My car hesitates upon acceleration in 1st and 2nd gear & battery light comes on. on 1994 Honda Civic

I checked altntr by startin engine and removing pos battery cable and engine did not die.

Asked by for the 1994 Honda Civic
2 answers
CHARGE battery (out of or disconnected) and THEN check voltage while running ABOUT 13 volts MINIMUM at idle with loads on , and then raise to 2000 RPMs and check for higher voltage , up to 14.5 volts (with ALL loads OFF) DON'T waste time guessing on an alternator , with a battery that's not fully charged , you will not get correct readings.
check volts 14.0 at battery,if no 14.0 volt ,bad alt..