I have a sealed box inside which there is a pcb and electronic components. This box is to be used under water, under a pressure of 45 bar. Will the components experience the same pressure?
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If the box is sealed so that no water gets in, and the sides are strong enough to not be crushed under the pressure, then the inside of the box will have significantly less pressure. In fact, the air inside the box will only have slightly greater than normal atmospheric pressure (that is, it will keep the ambient air pressure from when it was sealed). After submersion, the air pressure inside the box will be slightly greater because the walls of the box will be pressed inward, but this should be a small amount if you build the box walls strong enough.
This is why people can survive on submarines deep beneath the ocean surface.
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Let's start from the ideal gas law: $$p V = n R T$$ We are interested in the pressure $p$, so $p = \frac{n R T}{V}$.
If the box is almost incompressible, the box will experience a negligible increase in pressure, but this is well balanced from the drop in temperature, that lowers the internal pressure probably in a less negligible way.
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$\begingroup$ The main point to note here is that as the box is not significantly changing it's shape, it's volume, $V$, does not change. So the pressure is not changed either. The point about the temperature assumes that the water is colder than the starting temperature (depends on the application - might not be true down an oil-well, for instance). $\endgroup$ Commented Nov 3, 2017 at 10:56
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$\begingroup$ @OscarBravo: The question says "underwater, under a pressure of 45 bar", which means more than 400 meters deep. In this situation it makes sense to assume a change in temperature. $\endgroup$– GRBCommented Nov 3, 2017 at 11:21