A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these…

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 together in parallel. Then these two sets are added in series. The net effective resistance of the combination is:

1. A. R/64
2. B. R/32
3. C. R/16 (Correct answer)
4. D. R/8

Correct Answer

Option C — R/16

Detailed Solution & Explanation

The correct answer is $\dfrac{R}{16}$.

Key Points

• Each of the 8 pieces has resistance $\dfrac{R}{8}$.
• Four pieces in parallel: $\dfrac{R/8}{4}=\dfrac{R}{32}$ (one set); the second set is likewise $\dfrac{R}{32}$.
• The two sets in series: $R_{eq}=\dfrac{R}{32}+\dfrac{R}{32}=\dfrac{R}{16}$.