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 = 4.30 A. The radius of cross-section A1 is r1 = 0.420 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?

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

Assume A2 = 3A1

(d) Specify the radius at (A2).

(e) Specify the current at A2.

(f) Specify the current density at A2.

Explanation / Answer

a. current density is calculated as follows:

    J = I/A1 = 4.3 / (0.420/100)2 = 77631.9 A/m2

b. the current remains the same at both points.

c.

current density is inversely proportional to area.

that is J proportional A (or = r^2). if, the radius is increased,

the current density is decreased. so, the value of current density is smaller at A2

than A1.

d. if A2 = 3A1, the radius at A2 is,

           r22 = 3(0.420/100)2

              r2 = 7.2746x10-3 m

e). current at A2 = current at A1 = 4.30 A .

f) current density = I/A2 = 4.30/(7.2746x10-3 )2 = 25877.4 A/m2

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