Ohm’s Law Lab Eli Bashwinger Lab Partners: Jennifer Morriesey, Matthew De Waal Malefyt OBJECTIVE: You will determine if certain resistors “obey” Ohm’s Law by making measurements of voltage versus current. If the data fits Ohm’s Law, then a plot of V vs I will be linear and pass through (0,0). Furthermore, the slope will equal the resistance. You will also make predictions of voltage and current using Ohm’s Law, and see how resistors combine in “series” and “parallel”. A R Theory: Ohms’ law states that electric current through a conductor between two points is proportional to electric potential difference, and inversely proportional to the resistance that the current experience between these two points. In mathematically terms, , where I is the electric current, V is the electric potential difference, and R is the resistance a circuit, This section of theory will be devoted to explaining constituents (electric current, electric potential, electrical resistance) of Ohm’s Law in more detail: Electric current is, when flow is steady, the measure of how much charge flows past some reference point during a time interval: , which is in units of amperes. Since electric current does not always flow steadily, it’s better to state electric current more generally as , the infinitesimal unit of charge that flows past some reference point during an infinitesimal time interval Resistance is a measure of the inherent opposition a conductive material imparts to the flow of charge. Electrical resistance depends on a few quantities: it depends on the physical properties of the material used to make the electrical wire; it depends on the cross-sectional area of the wire; and, finally, it depends on the length of the wire. Electric potential, V, has many countenances, but its simplest form and most applicable form, at least to our situation, is , where the ratio can be thought of—not in a strict and formal sense, mind you—as the potential energy a positive unitary charge possesses, as it is moved an from a position of zero electric potential (this point can be chosen arbitrarily, and is usually chosen at a point infinitely far away), to a point of interest. Electric potential is a property of an electric field; it has a different scalar value at every point in the electric field generated by a source charge distribution, given that you aren't comparing equipotential regions. For instance, let’s take a simple example of a positive point source charge to help understand electric potential. (Before we proceed, though, a little preliminary work is needed.) The electric field due to a point charge can be obtained from Coulomb’s Law: , where is the electric force described by Coulomb’s Law, and is a positive test charge placed in the electric field, used to quantify the direction of the electric field and its strength at a particular position. Substituting in our expressions and simplifying, the electric field becomes, , where the source charge (in our example, it will be the positive point source charge). Now, we know the general expression for electric potential is , where is some initial point and is some final point in the electric field created by the source charge. Because we are dealing with a point source charge, through modification, our expression becomes , because the strength of the electric field at some particular point only depends on the radial distance between that point and the point source charge, and so will our electric potential at some point in the electric field. Integrating and simplifying, we arrive at an expression for the electric in some electric field due to a point source charge, that only depends on the radial distance: , where we take to be zero at . Now, suppose we have a positive point source charge, fixed at some position, whose charge is + 20 C. At a radial distance of 10 m, the electric potential due to the source charge’s field would be 4.45e10 J/C. Now, let’s move a positive point charge of 1 C to this point, from its place at infinity. As one might imagine, the charges will repel each other, so this going against the nature of things, object’s in nature like to be in places of low potential energy; so, this particle will have to have an external force applied to it over a distance, thereby doing work, furthermore exhausting the external agents energy and transferring it into the particle. What potential energy would this particle possess at this point? Using our relationship between electric potential and potential energy, . This justifies our notion that we can think of electric potential as the amount of energy that would be put into a positive point charge of 1 C in moving it from infinity to a point of interest in the electric field. What if we had a 2 C particle? Well, we know that for every 1 C of a particle stationed at this point, it will possess 4.45e10 J of energy. We have 2 C, so it would be twice as much, which is consistent with our mathematical formulas and intuition. Conclusion: Summary Questions: 1. How (what configuration) do you place an ammeter in a circuit to measure a current? First of all, it must be placed in the region where we are interested in measuring the current. Secondly, after placing it in the region on interest, the ammeter must then be placed in series, so that the current can flow through it and measure it can measure it. 2. What effect on the current does placing the ammeter in a branch of a circuit have? The only effect that an ammeter has on the branch it is placed on, is that is measures it. The ammeter has effectively no resistance. 3. How (what configuration) do you place a voltmeter in a circuit to measure the potential difference (“voltage”) across a resistor in a circuit? A voltmeter measures the potential difference across two points. For a voltmeter to properly measure the voltage difference across two points, it must be placed in parallel to the wire connecting the two points of interest. 4. How do you know if your carbon resistor conformed to Ohm’s Law? Did your resistor fit the Ohm’s Law relationship? From our data, we were able to ascertain that our chosen resistor obeyed Ohm’s Law, that is, it was Ohmic,. When we performed our experiment, and collected our data, we found from our Voltage vs. Current graph, of which the slope is the magnitude of the resistance, that the graph was a linear, meaning it fits Ohm’s law. 5. Did all three ranges for the resistance of your carbon resistor overlap? Cite them. The manufacture rating of our chosen resistor, R label, was 1500 omhs, with a range of error [1425 ---- 1575]omhs. When we measured it with an ohmmeter, R meter, it yielded a measurement of 1470 omhs, having the range of error [1462.65 ---- 1477.35]omhs. When we performed our experimented, and graphed our data, we found R experimental to be 1481.4 omhs, having a confidence interval of [1468.089 ---- 1500.612]ohms. As one may note, our experimental range doesn’t quite capture all of the R label range, but it does capture most of the R meter range. 6. How did the predictions of the voltages using Ohm’s Law in step 4 turn out? For the 100 omh resistor, the predicted value was 0.488 V; the experimentally determined value 0.458 V; and the percent difference 6.55%. For the 150 omh resistor, the predicted value was 0.672 V; the experimentally determined value 0.681 V; and the percent difference 1.32%. Finally, for the 200 omh resistor, the predicted value was 0.896 V; the experimentally determined value 0.912 V; and the percent difference 1.75% 7. How did the predictions of the currents using Ohm’s Law in step 4 turn out? For the 100 ohm resistor, the predicted value was 6.29 x 10^3 A; the experimentally determined value 6.31 x 10^3 A; and the percent difference 0.317%. For the 150 ohm resistor, the predicted value was 6.25 x 10^3 A; the experimentally determined value 6.31 x 10^3 A; and the percent difference 0.951%. Finally, for the 200 ohm resistor, the predicted value was 6.30 x 10^3 A; the experimentally determined value 6.31 x 10^3 A; and the percent difference 0.158%.