Parallel combination determines effective area

Steps:

• Identify components: one thick strand (area 4A) and eight thin strands (area A each), all length L, in parallel.
• Compute effective cross-sectional area: 4A + 8 × A = 12A.
• Total resistance R = ρ L / (12A), using the formula for resistance of parallel conductors.
• Solve for resistivity: ρ = 12AR / L, or equivalently \frac{12RL}{A} after rearranging terms to match option form.

Why D is correct:

• Effective area of 12A from parallel strands gives factor of 12 in ρ = R × (effective area)/L, matching the formula for resistivity.

Why the others are wrong:

• A: Factor 3 undercounts strands (e.g., ignores most thin strands).
• B: Factor 1 assumes single thin strand only.
• C: Factor 4 assumes thick strand alone.

Final answer: D