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

The resistance of wire is R. This wire is cut into five equal pieces, so the resistance of each piece of the wire will be `(R)/(5)`. Now, five pieces of wire, each piece of wire having resistance of `(R)/(5)` are connected in parallel to give the equivalent resistance R'. So,
`(1)/(R') = (1)/(R_(1))+(1)/(R_(2))+(1)/(R_(3))+(1)/(R_(4))+(1)/(R_(5))`
`(1)/(R')=(5)/(R)+(5)/(R)+(5)/(R)+(5)/(R)+(5)/(R)`
`(1)/(R') = (5+5+5+5+5)/(R)`
`(1)/(R') = (25)/(R)`
To obtain the ratio `(R)/(R')` we multiply both sides of the above equation by R. This will give us:
`(R)/(R') = (25 xx R)/(R)`
or `(R)/(R') = 25`
Thus, the correct answer is : (d) 25.