Why does an aqueous solution of an acid conduct electricity ?

As said by your friends, an aqueous solution of an acid conducts electricity because of the presence of H+ ions in solution. The hydrogen ion is a charged species and its movement causes the flow of current. 

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when we add acid to water we obtain the aqueous solution of acid

and the acid dissociated in its resective ions that is H+ ions and ions conduct electricity 

so aqueous solutions of acids conduct electricity

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