A thick wire is stretched so that its length become two times. Assuming that there is no change in its density, then what is the ratio of change in resistance of wire to in initial resistance of wire

Options

A. `2:1`
B. `4:1`
C. `3:1`
D. `1:4`

Answer

C

Explanation

Resistance of the wire is given by
`R = rho (l)/(A) = rho (l^(2))/((Al))=(rho l^(2))/(V) " " (because Al = V)`
So, `R prop l^(2) " "` (If density remains same)
or `(R')/(R )=((2l)^(2))/((l)^(2))=4`
`rArr " " R'=4R`
Hence, change in resistance `= 4R - R = 3R`
Therefore, `("change in resistance")/("original resistance")=(3R)/(R )= 3 :1`