Varistors have a capacitance and could be called capacitors; likewise, all capacitors have a breakdown voltage. The difference is that in most capacitors, breakdown is highly undesirable, and usually results in the destruction of the device. Varistors on the other hand are designed to repeatedly withstand breakdown.
Important parameters for varistors are response time (how long it takes the varistor to break down), maximum current and a well-defined breakdown voltage. Capacitance is undesirable since high capacitance allows high frequency signals to leak away.
See also transient voltage suppression diode[?]
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