A piece of wire of resistance R is cut i...

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

Text Solution

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Resistance of this wire, `R= rho(l)/(A)`
Resistance of a piece of length `(l)/(5)= rho (l)/(5A)= (R)/(5)`
The equivalent resistance of the 5 wires in parallel is R.. Then
`(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)`
`(1)/(R.)= (25)/(R)`
`(R)/(R.)= 25`
Hence, the correct answer is (d).

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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 :

`1//25`

`1//5`

`5`

`25`

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, the ratio R/R is

`(1)/(25)`

`(1)/(5)`

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 .