Question

A wire is broken in four equal parts. A packet is formed by keeping the four wires together. The resistance of the packet in comparison to the resistance of the wire will be

• A. Equal
• B. One fourth
• C. One eight
• D. $\frac{1}{16}th$

Answer 1

Answer: (D)

$\frac{1}{16}th$

Answer 2

Let the resistance of the wire be R, and then we know that resistance is proportional to the length of the wire. So each of the four wires will have R/4 resistance and they are connected in parallel. So the effective resistance will be

$\frac{1}{R_{1}} = \left( \frac{4}{R} \right)4 \Rightarrow R_{1} = \frac{R}{16}$