Two circular coils made of same material having radii `20 cm & 30 cm` have turns `100 & 50` respectively. If they are connected `a )` in series `b)` in parallel `c)` separately across a source of ef find the ratio of magnetic inductions at the centre of circles in each case

Explanation

`a)` `B=(mu_(0)ni)/(2r),` coild are in series `impliesi` is same in both `B alpha(n)/(r),(B_(1))/(B_(2))=(100)/(50)xx(30)/(20)=3:1`
`b)` coilds are parallel `implies` potential difference is same `I alpha (1)/(R)` Where `R=(rho(npir))/(A),` Where `A` is area of cross section of wire which is same for both
`impliesR alphanr, ialpha(1)/(nr)` but `B_(0)=(mu_(0)ni)/(2r)impliesBalpha(n)/(r)xx(1)/(nr)impliesBalpha(1)/(r^(2))`
`:. (B_(1))/(B_(2))=((30)/(20))^(2)=(9)/(4)`
`c)` For the coils, potential difference is same
`ialpha(1)/(nr)` where`R=(rho(npir))/(A),` `Ralphanr`
`Ialpha(1)/(nr)implies B_(0)alpha(1)/(r^(2)), :. (B_(1))/(B_(2))=(9)/(4)`