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= 5.20 A. The radius of cross-section A, is r = 0.590 cm. .0 . > (c) Is the current density at A2 largersmaller, or the s O The current density is larger. (a) What is the magnitude of the current density across Af? o The current density is smaller 45721 The current density is the same. What is the definition of the current density? A/m The radius r2 at A2 is larger than the radius r at A1. Assume A2 - 5A1. (b) Is the current at A2 larger, smalleror the same? (d) Specify the radius at A2. The current is larger 1.180 O The current is smaller How is the area of a circle related to its radius? mm a The current is the same (e) Specify the current at A2. 5.20 VA (c) Is the current density at A2 largersmaller, or the same? (W) Specify the current density at A2. O The current density is larger. Am O The current density is smaller. O The current density is the same.

Explanation / Answer

a) current density is J1 = I/(pi*r1^2) = 5.2/(3.142*(0.59*10^-2)^2) = 47544 A/m^2

given that A2 =5A1

d) pi*r2^2 = 5*pi*r1^2

r2^2 = 5*r1^2

r2 = sqrt(5)*r1

r2 = sqrt(5)(0.59*10^-2) = 0.0132 m = 1.32 cm = 13.2 mm

e) current at A2 = current at A1 = 5.2 A

f) cuirrent density is j = I/A2 = 5.2/(pi*r2^2) = 5.2/(3.142*0.0132^2) = 9498 A/m^2 = 9500 A/m^2( approx)

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