Two uniform wires A and B of same metal and have equal masses, the radius of wire A is twice that of wire B. The total resistance of A and B when connected in parallel is

Options

A. `4 Omega` when the resistance of wire `A` is `4.25 Omega`
B. `5 Omega` when the resistance of wire `A` is `4.25 Omega`
C. `4 Omega` when the resistance of wire `B` is `4.25 Omega`
D. `4 Omega` when the resistance of wire `B` is `4.25 Omega`

Answer

A

Explanation

(a) `(R_(A))/(R_(B)) = ((r_(B))/(r_(A)))^(4) implies (R_(A))/(R_(B)) = ((1)/(2))^(4) = (1)/(16) implies R_(B) = 16 R_(A)`
When `R_(A)` and `R_(B)` are connected in parallel the equivalent resistance `R_(eq) = (R_(A) R_(B))/((R_(A) + R_(B))) = (16)/(17) R_(A)`
If `R_(A) = 4.25 Omega` then `R_(eq) = 4 Omega`