On its own Meg,
"voltage ... only appears when a current is demanded by one of the circuits",
is an incorrect statement. The Voltage is there across the Battery terminals all the time (assuming it is charged). even if the battery is not connected to anything.
The confusion arises because that phrase should read: "voltage DROP... only appears when a current is demanded by one of the circuits",
The phrase basically relates to the portion of the supply voltage that you see across a component when a current is flowing in it.
Imagine a simple circuit which has a 12 volt battery and three one ohm resistors connected in series, but with an open isolator switch in the negative side. This is Diagram 1 below.
While the isolator E-F is open, no current is flowing so because all of all of A,B,C,D and E are connected, all are at 12 volts relative to the chassis, hence the voltage drop across the second resistor B-C is 12v minus 12v i.e zero, which can be loosely described as "there is no voltage across resistor B-C".
However when you close the isolator switch E-F. A current of 12/3 i.e 4 amps will flow. The voltages relative to the chassis will then be as shown in diagram 2.
A at 12v, B at 8v, C at 4v, D at 0 v. So the voltage across B-C is (8 volts minus 4 volts) i.e 4 volts. so you could loosely say that the 4 volts across B-C appeared when the current flowed. {actually it's the other way around, the 4 volts CAUSED the current to flow.}
- SimpleCircuit