Can you use one length of 3-wire cable to provide electricity to 2 separate circuits?

In countries that use a single phase split secondary service you can. In modern homes this is the type of circuitry that is used for kitchen split receptacles. On the receptacle the tie bar is removed from the "hot" side of the receptacle. A red wire of the three wire cable is placed on the upper terminal of the receptacle. A black wire of the three wire cable is placed on the lower terminal of the receptacle. The white wire is placed on the opposite side of the receptacle under the silver coloured screw. This will give you a full 15 amps capacity on the top portion of the receptacle and a full 15 amp capacity on the bottom half of the receptacle.