Two infinitely long solenoids (shown in cross-section) pass through a circuit as shown in the figure. The magnitude of `vec(B)` inside each is the same and is increasesing at the rate of `I00T//sec` . What is the current in each resistor ?

Explanation

Flux in left loop `phi_(1)Bpir_(1)^(2)`
`e_(1)=(dphi_(1))/(dt)=(dB)/(dt)pir_(1)^(2)(100)pi(0.1)^(2)=piV`
Flux is increasing, current will be anticlockwise
Flux in right loop
`phi_(2)=Bpir_(2)^(2)`
`e_(2)=(dphi_(2))/(dt)=(dB)/(dt)pir_(2)^(2)(100)pi(0.15)^(2)=2.25piV`
Flux is increasing, current will be clockwise
`e=((e_1)/(r_1)+(e_2)/(r_2))/((1)/(r_1)+(1)/(r_2))=((pi)/(6)+(2.25pi)/(5))/((1)/(6)+(1)/(5))=((18.5pi)/(30))/((11)/(30))`
`=(18.5pi)/(11)V`
`i=(e)/(3+r)=(18.5pi//11)/(3+(30)/(11))=(18.5pi)/(63)=0.92A`
`p.d` . across `3Omega=ixx3`
`=0.92xx3=2.76V`
`e_(1)-i_(1)r_(1)=2.76`
`pi-i_(1)xx6=2.76` implies `i_(1)=0.06A`
`e_(2)-i_(2)r_(2)=2.76`
`2.25pi-i_(2)xx5=2.76` implies `i_(2)=0.86A`