Question

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

Answer 1

Correct Answer - A
(a) `R = rho (1)/(A)` and mass `m` = volume `(V) xx` density `(d) = (A l) d`
Since wires have same material so `rho` and `d` is same for both.
Aslo they have same `implies Al =` consatnt
`implies prop (1)/(A)`
`implies (R_(1))/(R_(2)) = (l_(1))/(l_(2)) xx (A_(2))/(A_(1)) = ((A_(2))/(A_(1)))^(2) = ((r_(2))/(R_(1)))^(4)`
`implies (34)/(R_(2)) = ((r)/(2r))^(4) = R_(2) = 544 Omega`