In the circuit shown in figure, current through the battery at $\mathrm{t}=0\mathrm{and}\mathrm{t}=\mathrm{\infty }$ is

At  t=0, current will flow from the capacitor and at $\mathrm{t}=\mathrm{\infty }$ current will flow from the inductor. So, current in both cases will be 1.5A.