Step 1: Identify carbolic acid.
Carbolic acid is phenol with molecular formula \(\mathrm{C_6H_5OH}\).
Step 2: Count the sigma bonds.
In the benzene ring, there are 6 \(\mathrm{C{-}C}\) sigma bonds and 5 \(\mathrm{C{-}H}\) sigma bonds.
The \(\mathrm{C{-}O}\) bond contributes 1 sigma bond and the \(\mathrm{O{-}H}\) bond contributes 1 sigma bond.
Step 3: Total sigma bonds.
\[
6 + 5 + 1 + 1 = 13
\]
Step 4: Conclusion.
Thus, carbolic acid contains a total of \(13\) sigma bonds.