If the ribs have the thin white membrane along the back, remove it. To do this, run a butter knife under the membrane and then use a paper towel to grip the membrane and pull it off.
Combine paprika, garlic powder, onion powder, chili powder, salt and pepper in a small bowl. Rub this dry rub mixture over both sides of the ribs.
Pour 1 cup water into the bottom of the Instant Pot inner pot. Put the metal trivet in the pot.
Put the ribs on top of the trivet, standing them up so that the rib bones are going up and down. You can lean the ribs against the side of the pot. If your rack of ribs is cut in half it is ok to have the slabs of ribs touching each other. If your rack is whole, curve it as needed to fit it into the pot.
Close the Instant Pot lid and turn the steam release valve to the sealing position. Set the pressure cook time to 25 minutes at high pressure for baby back ribs. (Cook spareribs for 35 minutes at high pressure.)
The Instant Pot will take about 15 minutes to reach pressure and then the cook time will start counting down. When the cook time ends, allow the pressure to naturally release for 15 minutes (just leave the Instant Pot alone) and then quick release any remaining pressure by carefully turning the steam release valve to the venting position. (Allow for a full natural release for spareribs.)
Take the ribs out of the Instant Pot and put them on a foil-lined baking sheet. Brush ribs with BBQ sauce and put them in the oven under the broiler for 3-6 minutes, until they begin to brown and the BBQ sauce begins to caramelize. Watch the ribs carefully so that they don't burn.
Serve with additional BBQ sauce.