Two wires A and B are made of the same material and have the same length but different cross-sectional areas. If the resistance of wire A is 16 times the resistance of wire B, the ratio of the cross-sectional area of wire A to that of wire B is:

Explanation

To find the ratio of the cross-sectional area of wire A to that of wire B, we can use the formula for the resistance of a wire: R=χL/A where: R is the resistance, χ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire. Since both wires A and B are made of the same material and have the same length, we can write: R_A = χ L / A_A and R_B = χ L / A_B Given that the resistance of wire A is 16 times the resistance of wire B, we have: R_A = 16 R_B Substitute the expressions for R_A and R_B : χ L / A_A = 16 · χ L / A_B Since χ and L are the same on both sides, they cancel out: 1 / A_A = 16 · 1 / A_B Rearrange to find the ratio of A_A to A_B : A_B = 16 A_A So, the ratio of the cross-sectional area of wire A to that of wire B is: A_A / A_B = 1 / 16 Answer: The ratio of the cross-sectional area of wire A to that of wire B is 1:16.