Correct Answer - B
At the centre of coil-1
`B_(1)=(mu_(0))/(4pi)xx(2pii_(i))/(r_(1))" "......(i)`
At the centre of coil-2
`B_(2)=(mu_(0))/(4pi)xx(2pii_(2))/(r_(2))" ".......(ii)`
But `B_(1)=B_(2)`
`:.(mu_(0))/(4pi)(2pii_(1))/(r_(1))=(mu_(0))/(4pi)(2pii_(2))/(r_(2))or(i_(1))/(r_(1))=(i_(2))/(r_(2))`
As `r_(1)=2r_(2)`
`:.(i_(1))/(2r_(2))=(i_(2))/(r_(2))ori_(1)=2i_(2)`
Now, ratio of potential differences,
`(V_(2))/V_(1)=(i_(2)xxr_(2))/(i_(1)xxr_(2))=(i_(2)xxr_(2))/(2i_(2)xx2r_(2))=(1)/(4)`
`implies(V_(1))/(V_(2))=(4)/(1)`