Since my knowledge of electrical circuits in very limited I will use a door bell to try to explain what I wish to accomplish:
I know that when I push the door bell button that the circuit is completed and the door bell rings. When I remove my finger from the button the circuit is broken and the bell stops ringing.
Basically, what I want is for the bell to continue ringing AFTER I take my finger off the button.

Actually, in my project, it is a light instead of a bell that I want to stay on after I remove my finger from the button.
Then I want to push this same button again to turn the bell or light off.
The project will be battery powered. The light will require a 12 volt battery.

You might think of it this way, although this is NOT my project:
Consider one of those security floor mats where when a person steps on it, an elarm sounds. But when they step off, the elarm stops. What I want is for the alarm (or light) to stay on after they step off the mat. Then, if they step back on, the elarm (or light) goes off.

Your help will be sincerely appreciated.

 

I re-reading my question about the door bell thing, I don't think it was as clear as it might have been.
Let's stay with the Floor Mat elarm example:
When a person steps on the mat, the circuit is completed and an elarm rings.
When the person steps off the mat--even though that circuit is broken--the elarm continues to ring.
If the person steps back onto the mat, the elarm stops ringing.
I am guessing that the first closing of the circuit must activate a second circuit that keeps the elarm (or in my project, a light) closed or completed?????.

 

You need a "Toggle" circuit.
Using either a 4013 or 4027 driving a transistor should work fine.

http://forum.allaboutcircuits.com/showthread.php?t=3187

 

Thanks Gadget:
I get the idea of the Toggle Circuit, but I am still some what in the dark, and need more help.
Staying with the Floor Mat elarm example:
Consider the following and please tell me more:
When one steps on and off of the mat there is only a momentary closing and opening of the circuit. When a person steps off of the mat the contacts separate (by way of a spring).
No mechanical buttons or switches can be mounted in or at the mat because it will take a real beating with people "jumping" on and off the mat.
I visualize just two power wires (negative and positive) leading from the contacts inside the mat to the light.
To avoid damage can this Toggle Circuit be mounted say, at the light, or somewhere in between to avoid damage.
Also, can the Toggle Circuit be purchased as a ready-made unit or device?

 

Hi,

You could also use a latching relay. Current through the coil will switch it, and it will stay in that state until the coil is activated again.

 

Here is a circuit for a bistable flip flop using transistors and one push botton:

http://ourworld.compuserve.com/homepages/Bill_Bowden/page9.htm#toggle.gif