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NASA writes to say

As the electrical power becomes less and less, power loads on the spacecraft must be turned off in order to avoid having demand exceed supply.

A lead battery would 'die' if demand were to exceed supply for any sustained duration ; What happens to an RTG in the same situation?

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As you demand more current, the voltage goes down. You eventually brown-out the system. The RTG doesn't care. If you then reduce the load, the voltage goes back up.

You cannot drain an RTG like a battery. Its power output depends only on its radioactivity (which goes down over time), the efficiency of the thermocouples (which also goes down a little over time), and the temperature of the sink.

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