Also, I've seen dwight mention Jacobi's law (also known as Maximum Power Transfer Theorem) in a couple places. Since this1 as well as Ohms law2 are probably the two most misunderstood equations I've seen, I feel it necessary to set the record straight.
MPT Theorem applies only to passive impedances, and it is not guaranteed that maximum power will occur at half-voltage when the circuit has semiconductors with a non-linear IV characteristic or an actively controlled circuit like this.
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I've seen people in school think that the Termination Impedance = Line Impedance rule for transmission lines is a consequence of this law, rather than a separate, unrelated consequence of the physics of signal propagation. I've also seen others think that you should adjust the source impedance to match the load also. This is wrong. When you are picking source impedances, lower is always better.
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Specifically, the common misunderstanding is trying to apply it to a transformer. "How does increasing voltage decrease the current? That's not how Ohm's law works!"