How long is a wire made from 50 cm³ of copper if its resistance is 8 ohms? The resistivity of copper is 1.7 × 10^-5 Ω·m. A) 4.9 m B) 1.7 × 10² m C) 1.6 × 10² m D) 1.5 × 10³ m E) 23.5 m

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The resistance of a wire is given by the formula:R = ρ * L / Awhere:R is the resistance in ohmsρ is the resistivity of the material in ohm-metersL is the length of the wire in metersA is the cross-sectional area of the wire in square metersWe are given that the resistance of the wire is 8 ohms, the resistivity of copper is 1.7 × 10^-5 ohm-meters, and the volume of copper is 50 cm^3. We need to find the length of the wire.First, we need to convert the volume of copper from cubic centimeters to cubic meters:50 cm^3 = 50 * (10^-2 m)^3 = 5 * 10^-5 m^3Next, we need to find the cross-sectional area of the wire. We can do this by dividing the volume of copper by the length of the wire:A = V / LWe don't know the length of the wire yet, but we can solve for it by rearranging the formula:L = V / ASubstituting the values we know into the formula, we get:L = 5 * 10^-5 m^3 / ANow we can substitute the formula for the cross-sectional area into the formula for the resistance:R = ρ * L / AR = ρ * (5 * 10^-5 m^3 / A) / AR = ρ * 5 * 10^-5 m^3 / A^2Solving for A, we get:A = √(ρ * 5 * 10^-5 m^3 / R)A = √(1.7 × 10^-5 ohm-meters * 5 * 10^-5 m^3 / 8 ohms)A = 2.5 × 10^-6 m^2Now we can substitute the value of the cross-sectional area back into the formula for the length of the wire:L = V / AL = 5 * 10^-5 m^3 / 2.5 × 10^-6 m^2L = 4.9 mTherefore, the length of the wire is 4.9 meters.

How Long Is a Wire Made from 50 Cm3 of Copper

How Long Is a Wire Made from 50 Cm³ of Copper