How your 3-ton A/C could only be operating at One Ton (Awe, you're kidding; NO I'm NOT!) Only two of many diverse factors that can cause very low Btu/hr evaporator heat-load absorption and transfer scenarios.
Every refrigerant has a "vaporization" heat absorption factor per pound. This heat-absorption effect is rated in Btu per pound of refrigerant. (Btu/lb); if the total heat-load of the conditioned space is known (in Btu/hr) we can find the total number of pounds of ("evaporated") (R) refrigerant that must be circulated by the compressor and metered through the evaporator coil.
The closer that Btu/hr match is, the more efficient the system "can be." Many other factors determine overall efficient A/C operation.
It requires a specific level of heat to (boil) evaporate a particular refrigerant. The amount of the heat-load on the DX-coil determines the maximum amount of (R) refrigerant that a DX-coil can evaporate. A TXV (R) metering devices will better adjust to the heat-load and help protect the compressor from flood-back. Flow-rator metering devices will flood the coil and usually destroy the compressor!
Many older gas furnaces had small blowers and motor HP and unloaded at higher static pressures, along with under sized ductwork. Couple those factors with dirty filters that begin to by-pass lint and you have blower wheel blades and evaporator fins and coils insulated and even blocked. You end up with a coil that is not evaporating but little liquid (R) to absorb latent and sensible heat from the air.
You could have a 3-ton DX-coil (36,000-Btu/hr) only boiling enough (R) to absorb one ton (12,000-Btu/hr of heat from the air. If it only boils one-third the (R) per hour it will only absorb and transfer to the condenser 1/3rd the Btu/hr of heat to the condenser.
Here is another scenario with the same result: The beer-can-cold boy installs a unit on a home that has a very hot interior. This time the blower is producing too much CFM per ton of cooling. So he thinks he has to get the suction line beer-can-cold and begins to pour I the (R). Later when the interior cools down and then return air filter begins to load-up, the coil becomes flooded liquid (R) begins. Same scenario, DX-coil, two-thirds flooded and only one-third of liquid (R) vaporizing to absorb heat. (A rated three tons, becomes a one ton operating system.)
When the relative humidity is high, the ability of the evaporator to absorb latent heat increases. Later, I will graph the increased ratio as humidity goes up. The latent capacity of an air-conditioner depends on the specific engineering of that specific evaporator and condenser match. In a 75-F conditioned space you need 55-F discharge supply air over a period of long run-time, mixing with the 75-F air to reach the 50% RH point. - udarrell - Darrell
-- Air Conditioning System - Excessive Airflow - Excessive Charge