RH has more to do with how tight, insulated and if has a vapor barrier. If a house is tight fan on or auto doesn't make a difference. Coil doesn't hold enough water to change RH. Loose house will make a difference, with fan on the constant air movement will pull RH into the house by being cooler than outside and leaking air around windows and through walls. Blower door test is one way to see how tight a house is.
The major source of moisture is the infiltrating/ventilating fresh outdoor air. A healthy home needs a fresh air change in 4-5 hours. If the outdoor fresh air is <55^F dew point with a 75^F indoor temperature is 50%RH, acceptable, yes. The occupants in the home add their moisture to ventilation as it passes through the home. four occupants add 1-2 lbs of moisture per hour according to ASHRAE.
Summers in St. Louis and throughout the green grass climates have outdoor dew points of about 70^F. During winds and operation of exhaust fans including kitchen hood and clothes drier, you may hours of +100 cfm of fresh air passing through the home. Many suggest having a 80-100 cfm of filtered fresh make-up air circulated throughout the home at a minimum when occupied.
Doing a Manual J shows that 5-7,000 btus of latent cooling loads are common during the summer during the 24 hours of a day. The sensible cooling at peak heat is 28,000-30,000 btus of sensible cooling per hour.
Evenings and rainy days commonly have 5,000-7,000 btus of latent during the 24 hours of the day.
Turning off the a/c will quickly demonstrate that the indoor dew point will rise above the outdoor dew point when occupants are present.
In a perfectly sealed home with occupants, the indoor dew point will rise because of the occupants adding moisture from respiration and activities until they die from a lack of oxygen. Fresh air ventilation is suggested to delute indoor pollutants and renew oxygen.
During high cooling loads, a properly adjust a/c will remove about 3 lbs. of moisture per ton of cooling. That would 9lbs. or 1 gallon of mositure per hour. As the sun sets and throughout the evening, the cycles on/off, removing less moisture. The indoor moisture level rises accordingly. On a wet rainy day with a 70^F dew points outdoors, the home will get damp from the fresh air and the occupants. At 60%RH inside,expect dust mites to grow. 80-90%RH under carpets on concrete and in mechanical equipment will also go mold.
This goes back to the original discussion about fan "on" or "auto". Fan "on"circulates the house air through the ducts evaporating the moisture in the ducts. The reduces moisture in the ducts but raises moisture in the home. Therefore less mold problems in the ducts, a high %RH in the home.
It is important to setup the a/c to remove enough moisture
Adding a small whole house is necessary to maintain <50%RH during any significant cooling.
Many now are opting to add a small whole house dehumidifier to supplement the a/c in maintain <50%RH throughout the home even when the a/c is off and it is raining outside.
Get a $10 %RH meter and follow what really happening your home.
Looking forward to hearing from all.
Regards Teddy Bear