VDU_Physics_3_009

Solved University-Physics Problems

Physics 3:  Introduction to Electricity & Magnetism 

<<<  Resistivity, Conductivity and Resistance  >>>

Javier Montenegro Joo

jmj@VirtualDynamics.Org

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(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.

[01234]

 

 

(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.-

[56789]

 

 

(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.

Libro sobre Caos escrito por Javier Montenegro Joo .-    Anatomía del Caos:   Estudio del Caos en modelos matemáticos, basado en Física Computacional y Simulacional:

https://www.researchgate.net/publication/326092163 

(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.-

 

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