I think it's the alternator, engine light comes.

Measure the battery voltage with the engine off and with it running. Off it will be 12.6 volts if it's fully charged. If it's around 12.2 volts, it's good but discharged. At closer to 11 volts it has a shorted cell and must be replaced.

With the engine running you must have between 13.75 and 14.75 volts. If it is low, suspect the generator. It is common to go through four to six of them in the life of the car. To reduce the repeat failures, replace the battery at the same time unless it is less than about two years old. Due to their design, these generators produce huge voltage spikes that destroy the internal diodes and voltage regulator. As the battery ages, it loses its ability to dampen and absorb those spikes.