Is it normal for cars to run a bit rough when at idle when the a/c is on?

I recently got this car to replace my last one that died, I had the a/c on today and whenever I got to a stop light, the rpms would drop down to 400-500 for a few seconds, act like it was going to die, then surge back up to 600-700 where it's supposed to be. It did this every 3 seconds or so and I was starting to worry it would stall so I was putting it in park at every stop to prevent it. Halfway home I turned the a/c off and it ran like normal the rest of the way home. I asked my grandpa and he told me that was SUPER common back in the day, especially if the a/c pulls alot of power or the idle is already on the low side. I'm pretty convinced it's normal now at this point, but I'm still afraid the car will stall out at one of these lights and I'll end up holding up traffic