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So how much power does it take to connect to another stargate? Is it a constant value or does it vary?
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The gate that is being used to dial is always the one that supplies the initial power to both. Depending on the wiring of the gate, it takes between 12 and 24 volts of electricity to establish a stable wormhole (this is proven in the episode titled "1969" where they use jumper cables hooked to trucks to power up the gate. A gate only needs enough power to connect, because if the other gate has a DHD it would take over should the connecting gate fail. Hope this helps!
In the episode Ascension Orlin builds a small stargate in Carter's home, so the power requirements for a stargate can be achieved with household grid connection. Here in Germany a typical household connection has around 14.5 kW, sometimes up to 34 kW (in case you have electrical heating). As per @Xantec's comment below, in the US the maximum can be as high as 44kW.
So it is safe to assume that 44kW is sufficient to build a stable stargate. (This also holds in case Orlin hat to use all sockets in the house, since 44kW is the rating of the whole household).
The majority of the power requirements for the activation of a wormhole are unspecified. Primary power to the gate is provided by ambient sources (background radiation, etc) which is continually being absorbed by the gate. It's only the activation of the gate which appears to require the use of an external source - necessary to unlock the ring to perform the dialling sequence.
While some/most of the power requirements for a standard wormhole can be handled by the gate itself, the power requirements are also relative to the distance travelled - hence the need for a ZPM or similar when opening a wormhole between galaxies - the external power source has to account for the difference between the power supply capabilities of the gate and the requirements for the trip. This may also account for why the SGC seems to require a constant power supply to operate their gate - the frequent use of the gate may not allow sufficient time to build up any reasonable store of energy for use.