2001 Honda CRV

I was going to work and the radio went off
then lights started to dim them the motor
started sputtering losing power. I turned
the lights off and it gained power just
enough to get a couple miles to work. On
the way home the radio dimmed and I
pulled up to a stop sign and it cut off. I had
my dad jump me off and got it home which
I was a couple miles away. I live like 18
miles from work so it drove fine 16 miles
there and back. I changed the alternator
and it crank up fine. Took the battery cable
off and the car cut off. Took the alternator
to get.checked and it passed. What's my
problem. Please help