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That's a thought, and very easily done. Well, .. depends on the your
domestic supply. Nearly everywhere in the US 240V is supplied with
three wires -- discussed interminably on phys-l. the "middle"
wire is grounded physically and spiritually. its common as the
"return" for the other two which must be Pi phased otherwise one
wouldn't obtain 240 V. So the prob. is connecting one lamp to one
leg and tother tother.
I once wired a power fan out so adjacent sockets were alternate legs.
The sockets were spaced, so one could plug a plug in half of adjacent
sockets to obtain 240V. Or may be this was, more likely, a wall
socket.
Now the question dose this result in a constant illumination.
Ideally I think so. the EMFs are sin(120Hz*2PI*t) and cos