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. `5.5 Omega`
C. `6Omega`
D. `8Omega`

Answer

A

Explanation

Resistance of 9 mm cable is `5 Omega` .
Now,`R prop (1)/(A) :.R prop (1)/(r^(2))`
`:.` Resistance of 3 mm cable `= 9 xx 5 = 45 Omega`.
In second case, six wires are connected in parallel.
Thus, its resistance is given by,
`R_(p)=(45)/(6)=7.5Omega`.