Determine the required length of a copper wire having a cross-sectional area of 0.01 mm ^2 to produce a resistance of 1 k . The resistivity of copper is given as 1.7 10⁻⁸ m .

Step-by-step solution

The resistance of a wire is given by the formula: R = l A Rearranging for length l : l = R A Given values are: R = 1 k = 10^3 A = 0.01 mm ^2 = 0.01 10⁻⁶ m ^2 = 10⁻⁸ m ^2 = 1.7 10⁻⁸ m Substituting the values into the formula: l = 10^3 10⁻⁸ 1.7 10⁻⁸ l = 1000 1.7 m l 588.2 m l 0.588 km 0.59 km