When a potential difference is applied across a piece of wire made of metal A, a $5.0 - \mathrm { mA }$ current flows. If the metal-A wire is replaced with a wire made of metal B having twice the diameter of the metal-A wire, how much current will flow through the metal-B wire? The lengths of both wires are the same, and the voltage difference remains unchanged. The resistivity of metal A is 1.68 × 10^-8 ? ? m, and the resistivity of metal B is 1.59 × 10^-8 ? ? m. A)21 mA B)19 mA C)11 mA D)5.3 mA

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The current through a wire is given by the equation:$$I = \frac{V}{R}$$where:* I is the current in amps* V is the voltage in volts* R is the resistance in ohmsThe resistance of a wire is given by the equation:$$R = \rho \frac{L}{A}$$where:* R is the resistance in ohms* ρ is the resistivity of the material in ohm-meters* L is the length of the wire in meters* A is the cross-sectional area of the wire in square metersIn this problem, the voltage and length of the wire are the same for both wires. Therefore, the only factor that will affect the current is the resistivity of the material and the cross-sectional area of the wire.The resistivity of metal B is slightly less than the resistivity of metal A. This means that metal B will have a lower resistance than metal A.The cross-sectional area of the metal-B wire is twice the cross-sectional area of the metal-A wire. This means that the metal-B wire will have a lower resistance than the metal-A wire.Therefore, the current through the metal-B wire will be greater than the current through the metal-A wire.The correct answer is A: 21 mA.

When a Potential Difference Is Applied Across a Piece of Wire