It depends what you mean by "electrical circuits". I don't know of any simulators designed for power engineering but you can certainly get some of what you want from a simulator called Simetrix. You can download a free demo from
We use the full package for electronic circuit simulation and its brilliant! For general electrical engineering it at least has the basics such as resistors, inductors, capacitors, voltage sources, etc. and can do transient analysis, so it may provide what you are looking for.
Following my earlier posting I just thought I would check the Newbury site latest news. They have changed their name to Catena Software and they now have a POWER simulator package called Simetrix/SIMPLIS !