A cylindrical metal rod is 1.60 m long and 5.50 m in diameter. The resistance between its two ends (at ) is . (a) What is the material? (b) A round disk, 2.00 cm in diameter and 1.00 mm thick, is formed of the same material. What is the resistance between the round faces, assuming that each face is an equi-potential surface?
a) The material is silver.
b) The resistance between the round faces of the disk is .
The given data can be listed below as:
Here, we need to use the equation relating to resistance and resistivity. By using that equation, we can find the type of material and then the resistance between the faces of the disk.
The cross-sectional area of the circle is,
The resistance of a material is,
The resistivity of a material is,
Area of cross section of the rod can be calculated using the given data in equation (i) as follows:
Using value of area and all given values in equation (iii), we can get the resistivity of the material as follows:
This is the resistivity of the silver.
Therefore, the material of the rod is silver.
As we know, that rod and disk are of same material. Thus, the resistivity of the disk is given by, .
Distance between two faces is the thickness of the disk.
Thus, the value of the length is given by, .
Now, the area of the round disk can be calculated using the diameter value in equation (i) as follows:
Using value of area and all the given values in formula of equation (ii), we can get the value of the resistance between the two ends of the rod as follows:
Hence, the value of the resistance is .
A certain cylindrical wire carries current. We draw a circle of radius r around its central axis in figure-a to determine the current i within the circle. Figure-b shows current i as a function of r2. The vertical scale is set by ,and the horizontal scale is set by, . (a) Is the current density uniform? (b) If so, what is its magnitude?
When a metal rod is heated not only its resistance, but also its length and cross-sectional area is changed. The relation suggests that all three factors should be taken into account in measuring r at various temperatures. If the temperature changes by , what percentage changes in (a) L, (b) A, and (c) R occur for a copper conductor? (d) What conclusion do you draw? The coefficient of linear expansion is .
Figure 26-17 shows a rectangular solid conductor of edge lengths L, 2L, and 3L. A potential difference V is to be applied uniformly between pairs of opposite faces of the conductor as in Fig. 26-8b. (The potential difference is applied between the entire face on one side and the entire face on the other side.) First V is applied between the left–right faces, then between the top–bottom faces, and then between the front–back faces. Rank those pairs, greatest first, according to the following (within the conductor): (a) the magnitude of the electric field, (b) the current density, (c) the current, and (d) the drift speed of the electrons.
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