A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R., then the ratio `R/(R.)` is ………………. .

Options

A. `1/25`
B. `1/5`
C. `5`
D. `25`

Answer

D

Explanation

Here, the resistance of a piece of wire is R. This piece of wire is cut into five equal parts, so the resistance of each part would be `R/5`.
Now, these five parts each having resistance of `R/5` are connected in parallel.
The equivalent resistance R. of this combination is given by
`1/(R.) =(1)/(R/5) + 1/(R/5) +1/(R/5) +1/(R/5) +1/(R/5)`
`:. 1/(R.) = 5/R + 5/R +5/R + 5/R +5/R = (25)/R`
`:.R/(R.) =2 5`