Q: The Inductors of 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 voltage 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 reach their steady state values is …..

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$\displaystyle U = \frac{1}{2}L_1 I_1^2 + \frac{1}{2}L_2 I_2^2 + M I_1 I_2 $

$\displaystyle U = \frac{1}{2}(10\times 10^{-3})1^2 + \frac{1}{2}(20\times 10^{-3})2^2 + (5 \times 10^{-3})\times 1 \times 2 $

= 55