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Tesla's Wardenclyffe Tower could be powered with an Earthly power source (Tesla just lacked funds). But, when The Doctor powered it with TARDIS in the recent episode "Nikola Tesla's Night of Terror", she had to turn off the force field. Maybe, to destroy the spaceship, Wardenclyffe Tower needed more power. But, earlier in the series, the TARDIS:

  • almost destroyed the universe.

  • kept Earth warm for billions of years (during "Total Event Collapse" before Big Bang 2.0).

  • dragged Earth from one part to another part of the universe.

In the episode "Journey to the Center of TARDIS", The Doctor said this about TARDIS' power source:

The Eye of Harmony. Exploding star in the act of becoming a black hole. Time Lord engineering. You rip the star from its orbit, suspend it in a permanent state of decay.

This seems an infinite power source. Why, then, couldn't the TARDIS sustain a force field after powering Tesla's Wardenclyffe Tower?

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    Because the plot demanded it
    – OrangeDog
    Jul 30, 2020 at 13:50
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    Plot requirements or authors with no concept of the power levels involved. The Wardenclyffe tower was to be driven by a 200 kilowatt AC generator. If the Tardis has the power output needed for all those other things, then power output limits can't be the reason for the Tardis not being able to power the Wardenclyffe tower. A better "explanation" would have been using the force field generators to produce the AC power needed by tge tower.
    – JRE
    Jul 31, 2020 at 5:58

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Instantaneous vs Sustained energy

The Doctor in the episode itself telling us the TARDIS doesn't have the power for both as fact is all we have to go on. So either we use other considerations to determine she's wrong or lying, or we try to find considerations that provide a rationale for her statement. There's no way to know for certain, but there is at least a plausible explanation in considering the TARDIS' energy output at any given moment may be far below its total sustained output over long periods of time, which is true of power sources in reality as well.

While the TARDIS does have the Eye of Harmony as a power source, that doesn't necessarily mean it can utilize all that energy all at once. As an example, a lightning bolt contains 10 billions watts of electric power, which is roughly equivalent to what the Palo Verde nuclear power plant in Arizona puts out in 2.5 hours. But you couldn't just pull all that energy out of the power plant instantaneously, nor could you simply charge 10 billion watts worth of batteries with a lightning bolt. The load has to be drawn out over time. As a general rule of thumb, capacitors are needed for large bursts of instantaneous energy, after which they have a recharge time to regain their potential.

So for all the power the TARDIS has at its disposal, it's entirely plausible that in order to output enough energy to charge the tower with spacecraft destruction-worthy amounts of instantaneous electric potential, the TARDIS shields would be drained enough to no longer be an effective defense until the capacitors could be recharged. Considering the we've never seen the TARDIS to have any apparent offensive capabilities that would require such an instantaneous drain of its power reserves, it just may not have been designed to need to support that sort of power utilization.

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  • Do you know how much sustained power required to drag Earth at high speed?
    – Satellite of Sin
    Jul 31, 2020 at 11:03
  • @UmbrellaCorporation I do not, although given anti-gravity technology, probably much less than the same feat by conventional means. Neither do we know how much energy was used in the tower blast. What we do know is that the Doctor herself made the claim, and unless we assume her to be lying or wrong, then considering that we see factually that the TARDIS is capable of hauling Earth yet it could not power the tower and keep up its force field up at the same time, then the latter must have taken more sustained power to accomplish.
    – Mwr247
    Jul 31, 2020 at 21:52
  • Why are you thinking about Anti-gravity? To move the Earth, gravity doesn't need to be countered. It's the inertia.
    – Satellite of Sin
    Aug 1, 2020 at 16:03
  • @UmbrellaCorporation Because gravity has a relationship with mass as does inertia, so it's possible that antigravity effects it too. Nonetheless, this is irrelevant since that wasn't the point of my argument anyways. In a fictional universe with made up technology that can accomplish anything, we can only operate by what we've been shown and told. Dragging a planet probably takes less energy than recreating the entirety of the big bang, and yet we know the TARDIS pulled off this feat and yet couldn't power the tower and force field simultaneously.
    – Mwr247
    Aug 1, 2020 at 22:41

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