a uniform resistance wire of length L and diameter d has a resistance R. another wire of same material has length, 4Lnand diameter 2d, the resistance will be

Explanation

We can find the new resistance of the second wire by considering the relationship between resistance, length, and cross-sectional area in a wire made of the same material.Resistance Formula:The resistance (R) of a wire is related to its resistivity (ρ), length (L), and cross-sectional area (A) by the formula:R = ρ * (L / A)Given information:First wire: Length (L1) = L, Diameter (d1) = d, Resistance (R1) = RSecond wire: Length (L2) = 4L, Diameter (d2) = 2dCalculate Cross-sectional area:The area is calculated as π * (diameter^2) / 4.First wire: A1 = π * (d1^2) / 4Second wire: A2 = π * (d2^2) / 4 = π * (2d)^2 / 4 = 4 * π * (d^2) / 4 (since d2 = 2d)Find the new resistance (R2):Substitute the values for the second wire into the formula:R2 = ρ * (L2 / A2)R2 = ρ * (4L / (4 * π * (d^2) / 4))Simplify the equation:Since the resistivity (ρ) remains the same for both wires, we can cancel out:R2 = ρ * (L / (π * (d^2) / 4))This equation is exactly the same as the formula for the first wire's resistance (R1) with L = L and A = A1.Therefore, the new resistance (R2) of the second wire is equal to the original resistance (R) of the first wire (b).