How does CRA-cAMP positively regulate the lac operon?

The CRA-cAMP complex increases the rate of expression of lac operon when glucose is absent and lactose is present as nutrient.

Explanation:

CRP is the catabolite gene activator protein that forms a complex with cAMP. The CRP-cAMP complex facilitates the binding of RNA polymerase to the promoter region of the lac operon. This robust binding as stimulated by CRP-cAMP complex is followed by the formation of open complex and initiation of gene expression.

Hence, the CRP-cAMP complex positively regulates the lac operon and increases its expression when glucose is not present.