Question

A wire with a length of 150 m and a radius of 0.15 mm carries a current with a uniform current density of 2.8 × 107 a/m 2 . the current is:

a. 0.63 a2
b. 2.0 a
c. 5.9 a2
d. 296 a
e. 400 a2

Answer 1

The current flowing through the wire is found by multiplying the given current density by the cross-sectional area of the cylindrical wire. After calculating the area using the radius, the current is determined to be approximately 19.74 amperes.

Step-by-step explanation:

The question asks for the calculation of the current that flows through a cylindrical wire with a given length, radius, and uniform current density. To find the current (I), we use the formula I = J × A, where J is the current density and A is the cross-sectional area of the wire. The cross-sectional area (A) of a cylindrical wire is given by A = πr², where r is the radius of the wire. Knowing the current density (J) and the radius (r), we can calculate the current (I).

Given:

J = 2.8 × 10·· a/m²

r = 0.15 mm = 0.15 × 10²³ m

A = π × (0.15 × 10²³)² m²

Let's calculate the cross-sectional area:

A = π × (0.15 × 10²³)² = π × 2.25 × 10²¶

Now, calculate the current:

I = J × A = 2.8 × 10· a/m² × π × 2.25 × 10²¶ m² = 2.8 × π × 2.25 × 10 a = 19.74 a

The correct answer is the closest value to 19.74 a.