Final answer:
In AC circuits, the maximum power transfer occurs when the load impedance equals the source impedance, generally at resonance in an RLC circuit, represented by Vs/R. For blackbody radiation, Wien's displacement law calculates the maximum power emission by the equation λmax = b / T.
Step-by-step explanation:
The equation representing the maximum power-transfer condition depends on the context of the circuit or system being described. In general, for AC circuits, maximum power transfer occurs when the impedance of the load is the complex conjugate of the internal impedance of the source. Specifically, in an RLC circuit at resonance, the condition is given by Vs/R when the reactance is minimum and the circuit behaves purely resistive (Z = R). However, for maximum power efficiency in transferring a signal, the load resistance should equal the source resistance to maximize power transfer, described by the equation Ptransmitted = (Vrms)2 / R, given by the root-mean-square (RMS) voltage divided by the resistance.
In the realm of blackbody radiation, the wavelength for maximum power emission can be calculated using Wien's displacement law, which relates emission to temperature by the equation λmax = b / T, where 'b' is a constant and 'T' is the temperature.