Calculate the current through a 10.0-m long 22-gauge nichrome wire with a radius of 0.321 mm if it is connected across a 12.0-V battery.The resistivity of the nichrome is 1.00 × 10^-6 Ω ∙ m. A)30.9 A B)61.8 A C)0.388 A D)0.776 A

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First, calculate the resistance of the wire using the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area. The area $A$ of the wire can be found using the formula for the area of a circle, $A = \pi r^2$, where $r$ is the radius of the wire. Given that the radius $r = 0.321 \times 10^{-3}$ m (since 1 mm = $10^{-3}$ m), the area $A = \pi (0.321 \times 10^{-3})^2$ m$^2$.$$A = \pi (0.321 \times 10^{-3})^2 = 3.23 \times 10^{-7} \text{ m}^2$$Given that the resistivity $\rho = 1.00 \times 10^{-6} \Omega \cdot m$ and the length $L = 10.0$ m, the resistance $R$ can be calculated as:$$R = 1.00 \times 10^{-6} \Omega \cdot m \times \frac{10.0 m}{3.23 \times 10^{-7} m^2} = 31.0 \Omega$$Using Ohm's law $V = IR$, where $V$ is the voltage and $I$ is the current, we can solve for $I$:$$I = \frac{V}{R} = \frac{12.0 V}{31.0 \Omega} = 0.387 \text{ A}$$Rounding to three significant figures, the current $I$ is approximately 0.388 A.

Calculate the Current Through a 10