Is RL-AC circuit's current higher at the first time?
This is because of the inductance. If you simulated it with the AC being applied at the point when the waveform peaked, you would see the behaviour you desired. 

You must consider that the current in an inductor lags its terminal voltage by 90º when things have settled down and this means that applying a sinewave at the point it is zero volts means the peak current will be higher on the first cycle.

This is the most common problem with inrush current on power transformers - that initial peak causes the magnetic core to saturate and fuses blow. Always best to apply power on a peak of the waveform.