Step 1: Recall the relation between absorbance and transmittance.
Absorbance is given by
\[
A=-\log_{10}(T),
\]
where \(T\) is the transmittance expressed as a fraction.
Step 2: Calculate the absorbance.
Given,
\[
T=10\%=0.1.
\]
Therefore,
\[
A
=
-\log_{10}(0.1)
=
1.
\]
Hence,
\[
\boxed{A=1.}
\]
Therefore,
\[
\boxed{(B)}
\]
is the correct answer.