In given LR circuit the switch S is closed at time `t=0` then

Options

A. The ratio of induced emfs in the inductors of inductance L and 2L will be constant
B. The ratio of induced emfs in the inductor of inductance L and 2L will be time varying
C. the potential difference `V_(A)-V_(B)` increases with time
D. The potential difference `V_(A)-V_(B)` will be constant

Answer

A, D

Explanation

`i_(1)=(epsi)/(R)(1-e^((-Rt)/(L)))`
`i_(2)=(epsi)/(2R)(1-e^((-R)/(L)t))`
`(epsi_("ind")_(L)=L(di_(i))/(dt)=epsie^(-(Rt)/(L))`
`(epsi_("ind")_(2L)=2L(di_(2))/(dt)=epsi(e^(-(Rt)/(L)t)`
`((epsi_("ind"))_(L))/((epsi_("ind"))2L)=1`
`V_(A)-V_(B)=0=` cosntant