Specific resistance of material of one wire is `rho`. Its volume is 3 `m^(3)` and its resistance is `3 Omega`. Its length would be ..... .

Options

A. `sqrt((1)/(rho)) `
B. `(3)/(sqrt(rho))`
C. `(sqrt(3))/(rho)`
D. `(rho)/(sqrt(3))`

Answer

B

Explanation

`(3)/(sqrt(rho))`
volume V = area A `xx ` length l
`therefore A = (V)/(l) = (3)/(l) " "` ... (1)
`rArr R = (rho l)/(A) = (rho l)/((3)/(l)) " " [ because " from equation (1)" ] `
`therefore 3 = (rho l^(2))/(3) " " [ because R = 3 Omega ] `
`therefore l^(2) = (9)/(rho)`
`therefore l = (3)/(sqrt(rho))`