Question

A wire of resistance $R$ and length $L$ is cut into 5 equal parts. If these parts are joined in parallel, then the resultant resistance will be:

• A. 5 R
• B. 25 R
• C. $\frac{R}{25}$
• D. $\frac{R}{5}$

Answer 1

Answer: (C)

$\frac{R}{25}$

Answer 2

Each part will have resistance:

$R' = \frac{R}{5}$

When connected in parallel, the total resistance $R_{eq}$ is:

$\frac{1}{R_{eq}} = 5 \times \frac{1}{R'} = 5 \times \frac{1}{R/5} = 5 \times \frac{5}{R} = \frac{1}{R/25}$

Thus,

$R_{eq} = \frac{R}{25}$