Why Arc Lights and Vaccum Tubes does not obey ohm's law

These do not  obey  Ohm's  law because, the resistance they possess is not independent of the current through them,or the voltage across them, or the temperature at which they operate.

The easiest circuit that does not obey Ohm's law is a circuit that has a resistance that depends on temperature. For example, if you take a light bulb and draw a current-vs-voltage, you see that in the beginning (under low voltage) the graph is NOT a straight line, but under high voltage the graph is linear. This is because the resistance depends on temperature. the equation V=IR isn't consistent with the graph's shape.

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regards

Ramesh