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The piezoelectric element, P, is interesting as it influences performance during stress and vibration. (It
also could
represent a magnetostriction response to a magnetic field.) Stress can change the resistance depending on the resistor chemistry, and vibration can be converted into small AC voltages, which then add to the electrical noise.
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Power rating is simple, right? Voltage times the current (V × I) tells you what wattage rating to choose so the resistor does not burn up from self-heating. Right? No, wrong (or, maybe)? The answer, of course, depends on the application. A series resistor to limit current in a light-emitting diode (LED) can be a plain “vanilla” circuit where little additional concern is necessary. If the resistor has a negative tempco the resistance is reduced as the temperature increases. This, in turn, causes the resistor to draw more current at higher temperature, and that can contribute to overheating. At the other extreme, bias and modulation currents are critical in radio and laser communications systems.