checking time for a circuit of size in polynomial k On the page 1073 of CLRS(Introduction to Algorithms),

Given a circuit C, we might attempt to determine whether it is satisfiable by simply checking all possible assignments to the inputs. Unfortunately, if the circuit has k inputs, then we would have to check up to 2^k possible assignments. When the size of C is polynomial in k, checking each one takes Ω(2^k), which is superpolynomial in the size of the circuit.

Can I ask what is the reason that checking if one truth assignment is a satisfying assignment takes Ω(2^k)?
You've misunderstood.  They are saying that the running time to check all $2^k$ assignments (not the time to check one assignment) is $\Omega(2^k)$.  It's a reasonable misunderstanding, as their wording is unclear, but that's what they mean.