All acids only conduct electric current when they are dissolved in water, because when they are in an aqueous medium, they undergo ionization, i.e. release ions.
HCl --> H⁺ + Cl⁻
The bases also conduct electric current in solution, because the Ionic dissociation sufferers (release the existing ions in the formula) and molecular ionization, suffer the reacting with water and releasing ions.
NaOH ---> Na⁺ + OH⁻
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