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Is there some drawback in having a BJT transistor saturating without a load?

The scenario is this: BJT is driving a relay, but there is a switch to have the relay always on or off leaving the BJT collector open. In this case there is just the Ib flowing in the transistor, my worry is that strange situation can damage the BJT or decrease its life duration.

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Providing the base current does not exceed the manufacturer's recommendation this should not be a worry. You should calculate base current when the collector is open circuit. This is likely to be the worst case scenario.

One thing to watch for is the switch open-circuiting the relay - I'm not sure how you plan to do this but it might be a good idea to put a reverse connected diode across the relay. In case you weren't aware - when you open-circuit a conducting relay or coil or inductor you will get a small spark that can damage a transistor. If you are using the collector switch correctly this stops most of the problem but it's still worth the small investment.

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