In an electrical cable there is a single wire of radius `9 mm` of copper. Its resistance is `5 Omega`. The cable is replaced by 6 different insulated copper, wires the radius of each wire is `3 mm`. Now the total resistance of the cable will be

Options

A. `7.5 Omega`
B. `45 Omega`
C. `90 Omega`
D. `17 Omega`

Answer

A

Explanation

(a) Initially : Resistance of given cable
`R = rho (1)/(pi xx (9 xx 10^(-3))^(2))`
Finally, equivalent resistance of cable
`R' = rho (1)/(pi xx (3 xx 10^(-3))^(2))`
Hence, equivalent resistance of cable `R_(EQ) = (R')/(6) = (1)/(6) xx (rho (1)/(pi xx (3 xx 10^(-3))^(2)))`
On solving equaiton (i) and (ii) we get `R_(eq) = 7.5 Omega`