Each household electrical circuit branch contains either a fuse or a circuit breaker to protect that circuit from being subjected to excessive current. This is a safety feature that protects circuits from being overloaded. These safeguards are designed into most homes to prevent specific problems related to overloading a circuit. When the total current flowing through a 10 amp circuit exceeds 10 amps, the fuse will blow or the circuit breaker will trip. The tripped circuit breaker or blown fuse will break the circuit, automatically cutting power to any devices connected to that circuit branch.
If an air conditioner that draws 12 amps is plugged into an unprotected circuit that is rated for only 10 amps, the circuit will begin to overheat. This can cause the insulation on the circuit's wires to break down, which can cause a short-circuit. Similarly, the excess heat can damage the power supply or the air conditioner. If enough heat builds up, it can start an electrical fire.
An inductive load -- such as the motor inside an air conditioning unit -- requires more power to start up than it does to run continuously. If the air conditioner requires 12 amps to start the motor, 10 amps will be insufficient to get the motor to turn. Attaching an incompatible power supply can also cause the motor windings to overheat and become damaged.
Attempting to operate a 12 amp air conditioner using a circuit that is rated only for 10 amps is unsafe. Damage may occur to the air conditioner, the power supply, or both. Before attempting to use any electrical device, always verify that the power supply circuit is rated for use at or above the device power rating.