My alternator don recharge the battery take it to repair they tell it gud help? on 2001 Volkswagen Beetle

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I remark on the dashboard the battery light I assume indicate the alternator is not light on even though the key is in ignition no light at all showing for the battery Try to jump start or put another battery it run great but as soon I disconnect one battery terminal it turn off I took the alternator to repair or check they told me its good .Plz help me.
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