Two wires `A` and `B` of same material and same mass have radius `2r` and `r`. If resistance of wire `A` is `34 Omega`, then resistance of `B` will be

Options

A. 544 `Omega`
B. 372 `Omega`
C. 68 `Omega`
D. 17 `Omega`

Answer

A

Explanation

`R=rho l/A`
and mass m = volume (V) x density (d) = (Al)d
Since wires have same material so `rho` and d is same for both.
Also they have same mass `rArr` Al = constant
`rArr l prop 1/A`
`rArr R_1/R_2 = l_1/l_2 xxA_2/A_1 =(A_2/A_1)^2=(r_2/r_1)^4`
`rArr 34/R^2 = (r/"2r")^4 R_2= 544 Omega`