The figure below represents a section of a circular conductor of nonuniform diam

Question

The figure below represents a section of a circular conductor of nonuniform diameter carrying a current of I = 6.00 A. The radius of cross-section A1 is r1 = 0.390 cm.

(a) What is the magnitude of the current density across A1?
??? A/m2

The radius r2 at A2 is larger than the radius r1 at A1.

(b) Is the current at A2 larger, smaller, or the same?

The current is larger.

The current is smaller.    

The current is the same.

(c) Is the current density at A2 larger, smaller, or the same?

The current density is larger.

The current density is smaller.    

The current density is the same.

Assume A2 = 3A1.

(d) Specify the radius at A2.
??? mm

(e) Specify the current at A2.
??? A

(f) Specify the current density at A2.
??? A/m2

Explanation / Answer

(a)The formula for current density is

J = I/A = 6A / pi ( 0.390 * 10 ^-2 m)^2 = 125629.71 A/m^2

(b) the current does not depend on the radius so the current is same

(c)

since area A2 is larger and current density is inversily proportional to area. so, the current density is smaller

(d)

. A2 = 3A1

pi r22 = 3 pi (0.390 * 10 ^-2 m)2

r2 = 6.75* 10 ^-3 m = 6.75 mm

(e) current is independnet of are a so A2 = 6.0 A

(f) current density = I/A2 = 6.0 A /?(6.75 * 10 ^-3 m)2

                         =41907.58 A/m^2

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