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When the forward voltage across the varistor reaches the threshold limit, it becomes an excellent conductor.
in this circuit the Transistor is switching a coil on and off, which makes a whump of back emf. if this Transistor has a max forward voltage collector to emitter of 40V, it would not survive.
The Metal Oxide Varistor contains a slushy mix of metal particles set in ceramic. At low voltages, not much can conduct between the insulated particles, so the current across the device is very low. But at high voltages, the insulation is insufficient, and current can flow quite nicely.
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