CALC The region between two concentric conducting spheres with radii a and b is filled with a conducting material with resistivity ρ. (a) Show that the resistance between the spheres is given by R = ρ 4 π ( 1 a − 1 b ) (b) Derive an expression for the current density as a function of radius, in terms of the potential difference V ab between the spheres, (c) Show that the result in part (a) reduces to Eq. (25.10) when the separation L = b = a between the spheres is small.
CALC The region between two concentric conducting spheres with radii a and b is filled with a conducting material with resistivity ρ. (a) Show that the resistance between the spheres is given by R = ρ 4 π ( 1 a − 1 b ) (b) Derive an expression for the current density as a function of radius, in terms of the potential difference V ab between the spheres, (c) Show that the result in part (a) reduces to Eq. (25.10) when the separation L = b = a between the spheres is small.
CALC The region between two concentric conducting spheres with radii a and b is filled with a conducting material with resistivity ρ. (a) Show that the resistance between the spheres is given by
R
=
ρ
4
π
(
1
a
−
1
b
)
(b) Derive an expression for the current density as a function of radius, in terms of the potential difference Vab between the spheres, (c) Show that the result in part (a) reduces to Eq. (25.10) when the separation L = b = a between the spheres is small.
Problem 1: A cell phone battery uses chemistry to create a charge separation between the terminals (anode and cathode). Such a battery is listed as having a capacity of Q = 7.5E-08 C.
Part (a) How many free electrons does the battery contain, N?
Part (b) If there are 1.0 million electrons moving through the phone every second how long will the battery last in seconds?
Part (c) Current, I, is given in amps which are coulombs per second. What is the current passing through the phone?
A 0.68-mm-diameter copper wire carries a tiny current of 2.5 μA. The molar mass of copper is 63.5 g/mole and its density is 8900 kg/m^3. NA=6.02×10^23
Estimate the electron drift velocity. Assume one free electron per atom.
Express your answer to two significant figures and include the appropriate units.
vd=
A straight, cylindrical wire lying along the x axis has a length L and a diameter d. It is made of a material described by Ohm’s law with a resistivity ρ. Assume potential V is maintained at the left end of the wire at x = 0. Also assume the potential is zero at x = L. In terms of L, d, V, ρ, and physical constants, derive expressions for (a) the magnitude and direction of the electric field in the wire, (b) the resistance of the wire, (c) the magnitude and direction of the electric current in the wire, and (d) the current density in the wire. (e) Show that E = ρJ.
Chapter 25 Solutions
University Physics with Modern Physics, Books a la Carte Edition; Modified MasteringPhysics with Pearson eText -- ValuePack Access Card -- for ... eText -- Valuepack Access Card (14th Edition)
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How To Solve Any Resistors In Series and Parallel Combination Circuit Problems in Physics; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=eFlJy0cPbsY;License: Standard YouTube License, CC-BY