VirtualDynamics UniversitySolved UniversityPhysics 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

<<< 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 V_{o} , 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.

(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:

(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.

(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.

(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.

(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.
