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))`.

Answer

A, B, C, D

Explanation

After a long time capacitor will be fully charged, hence no current will flow through capacitor and all the current will flow from inductor. Since current is D.C., resistance of L is zero.
`:. R_(eq)=((R)/(2)+R)xx1/2+(r_1)+(r_2)=(3R)/(4)+(r_1)+(r_2)`

`I=(epsilon+epsilon)/(R_(eq)) implies I=(2 epsilon)=(R_(eq))=(2epsilon)/((3R//4)+(r_1)+(r_2))`
Potential drop across A is
`epsilon-I(r_1)=0implies epsilon=(2epsilon)/((3R//4)+(r_1)+(r_2))(r_1)`
(r_1)=(r_2)+3R//4 or R=(4/3)(r_(1)-r_(20)`.