sed variable issue

I'm writting a krn shell script and i'm having an issue with a variable using sed.
If someone enters a variable with a " /" the sed command doesn't read it right.
example.
a='12000/10-DC'
b='12000/10-AC'

cat file | sed "s/$a/$b/"

How can i correct this issue? Will the fix to this problem also work if someone enters a variable without a " /" ? What is it called when a variable has a character like this? I didn't know how to search for this issue correctly.
Thanks.

Here is one workaround -- use delimiting characters that are not in the user-defined strings (assumes the # character is not in the strings):

a='12000/10-DC'
b='12000/10-AC'

cat file | sed "s#$a#$b#"

Thanks it worked.