The inductors of the two LR circuits are placed next to each other , as shown in the figure . The values of the self-inductance of the inductors , resistances , mutual - inductance and applied voltages are specified in the given circuit . After both the switches are closed simultaneously , the total work done by the batteries against the induced EMF in the inductors by the time the currents react their steady state values is __________m]

Answer

55 or 35

Explanation

`epsi_(1) = L_(1) ""(di_(1))/(dt) + M ""(di_(2))/(dt)`
` d W_(1) = epsi_(1) i_(1) dt`
`= L_(1) (di_(1)) i_(1) + M(di_(2)) i_(1)`
`dW_(2) = L_(2) (di_(2))i_(2) + M(di_(1))i_(2)`
`dW_(1) + dW_(2) = L_1 i_(1) (di_(1)) + L_(2) i_(2) (di_(2)) + Md (i_(1) . i_(2))`
`W = (1)/(2) L_(1) i_(2)^(2) + (1)/(2) L_(2) i_(1)^(2) + M_(1) i_(2)`
`= 55 mJ`