Current and Voltage Ratings for Multi-Conductor Connectors

I am currently looking at some multi-conductor connectors that will handle reasonably high currents (approximately 30 A at 24 v). When reading datasheets, I see that the connectors have both a maximum current and a maximum voltage. For example,

Voltage Rating: 600 VAC / Current Rating: 9 Amps Max. in 2-position applications.

I am having a hard time interpreting this. My understanding is that the maximum current is dictated by the resistance of the pins. My intuition is that this means that it would be safe to use the conector for any application that draws less than (9 A)(600 V) = 5.4 kW of power as long as the voltage does not exceed 600 VAC.

Is this true? If so, why isn't there a single "maximum power" rating? If not, can you explain how to interpet the rating at different voltages?

Answer

The voltage rating is related to the breakdown voltage of the plastic between the pins. You shouldn't exceed the breakdown voltage even of theres no current at all.

The current rating is, as you say, relates to the pin resistance and how much the connector will heat up. You shouldn't exceed the current rating even at very low voltages.

Edit:

As KellenJB says in another answer, it looks like the key thing you're missing is that the power consumed in the connector (and so the self-heating which could damage the connector) is not related to the voltage between the pins, but to the current through the pin. This current, combined with the (very small) resistance of the pin or contact, generates a small voltage between one end of the pin and the other (or between one pin and the socket its mated to). This voltage, multiplied by the current, gives the heat generated in the connector.