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The positive lamp power comes from extra work by the primary current source. The secondary electric current creates a changing magnetic flux through the primary, so maintaining the same prescribed primary electric current requires an additional terminal voltage. With the preceding winding convention,Using phasors, ${\tilde{I}}_s=-i\omega M{\tilde{I}}_p/(R+i\omega L_s)$, hence the primary sees the complex impedanceIt follows directly thatThis is the reflected impedance of the secondary load. The self-inductance and mutual inductance terms exchange stored magnetic energy, while the lamp dissipates it. Multiplying the two coupled equations from Kirchhoff's voltage law by their respective electric currents also gives the instantaneous conservation of energy identityThe derivative averages to zero in periodic steady state. A fixed primary current source supplies the required extra voltage; a fixed voltage source would generally change its primary electric current when the lamp is connected.

The reflected impedance is the contribution of a coupled secondary load to a primary winding's input impedance. For two ideal mutually coupled inductors, choose winding signs so that positive electric currents reinforce their magnetic fluxes. If the secondary loop has complex impedance $Z_s$, its Kirchhoff's voltage law gives ${\tilde{I}}_s=-i\omega M{\tilde{I}}_p/Z_s$. Substitution in ${\tilde{V}}_p=i\omega L_p{\tilde{I}}_p+i\omega M{\tilde{I}}_s$ gives $Z_{\mathrm{in}}=i\omega L_p+{\omega }^2{M}^2/Z_s$. For $Z_s=R+i\omega L_s$, the reflected real part is ${\omega }^2{M}^{2}R/[R^2+(\omega L_s{)}^2]$, and primary mean input power equals secondary mean Joule heating.