A material is inserted between a pair of concentric metallic cylinders of radii a and b where b> a as shown in the figure. The kngth of the cylinders is e and >> h. Potential difference is applied bhetween the inner and the outer surfaces, which results in an outward current in the radial direction. Resistivity of the material is given by p = por where py is a constant and r is the cylindrical radial coordinate. What is the resistance of the material?

A material is inserted between a pair of concentric metallic cylinders of radii a and b where b> a as shown in the figure. The kngth of the cylinders is e and >> h. Potential difference is applied bhetween the inner and the outer surfaces, which results in an outward current in the radial direction. Resistivity of the material is given by p = por where py is a constant and r is the cylindrical radial coordinate. What is the resistance of the material?

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter9: Current And Resistance

Section: Chapter Questions

Problem 89CP: Consider a resistor made from a hollow cylinder of carbon as shown below. The inner radius of the...

See similar textbooks

Similar questions

An electronic device designed to operate at any temperature in the range from 10.0C to 55.0C contains pure carbon resistors. By what factor does their resistance increase over this range?
A wire of circular cross-section carries a current density that is not uniform but varies with distance from the center asj(r)=Ar/Rfor radius rin the range 0<r<R. Here, Ais a constant with units of amperes per square meter, and the radius of the wire is R=3.9mm. (a) If the total current is 4.5A , what is the constant A , in amperes per square meter? (b) What is the maximum value of the enclosed current, in amperes? (c) What is the maximum value of the magnetic field, in units of teslas?
Please help: Pacemakers designed for long-term use commonly employ a lithium-iodide battery capable of supplying 0.42 A•h of charge (A) How many coulombs of charge can such a battery supply? Express your answer using two significant figures (B) If the average current produced by the pacemaker is 5.6 micro Amps, what is the expected lifetime of the device? Express answer using two significant figures
Consider a wire of a circular cross-section with a radius of R = 3.00 mm . The magnitude of the current density is modeled as J = cr2 = 5.00 × 106 Am4r2 . What is the current through the inner section of the wire from thecenter to r = 0.5R ?
A potential difference V is applied to a wire of cross-sectional area A, length L, and resistivity r.You want to change the applied potential difference and stretch the wire so that the energy dissipation rate is multiplied by 30.0 and the current is multiplied by 4.00. Assuming the wire’s density does not change, what are (a) the ratio of the new length to L and (b) the ratio of the new cross-sectional area to A?
Taking R = 1.20 kΩ and ℰ = 470 V in the figure shown below, determine the magnitude and direction of the current in the horizontal wire between a and e. magnitude ?mA
In a cylindrical conductor of radius 2 cm, the current density increases linearlywith the distance from the axis from zero at the center to 5 C/m2atr= 2 cm. Find the total current I
A tungsten wire in a vacuum has length 15.0 cm andradius 1.00 mm. A potential difference is applied across it.(a) What is the resistance of the wire at 293 K? (b) Supposethe wire reaches an equilibrium temperature such that itemits 75.0 W in the form of radiation. Neglecting absorptionof any radiation from its environment, what is the temperatureof the wire? (Note: e = 0.320 for tungsten.) (c) What isthe resistance of the wire at the temperature found in part(b)? Assume the temperature changes linearly over this temperaturerange. (d) What voltage drop is required across thewire? (e) Why are tungsten lightbulbs energetically inefficientas light sources?
A wire with cross-sectional area "A", length "l" and conductivity "σ" is subjected to a potential difference "V". The applied potential difference is changed and the wire is stretched so that the power dissipated increases by a factor of 30 and the current increases by a factor of 4.Find the ratio of the final length "l" to the initial length "lo" of the wire
If a current of 80.0 mA exists in a metal wire, (a) howmany electrons flow past a given cross-section of the wire in10.0 min? (b) In what direction do the electrons travel withrespect to the current?
Calculate the specific conductivity of the conductor in Mega(Ωm)-1 since the current passing through a conductor with a cross-section (1.00nm x 1.00µm), length of 10.00mm, is 1.00mA and the voltage value falling on it is 1.00V.
A long coaxial cable, crossection of which is shown in the figure, is made up of a cylindrical inner wire of radius a and a cylindrical shell shaped coaxial outer wire of inner radius b and outer radius c. The current density with magnitude J = Kr2/a is spread over the cross section of the inner wire where the current has out-of-page direction. Outer wire carries uniformly distributed current i = πKa 3 having into-the-page direction. a) Find the total current of the inner wire iin in terms of ?.Find expressions for the magnitude of magnetic field, b) inside the inner wire (r < a) c) between the wires (a< r< b) d) inside the outer wire (b< r < c) e) outside the outer wire (r> c) in terms of i, π, μ and r. For each case indicate the direction of the magnetic field as well.