Anderson Video - Resistance and Temperature

Professor Anderson
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All right, resistance also varies with temperature. So resistivity at some temperature rho, this is resistivity rho at some particular temperature T, is in fact equal to rho naught, some calibrated resistivity. And then there is this scaling factor which is the following: 1 plus alpha t minus T naught. What are all these things? One is of course the number one. What's alpha? This is called the temperature coefficient of resistivity. This is still the temp T and the temp T naught, okay? This thing is rather critical to how the resistor behaves, and if it's a metal then alpha is a positive number, but if it is a semiconductor, then alpha is a negative number. All right, let's multiply both sides by L over A and then we can change this into resistance. So if we multiply both sides by L over A, what do we get? We get Rho L over A equals Rho naught L over A times 1 plus alpha T minus T naught, and now this thing is just a resistance. R equals R naught 1 plus alpha T minus T naught. Okay, and this is a relationship between resistance and temperature. So if I have a normal metal filament and we plot out R as a function of temperature T, what it looks like is this. Okay, and the resistance increases with temperature.
All right, resistance also varies with temperature. So resistivity at some temperature rho, this is resistivity rho at some particular temperature T, is in fact equal to rho naught, some calibrated resistivity. And then there is this scaling factor which is the following: 1 plus alpha t minus T naught. What are all these things? One is of course the number one. What's alpha? This is called the temperature coefficient of resistivity. This is still the temp T and the temp T naught, okay? This thing is rather critical to how the resistor behaves, and if it's a metal then alpha is a positive number, but if it is a semiconductor, then alpha is a negative number. All right, let's multiply both sides by L over A and then we can change this into resistance. So if we multiply both sides by L over A, what do we get? We get Rho L over A equals Rho naught L over A times 1 plus alpha T minus T naught, and now this thing is just a resistance. R equals R naught 1 plus alpha T minus T naught. Okay, and this is a relationship between resistance and temperature. So if I have a normal metal filament and we plot out R as a function of temperature T, what it looks like is this. Okay, and the resistance increases with temperature.