Can it be proved using the concept of induced emf that power supplied at the primary coil equals power consumed at the secondary. I tried following. Let primary coil be called 1 and secondary be called 2. Assuming there is no resistance in the primary and a purely resistive load on the secondary. Kirchoff's eqns for the two coils are:
Multiplying 1st eqn by $I_1$ and 2nd by $I_2$ and adding the two eqns one gets$V_1I_1-L_1I_1dI_1/dt+MI_1dI_2/dt+MI_2dI_1/dt-L_2I_2dI_2/dt-I_2^2R=0$
$L_1I_1dI_1/dt$ represents rate of change of energy of magnetic field due to coil 1 $L_2I_2dI_2/dt$ represents rate of change of energy of magnetic field due to coil 2 $I_2^2R$ represents power dissipated in the resistor. The sum of these three terms should equal $V_1I_1$. but I am getting the extra term of $MI_1dI_2/dt+MI_2dI_1/dt$. Can anybody help me out.