A piece of wire of resistance 10 ohm is drawn out so that its length is increased to three times its original length. Calculate the new resistance.

Explanation

Given: Resistance of wire , `R = 10 Omega`
Length is increased to thrice = 3L
To find : New resistance = ?
Resistance("R") = `("resistivity"(rho) xx "length"(L))/("area"(A))`
`R= (rho L)/(A) implies 10 = (rho L)/(A)`
When length is increased by three times (3L) the area of cross section is reduced by three times `((A)/(3))`.
New length = 3L
New area = `(A)/(3)`
`therefore` resistance R = `(rho. 3L)/((A)/(3)) = 9 ((rhoL)/(A))`
`R = 9.R implies 9 xx10 = 90 Omega`
`R = 90 Omega`