Ohm's Law and Material Identification Challenge
What is the relationship between the length of a wire, its cross-sectional area, and its electrical resistance?
Based on the given data, how can we determine the material X fused to the aluminum wire?
Understanding Ohm's Law
Ohm's Law states that the electrical resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. The formula is R = ρL/A, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area. To calculate the material X fused to the aluminum wire, we can use this formula.
Resistivity (ρ) can be determined by rearranging the formula as follows: ρ = R(A/L). By substituting the given values of resistance, length, and cross-sectional area, we can solve for ρ.
Calculating Material X
Given that the resistance (R) is 7.0 mΩ, the length of the aluminum wire is 8.21 cm, and the length of wire X is 6.63 cm, with a cross-sectional area of 3.25 mm2, we can calculate the resistivity (ρ) using the formula provided.
Substitute the values into the formula ρ = (7.0 mΩ)(3.25 mm2)/((8.21 cm) + (6.63 cm)) and simplify the calculation to determine the resistivity. Once we have the resistivity value, we can compare it to known resistivity values of different materials to identify the material X fused to the aluminum wire.
By understanding Ohm's Law and applying it in this context, we can solve the challenge of determining the material X based on electrical resistance, length, and cross-sectional area.