l=3; r=50; c=1/40; e=20; q[0]=1; i[0]=8;
i[t]=q'[t];
Solve[l i'[0]+r i[0]+(1/c) q[0]==e, i'[0]]
DSolve[{l Q''[t]+r Q'[t]+(1/c) Q[t]==e, Q[0]==1, Q'[0]==8}, Q[t], t];
charge[t]=N[(Q[t]/.%)[[1]]]
Limit[charge[t],t->Infinity]
DSolve[{l I''[t]+r I'[t]+(1/c) I[t]==0, I[0]==8, I'[0]==-140}, I[t], t];
current[t]=N[(I[t]/.%)[[1]]]
Limit[current[t],t->Infinity]