Battery light Help please

My battery light on my integra is turning on at idle and in low at low rpm's like about 2k rpm
And its makin a humming noise kind of, the only way I can explain the noise is it sounds like my intake but deeper and more noticably loud...
and i can just tap the gas and the light goes away instantly and it seems to be running fine
But there is a wierd smell, sorda like a burnt clutch smell..
Can someone please help me! It is my 1990 integra rs hatchback, daily driver.
Battery replaced less than 4months ago
Clutch is fine, just smells like the clutch

uh... idk, hows ur altenator??