Ohm's law: 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^-8 Ω ∙ m.

Question

Quizplus · Accepted Answer

First, we must use the formula for the resistance of a wire:
R = ρL/A
where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area. We can find A using the formula for the area of a circle:
A = πr^2
where r is radius. Substituting in the values given, we get:
A = π(0.321x10^-3 m)^2 = 8.121x10^-7 m^2
Now we can solve for resistance:
R = (100x10^-8 Ω∙m)(10.0 m) / 8.121x10^-7 m^2 = 1.229 Ω
Finally, we use Ohm's law to find the current:
I = V/R = 12.0 V / 1.229 Ω = 9.766 A = 9.77 A (rounded to three significant figures) or 388 mA (rounded to two significant figures). The closest answer choice is D, so that is the correct choice.

Ohm's Law: Calculate the Current Through a 10