When a potential difference is applied across a piece of wire made of metal A,there is a $5.0 - m A$ current through it.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 be through the metal-B wire? The lengths of both wires are the same,and the voltage across their ends remains unchanged.The resistivity of metal A is 1.68 × 10^-8 Ω ∙ m,and the resistivity of metal B is 1.59 × 10^-8 Ω ∙ m. A)21 mA B)19 mA C)11 mA D)5.3 mA

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Quizplus · Accepted Answer

The current through a wire is given by Ohm's law:$$I = \frac{V}{R}$$where I is the current, V is the voltage, and R is the resistance. The resistance of a wire is given by:$$R = \rho \frac{L}{A}$$where $\rho$ is the resistivity of the wire, L is the length of the wire, and A is the cross-sectional area of the wire.In this problem, the voltage and length of the wires are the same, so the only thing that will affect the current is the resistivity and cross-sectional area of the wires. The resistivity of metal B is slightly less than the resistivity of metal A, and the cross-sectional area of metal B is twice the cross-sectional area of metal A. Therefore, the resistance of metal B will be less than the resistance of metal A, and the current through metal B will be greater than the current through metal A.The current through metal B will be:$$I = \frac{V}{R} = \frac{V}{\rho \frac{L}{A}} = \frac{V}{\rho \frac{L}{2A}} = 2\frac{V}{\rho \frac{L}{A}} = 2I$$where I is the current through metal A.Therefore, the current through metal B will be twice the current through metal A, which is 10 mA.

When a Potential Difference Is Applied Across a Piece of Wire