Calculate the current through a 10.0-m long 22 gauge (having radius 0.321 mm) nichrome wire if it is connected to a 12.0-V battery. The resistivity of nichrome is 100 × 10^-8Ω ∙ m. A) 17.5 A B) 30.9 A C) 61.8 A D) 388 mA E) 776 mA

Question

Quizplus · Accepted Answer

Using Ohm's Law, we can calculate the resistance of the wire:

R = (ρL)/A

where ρ is the resistivity of nichrome, L is the length of the wire, and A is the cross-sectional area of the wire.

A = πr² = π(0.321 x 10⁻³ m)² = 3.24 x 10⁻⁷ m²

R = (100 x 10⁻⁸ Ω∙m)(10.0 m)/(3.24 x 10⁻⁷ m²) = 3.09 Ω

Using Ohm's Law again, we can calculate the current through the wire:

I = V/R = (12.0 V)/(3.09 Ω) = 3.88 A = 388 mA (to 2 significant figures)

Therefore, the answer is D) 388 mA.

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