A wire with a length of 150 m and a radius of 0.15 mm carries a current with a uniform currentdensity of 2.8 × 107 A/m2 . The current is:A. 0.63 A2B. 2.0 AC. 5.9 A2D. 296 AE. 400 A2
Question
A wire with a length of 150 m and a radius of 0.15 mm carries a current with a uniform currentdensity of 2.8 × 107 A/m2 . The current is:A. 0.63 A2B. 2.0 AC. 5.9 A2D. 296 AE. 400 A2
Solution
The current in a wire can be calculated using the formula:
I = J * A
where: I is the current, J is the current density, and A is the cross-sectional area of the wire.
The cross-sectional area of a wire can be calculated using the formula for the area of a circle:
A = πr²
where: A is the area, and r is the radius of the wire.
Given: J = 2.8 × 10^7 A/m² r = 0.15 mm = 0.15 * 10^-3 m (since 1 mm = 10^-3 m)
We can first calculate the cross-sectional area of the wire:
A = π * (0.15 * 10^-3 m)² = 0.0000707 m²
Then, we can calculate the current:
I = J * A = 2.8 × 10^7 A/m² * 0.0000707 m² = 1.98 A
So, the current in the wire is approximately 2.0 A. Therefore, the correct answer is B. 2.0 A.
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