Parallel resistors halve total resistance when equal

Steps:

• Resistance of a wire is R = ρL/A; for Y, same material means same ρ.
• Total resistance R/2 requires parallel connection, as series adds resistances and cannot reduce below R.
• For parallel: 1/Req = 1/R + 1/Ry; set Req = R/2, solve to get Ry = R.
• Ry = R requires Ly/Ay = L/A; option C has Ly = 4L, Ay = 4A, so Ly/Ay = L/A.

Why C is correct:

• Two equal resistances R in parallel give Req = R/2, per the parallel resistance formula 1/Req = 1/R1 + 1/R2.

Why the others are wrong:

• A: Assumes same A, so Ry = 0.25R; parallel Req = R/5 ≠ R/2.
• B: Ly/Ay = 8(L/A), so Ry = 8R; series Req = 9R ≠ R/2.
• D: Ly/Ay = L/A, so Ry = R; series Req = 2R ≠ R/2.

Final answer: C