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HARVARD PHYS 15b - Current, Ohm’s Law, Resistance, EMF

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Physics 15b Lab 2: Current, Ohm’s Law, Resistance, EMF In Chapters 1-3 of Purcell, the potentials and fields associated with stationary charges were studied. Chapter 3 allowed charges to move freely in conductors, but the resulting potentials and electrical fields were only evaluated after the charges stopped moving. Chapters 1-3 were the subject of the previous lab. Chapter four, which considers moving charges, is the basis for this lab. Conductivity as a macroscopic property of materials that depends upon the number of free charge carriers in a material and on the collisions experienced by the charge carriers as they move through the material. The resistivity and conductivity of various materials is presented in table 4.1. The number of free charge carriers in a metal is fixed. The number of free charge carriers in a semi conductor can be increased by doping, or by increasing the temperature of the material. The number of free charge carriers in a neutral gas can be increased by ionizing gas atoms, a process that is used in Geiger counters and neon signs. http://en.wikipedia.org/wiki/Neon_lamp. This lab will consider the temperature dependence of conductivity, as well as the effect of doping, temperature, and ionization on the number of free charge carriers. Just as the concept of capacitance underlies circuit element known as the capacitor, the concept of conductivity underlies the circuit element known as the resistor. The current, I, flowing through a resistor with resistance R is a linear function of the voltage, V, across the resistor where I=V/R. Many important systems have current to voltage relationships that are highly non-linear. Sparks and arcs are particularly dramatic manifestations of non-linear current to voltage relationships. This lab will consider systems with non-linear current to voltage relationships, where the non-linearities have different origins. Not only can current be a non-linear function of voltage, but the magnitude of the current can also depend on the sign of the voltage; therefore, the I/V for a positive voltage may be different from I/V for the corresponding negative voltage. To study such effects, you will measure the response of a system when charge is sent through the system in one direction and then the response when charge is sent through the same system in the opposite direction. If space is uniform, changing the sign of the voltage applied across a circuit element is the same as keeping the sign of the voltage the same, but reversing the direction of the device. As shown below, if the device is uniform reversing the device has no effect on the experiment at all. If the device is uniform, leaving the device fixed, but reversing the voltage results in a current that is also reversed; however, the ratio of I to V for the reverse voltage is exactly the same as for the case where the voltage went in the forward direction as long as the rest of the space is symmetric. In contrast, if the device is not uniform, then changing the sign of the voltage can make a physical difference. Purcell often stresses the role of symmetry in limiting what is physically possible (e.g. symmetry requires that the electric field of a spherical object have only a radial component), and much of modern physics studies and exploits different sorts of symmetries. Checking whether the response of a circuit to a voltage Vo>0 differs from its response to –Vo is a very simple example of a measurement that probes symmetry by reversing the direction of a potential and measuring the response of the system to the reversed potential.The current is not always a unique function of the voltage: in some cases, the same voltage can produce different currents. A system is hysteretic if its response to a stimulus depends on the history of the system, not just the present value of the stimulus. Biological systems can be hysteretic. Systems that experience avalanches are also hysteretic. Memories require hysteresis, and ferromagnetic systems are used in magnetic memories precisely because of their strong hysteretic properties. Thermostatic temperature control systems and battery rechargers are hysteretic, and their energy efficiency depends on how hysteretic they are. The hysteresis in battery charging is an important issue that has limited the successful exploitation of solar energy. Hysteresis can destabilize systems: factors affecting global warming show destabilizing affects. Hysteresis is also exploited to stabilize systems by making them less sensitive to noise. In this lab you will consider at least one hysteretic system. Current, voltage, energy, and power are not only interesting as basic science topics, they also play a significant role in public policy: energy generation and use are becoming subjects of vigorous debates for a number of reasons including national security and climate change. The relationships between current, voltage, energy, and power impose significant constraints on how much electrical energy efficiency can be achieved. Lighting consumes a large fraction of the electrical energy in the United States. At present, a large fraction of our lighting comes from incandescent light bulbs that are very energy inefficient. Australia is already banning incandescent light bulbs. Two alternatives are fluorescents lights and light emitting diodes LEDs. LED’s consist of an n doped semiconductor next to a p doped semiconductor, where a voltage source does work to move charge up the potential hill generated by the internal electric field of the LED. That potential energy is released in the form of light. The use of compactfluorescent light bulbs and LED’s is being heavily promoted. It has been suggested that if all of the incandescent light bulbs in the US were switched to LEDs, the US could lower its electrical energy consumption by approximately 30%. In this lab, you will consider how the current to voltage relationships for conductors, semiconductors, and plasmas determine the efficiency with which incandescent light bulbs, LEDs, and fluorescent light bulbs convert electrical energy to light. You will also consider some of the spectral and temporal properties of the light that is produced, as well as the power conversion efficiency. A consequence of the definition of temperature is that where ν is the frequency, T is the temperature in degrees Kelvin, h is Planck’s constant, and c is the speed of light. This distribution is


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HARVARD PHYS 15b - Current, Ohm’s Law, Resistance, EMF

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