You need to analyze the circuit as a transmission line to understand how signals propagate along the wires to other parts of the circuit:
http://en.wikipedia.org/wiki/Transmission_line
The velocity factor gives the speed at which the wavefront of a voltage pulse will travel along the transmission transmission line relative to the speed of light. A typical value for twin lead is 82%:
http://en.wikipedia.org/wiki/Wave_propagation_speed
On connecting the source to the transmission line, electrons will start to flow from the negative terminal of the source to the wire it's connected to, and from the other wire to the positive terminal of the source. This process propagates down each wire at 82% the speed of light in the case of twin lead. So after 100/82 x (time it takes light to travel one year), curent will start to flow along that part of the circut 1 light year away from the source, using your example.