just draw conclusions from the shape of the graph. Page | 8 The data here seems to not obey Ohm’s law. The data here appears to be in a shape that would be more consistent with a higher order polynomial fit.