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Solved University-Physics ProblemsPhysics 3: Introduction to Electricity & Magnetism <<< Resistivity, Conductivity and Resistance >>>Javier Montenegro Joo jmj@VirtualDynamics.OrgReturn to Electricity & Magnetism index page Return to VirtualDynamics University home page
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<<< Resistivity, Conductivity and Resistance >>> |
(1) The region between two hemispheric and concentric shells of radiuses ‘a’ and ‘b’ (with a < b) is filled with a material of conductivity So. Determine the resistance to the electric current between both shells, (a) When the inner shell is connected to the positive terminal of a battery of voltage Vo , while the outer shell is connected to its negative terminal. (b) When the connection is the opposite way. Solution.- In a material of known conductivity (or resistivity) the electric current travels a distance L = b - a, and traverses the area A of a hemisphere of radius r.
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(2) A wire segment has an electrical resistance R. Determine what happens with its resistance, when the wire is stretched until twice its length. Solution.- If the wire is stretched up to the double of its length, the wire becomes thinner and its transversal area reduces to half its original area. Original resistance of the wire:
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(3) Determine the electric field, the current, the current density, and the resistance for the case of two concentric spherical shells of radiuses ´a´ and ´b´ ( a < b) whose interior is filled with a conductive material of resistivity rho. It is known that the current flows from the inner to the outer sphere and that the electrical potential between these spheres is V. Solution.-
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(4) A coaxial cable having a nucleus of radius ‘a’ and hull of radius ‘b’, has insulation of resistivity rho between nucleus and hull. The length of the cable is L and the electric current radially flowing is ‘i’ . Determine: (a) The density of the radial electric current (b) The radial electric field (c) Potential difference between nucleus and hull (d) Resistance to the current that flows radially. Solution.- The electric current flowing from nucleus to hull travels a radial distance r and traverses the area of a cylinder of radius r and length L.
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Libro sobre Caos escrito por Javier Montenegro Joo .- Anatomía del Caos: Estudio del Caos en modelos matemáticos, basado en Física Computacional y Simulacional:
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(5)
Determine the resistance to the electric current flowing between the two
extremes of a truncated cone of length L, whose extremes have radii “a”
and “b”, respectively, (a < b), and which is made of a material of
resistivity rho. Assume the current uniformly distributes throughout the
cross section of the cone; actually this is not exact due to the
different radii of the bases. Demonstrate that the current density is
higher at the smaller base.
Solution.-
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(6)
A concentric hole has been opened in a silver dollar coin whose
resistivity is “rho”. The hollowed dollar has inner radius “a”, outer
radius “b” and width “h”. Determine the resistance to an electric
current: (a) radially traversing the coin (b) Perpendicularly traversing
the coin from one side to the other. Solution.-
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