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A uniform conductor of resistance R is cut into 20 equal pieces. Half of them are joined in series and the remaining are connected in parallel. If the two combinations are joined in series, the effective resistance of all the pieces is ______.

Asked in RS Academy GUJCET booklet · Symmetric and complex networks

• (1) R
• (2) R/2
• (3) (101R)/(200)
• (4) (201R)/(200)

Step-by-step solution

Why the other options are wrong

• (1) This is all 20 pieces in series, which is just the original wire. Ten of the pieces are in parallel, and that group adds only R/(200), not R/2.
• (2) Keeps only the series group, 10×R/(20) = R/2, and drops the parallel group, which adds R/(200) in series with it.
• (4) Adds the full R for the series group instead of R/2: R + R/(200) = (201R)/(200). Ten pieces of R/(20) in series make only R/2.

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