Question

A spool of iron wire 230 m long and with a diameter of 0.320 mm is at 20.0°C. For iron, the resistivity is 10.0 ✕ 10 ⁻⁸ Ω · m and the temperature coefficient of resistivity is 5.00 ✕ 10−3 (°C) ⁻¹.

Answer 1

The resistance of a wire increases by a factor of 4 when it is stretched to four times its original length.

Step-by-step explanation:

To find the factor by which the resistance of a wire increases when it is stretched, we need to use the equation R = ρL/A, where R is the resistance, ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area. Since the wire is stretched to four times its original length, its new length is 4L. The cross-sectional area will remain the same. Therefore, the new resistance (R') can be calculated as R' = ρ(4L)/A = 4(ρL/A) = 4R. So, the resistance of the wire increases by a factor of 4 when it is stretched to four times its original length.