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ADDITIONAL INFORMATION (For CET and understanding the subject), Expression for resistivity of a conductor, RA, A., For a metallic cylindrical wire with radius r, A = T r2, %3D, =d =(1), 1) Resistivity is constant for a given material. It is independent of dimensions (length and, area of cross-section) of the conductor. It indicates the nature of the material., 2) For good conductors like copper, its value is of the order of 10-8Q-m and for insulator, like quartz it is of the order of 10160-m., 3) For perfect conductors, the resistivity is zero and for perfect insulator the resistivity is, infinity., 4) Greater the value of resistivity, stronger the electric field required to establish a given, current., 5) Factors affecting the resistivity, We have, Conductivity, o =, (it will be proved later), But resistivity, p =, =d =, ne, %3D, Conductiviy, Resistivity is inversely proportional to the number of free electrons per unit volume, (n) of the conductor and relaxation time (t) of the electrons in a conductor. But for a given, conductor, n is constant and it depends on the nature of the material. So, resistivity of a, conductor depends on the nature of the material., But relaxation time decreases with increase in temperature. So, resistivity increases, with increase in temperature. It is discussed below., A wire of resistivity p is stretched to three times to length what will be its new, resistivity?, Resistivity will be same. This is because the resistivity depends on the nature, of the material and temperature. It does not depend on the dimensions of the wire., How does the resistivity of metals vary with temperature?, The resistivity of a metallic conductor is directly proportional to the, temperature., For a conductor, it can be shown that, pt =Po(1+ at), is the resistivity at a temperature toC, Po is the resistivity at a temperature 0°C, a is the temperature co-efficient of resistivity., where pt, NOTE, Manganin and Constantan coils are used in making of standard resistors because, they are having very low temperature co-efficient of resistivity. le their resistivity is verv, slightly affected by changes in their temperature when current flows through them., How does the resistivity of a semiconductor vary with temperature?, The resistivity of a semiconductor is inversely proportional to the temperature.