A wire of resistance R is cut into 8 equal pieces. From these pieces, two equivalent resistances are

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Question

A wire of resistance R is cut into 8 equal pieces. From these pieces, two equivalent resistances are made by adding four of these pieces together in parallel. Then these two sets are connected in series. The net effective resistance of the combination is:

Accepted Answer

Correct Answer: D — R/16Step-by-step Solution:Step 1: A wire of resistance R is cut into 8 equal pieces. Each piece has resistance R/8.Step 2: Four pieces in parallel form one set:Rset = (R/8)/4 = R/32(n identical resistors r in parallel: Req = r/n)Step 3: Two such sets in series:Reff = R/32 + R/32 = R/16Why Option A (R/8) is wrong: R/8 is the resistance of a single piece, not the final combination.Why Option B (R/64) is wrong: R/64 would result from placing all 8 pieces in parallel: (R/8)/8 = R/64. The problem specifies two groups of 4 in parallel, then those two groups in series.Why Option C (R/32) is wrong: R/32 is the resistance of each set of four parallel pieces. The question asks for the final resistance after two such sets are placed in series, giving R/32 + R/32 = R/16.Key Concepts from Current Electricity (NCERT Class 12, Chapter 3):When a wire of resistance R is cut into n equal parts, each part has resistance R/n (resistance ∝ length).For n identical resistors r in parallel: Req = r/n.For n identical resistors r in series: Req = nr.Important result: If a wire R is cut into n parts and all placed in parallel: Req = R/n². For n=8: R/64. Different from this problem.Resistivity ρ depends on material and temperature, not on dimensions. R = ρL/A.

A wire of resistance R is cut into 8 equal pieces. From these pieces, two equivalent resistances are made by adding four of these pieces together in parallel. Then these two sets are connected in series. The net effective resistance of the combination is:

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A wire of resistance R is cut into 8 equal pieces. From these pieces, two equivalent resistances are made by adding four of these pieces together in parallel. Then these two sets are connected in series. The net effective resistance of the combination is:

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