In the figure both cells A and B are of equal emf. Find R for which potential difference across battery A will be zero, long time after the switch is closed. Internal resistance of batteries A and B `(r_1) and (r_2)` respectively`(r_(1)gtr_(2))`.

Explanation

After a long time, inductor offers zero resistance and capacitor offers infinite resistance. After long time, circuit becomes
`R_(eq)=(3R)/(4)+r_(1)r_(2)`
`i=(2E)/((3R)/(4)+R_(1)+r_(2))`
P.d. across `A` , `V=E-ir (1)=0`
`E-(2Er_(1))/((3R)/(4)+r_(1)+r_(2))=0`
`(3R)/(4)+r_(2)+r_(1)`
`R=(4)/(3)(r_(1)-r_(2))`