An electric arc is a conducting (ionized) path through air (etc.) that carries a current. Normally the current is sufficiently high to heat the air strongly and to make the path incandescent. The clip shows a well developed arc at a substation. Convection distorts the ionized path upwards and lengthens the arc as time passes. An arc-welder strikes an arc by nearly touching the metal. He then draws the rod back from the work - maintaining a longer arc, sweeping gently from side to side to allow metal to melt and flow.
Lightning is an arc in air. Electron current flows repeatedly from the ground (or -ve cloud) along the same ionized path.
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