Ask the Captain: Are cabin electronics a drain on a plane's engine?
Answer: Modern airplanes have very large generators capable of supplying electrical power for all the modern devices. Each engine has at least one large generator the auxiliary power unit has a generator and most airline jets have a ram air turbine that can produce electricity. There are batteries, too. The engine generators do cause the engine to burn more fuel, but it is not a large amount.
A: I have seen active noise-canceling technology in business jets and turboprop aircraft, but not in airliners so far. The technology is available, but I suspect cost and weight are the reasons it has not been installed yet.