A wire has total resistance R and is cut into 8 equal lengths. Make two groups of 4 pieces; connect the four pieces in each group in parallel, then connect the two parallel groups in series. Find the total resistance.
Options

Question

A wire has total resistance R and is cut into 8 equal lengths. Make two groups of 4 pieces; connect the four pieces in each group in parallel, then connect the two parallel groups in series. Find the total resistance.

Options

G1 Physics · Accepted Answer

Step 1: With uniform wire cross-section, resistance is proportional to length; each of 8 equal pieces has r = R/8. Step 2: Four identical resistors r in parallel give equivalent R₁ = r/4 = R/32. Step 3: The second group of four gives the same R₂ = R/32. Step 4: The two groups in series give Rₑᵩ = R₁ + R₂ = R/32 + R/32 = R/16. Final answer: R/16, Option C.