The light is too powerful to be sustained continuously by the small-voltage battery that’s inside a camera. Instead it uses something called a capacitor. This capacitor is slowly charged by the battery with the energy needed for the flash. The capacitor can release all its energy very quickly and therefore – for a very short time – supply the large amount of energy needed for the flash.
So very(!) simplified: say the battery can supply 1 energy per second. And the flash needs 5 energy. Then the battery charges the capacitor for 5 seconds with 1 energy every second. The capacitor holds 5 energy. Then you take a photo. The capacitor releases the 5 energy in 0.1 seconds and makes a flash that lasts 0.1 second.
This is for conventional cameras. Phone cameras have smaller led lights and could in theory be on the whole time. I think it would blind too much though.
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