We calculate the second homology group of the current Lie algebra $L \otimes A$ for arbitrary Lie algebra $L$ and associative commutative unital algebra $A$. The main tool is the Hopf formula, expressing the second homology of a Lie algebra in terms of its presentation. We also give the formulas for the second homology group of the Lie algebra associated with algebra $A \otimes B$ for arbitrary associative unital $A$ and $B$.