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
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.
1 more answer
check volts 14.0 at battery,if no 14.0 volt ,bad alt..