In a circuit in which a sinusoidal voltage source drives its internal impedance in series with a load impedance, it is known that maximum power transfer to the load occurs when the source and load impedances form a complex conjugate pair. Suppose the source (with its internal impedance) now drives a complex load of impedance ZL = RL + jXL that has been moved to the end of a lossless transmission line of length ℓ having characteristic impedance Z0. If the source impedance is Zg = Rg + jXg, write an equation that can be solved for the required line length, ℓ, such that the displaced load will receive the maximum power.
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