Question

which of the following would have the same resistance as a copper wire that is 4 m long and has a cross - sectional area of 0.066 cm²?
a. a copper wire that is 2 m long and cross - sectional area of 0.132 cm²
b. a copper wire that is 8 m long and cross - sectional area of 0.132 cm²
c. a copper wire that is 6 m long and cross - sectional area of 0.022 cm²
d. a copper wire that is 1 m long and cross - sectional area of 0.022 cm²

Explanation:

Step1: Recall the resistance formula

The resistance formula is \(R =
ho\frac{l}{A}\), where \(
ho\) is the resistivity (same for copper wires), \(l\) is the length, and \(A\) is the cross - sectional area. For the original wire, \(R_1=
ho\frac{l_1}{A_1}\), with \(l_1 = 4m\) and \(A_1=0.066cm^{2}\).

Step2: Calculate the ratio for each option

• Option A: \(R_A=

ho\frac{l_A}{A_A}=
ho\frac{2}{0.132}=
ho\frac{4}{0.264}
eq
ho\frac{4}{0.066}\)

• Option B: \(R_B=

ho\frac{l_B}{A_B}=
ho\frac{8}{0.132}=
ho\frac{4}{0.066}\)

• Option C: \(R_C=

ho\frac{l_C}{A_C}=
ho\frac{6}{0.022}=
ho\frac{4}{0.0147}
eq
ho\frac{4}{0.066}\)

• Option D: \(R_D=

ho\frac{l_D}{A_D}=
ho\frac{1}{0.022}=
ho\frac{4}{0.088}
eq
ho\frac{4}{0.066}\)

Answer:

B. A copper wire that is 8 m long and cross - sectional area of \(0.132cm^{2}\)