This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values and convert units. The formula for resistance is R = (L)/(A), where R is resistance, is resistivity, L is length, and A is cross-sectional area. Given values: • Cross-sectional area, A = 0.60 mm^2. • Resistivity, = 7.2 × 10^-7 · m. (Note: The question states the unit as , but resistivity is typically measured in · m. We assume the intended unit is · m for dimensional consistency.) • Resistance, R = 3 . Convert the cross-sectional area from mm^2 to m^2: Since 1 mm = 10^-3 m, then 1 mm^2 = (10^-3 m)^2 = 10^-6 m^2. A = 0.60 mm^2 = 0.60 × 10^-6 m^2 Step 2: Rearrange the resistance formula to solve for length L. R = (L)/(A) Multiply both sides by A: R · A = · L Divide both sides by : L = (R · A)/() Step 3: Substitute the values and calculate the length L. L = (3 ) · (0.60 × 10^-6 m^2)7.2 × 10^-7 · m L = 1.8 × 10^-6 · m^27.2 × 10^-7 · m L = (1.8)/(7.2) × 10^-610^-7 m L = 0.25 × 10^(-6 - (-7)) m L = 0.25 × 10^1 m L = 2.5 m The length of the wire is 2.5 m.