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For the operation of Jacob’s Ladder, a transformer generated arc of ionized
plasma strikes at the small gap at the bottom of the rods, which is the point of
lowest breakdown voltage. The heated plasma arc climbs up the diverging rods.
Even when the arc reaches a width on one inch or greater, it still provides an
easier path for the current to follow than the surrounding air. It works on the
principle that the ionized air in the arc is at a lower resistance than the air
around it and also the principle that hot air rises. Warm air pushes the arc up
the ladder. The arc’s climb is also affected by the expected ‘high leakage’
or reactance curve of the transformer. For as long as Paschen’s Law will
allow, the transformer arcs electricity across the bottom of the two wires.
Paschen's Law states that the breakdown voltage is constant as long as the
product of gas density and gap length is constant. Once the arc is established,
the current in the arc will increase to the transformers preset limit. The arcs
heat causes increasing resistance. We might expect that the transformer would
try to decrease the voltage as the current increases. However, just above the
arc there is a path that the transformer can easily maintain and which will
lower its current. The arc climbs until the gap between the rods becomes too
great. At the pinnacle of the two-rod course, the arc has reached the upper
limits of the transformer’s power. Arc current is very low at the crest of the
rods, and so the arc extinguishes only to re-ignite at the base of the two rods.
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