Ideal inductor AC current LTspice
1H is a rather large inductor, and 1V is a rather low voltage, so it seems reasonable to me. 

The impedance of the inductor alone is \$2\pi fL\$ or about 314 ohms at 50Hz, so R1 isn't doing much and the current will be about 3.2mA.

Remember, the magnitude of the total impedance of an inductive and resistive component in series is \$\sqrt{X_L^2+R^2}\$ so unless the two components are fairly close in magnitude the larger one tends to dominate.