Resistance If we take a sample of conducting material; and connect its ends to a battery: Cross section, A
Resistance Cross section, A So: Or: Ohm s Law Current is directly proportional to the potential Where: is the Resistance of the sample Units of resistance: (pronounced ohm )
Whiteboard Problem: 27-7 The figure below is a current versus potential difference graph for a sample of material. What is the resistance of the sample?
Some Comments on Resistance & Ohm s Law Resistivity is a property of the material; whereas Resistance depends on the material and the geometry of the sample. Ohm s Law is not really a Law of Nature. It just expresses the fact that for some materials the current is proportional to the applied potential (ohmic materials) as you saw in the previous problem. There are some materials (e.g. semiconductors) that do not obey Ohm s Law (non-ohmic materials). The potential difference causes the current, not the other way around. (That s why I went so slow on the first two slides above.) In Chapter 28 on Circuits, we will work with three types of ohmic materials: Metallic Wires have a very low resistivity, so that to a good approximation we can assume that they have zero resistance (unless the wire is very long and/or very thin). Resistors are made of material with a fairly high resistivity, and are used to control the flow of current. Insulators are material with very high resistivities, and hence we can assume that their resistance is infinite.
Whiteboard Problem: 27-8 The terminals of a 0.70 V watch battery are connected by a 100 m long gold wire with a diameter of 0.10 mm. What is the current in the wire? (LC) Some necessary data
Whiteboard Problem: 27-9 Wires 1 and 2 are made of the same metal. Wire 2 has twice the length and twice the diameter of wire 1. What are the following ratios? (LC)
What Causes Resistance? As the electrons move through the lattice, they interact with the ions. This impedes the flow of electrons and also transfers energy to the lattice ions which shows up as thermal energy. electron PhET (batt/res circuit) For most materials, the resistance is somewhat dependent on temperature. Since the ions vibrate more vigorously at higher temperatures, they interact more readily with the electrons, and the resistance increases. The opposite happens at lower temperatures. For some materials at very low temperatures, the resistance actually goes to zero. These are called Superconductors. This is a quantum effect where two electrons move as a pair and don t interact with the lattice ions at all hence, no resistance! A short video on Superconductors and Magnetic Levitation
Resistance vs. Temperature Measurements Liquid Nitrogen Ice Water Room Temperature Boiling Water T (K) R (ohms) The diameter of the copper wire is 0.0056 inches. Use your value of resistance at room temperature and the resistivity of copper (1.7 X 10-8 Ohm-m) to calculate the length of the copper wire. (LC) On the grid, plot the four data points that we have for how resistance changes with temperature. How would you describe how resistance depends on temperature? Based on what we ve done in class, how should resistance depend on temperature? Does this agree with your plotted data? No, it shouldn t, your data should show a linear relation between R and T. What s going on here? Why doesn t our data agree with the theory? The electrons are not actually in a Maxwell-Boltzmann distribution. Instead, their motion is more accurately described by the quantum Fermi-Dirac distribution, and v rms is different. Also, the quantum wave nature of the electron is important in its interaction with the ions.
Table Challenge Problem 3 (4/4/2018) You are to solve the following problem as a group of your entire table. Work together on your whiteboards and the wall whiteboards. No computers or cell phones are permitted; use only your equation sheet and calculator. When the group has arrived at an answer, write it below and turn this sheet in. Only your answer will be graded. Table: Names: A resistor is in the shape of a truncated right circular cone. The end radii are a and b, and the length is L. If the taper is small, we may assume that the current density is uniform across any cross section. Calculate the resistance of the cone if it is made of silicone with resistivity,. Hint: you have to do an integral. Answer: