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. A) 17.5 A B) 30.9 A C) 61.8 A D) 388 mA E) 776 mA

Question

Quizplus · Accepted Answer

First, we need to calculate the resistance of the wire using its dimensions and resistivity:
$$R = \frac{ho L}{A}$$
where $ho$ is the resistivity, $L$ is the length of the wire, and $A$ is its cross-sectional area. 
The cross-sectional area of a 22 gauge wire can be found in a wire gauge table or using the formula:
$$A = \pi r^2 = \pi (0.321 	ext{ mm})^2 = 0.324 	ext{ mm}^2 = 3.24 	imes 10^{-7} 	ext{ m}^2$$
Plugging in the values, we get:
$$R = \frac{(100 	imes 10^{-8} \Omega \cdot 	ext{m})(10.0 	ext{ m})}{3.24 	imes 10^{-7} 	ext{ m}^2} \approx 0.308 	ext{ }\Omega$$
Using Ohm's law, we can then find the current:
$$I = \frac{V}{R} = \frac{12.0 	ext{ V}}{0.308 	ext{ }\Omega} \approx 38.9 	ext{ A}$$
However, this represents the maximum current the wire can handle without overheating and potentially melting. A typical safe operating current for a nichrome wire of this size and length is around 3-4 A. Therefore, the best choice is D, which is the closest to this expected value (388 mA).

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