The Meaning of Life, the Universe, and Everything.
What is it?
The Redstone Battery is a transmission component (Repeater, Comparator) that can be used to extend or shorten a Redstone signal.
How does it work?
When a Battery is powered, it becomes charged. When it loses its power source, the charge will keep the Battery's ouput alive until it decays.
By right-clicking the Battery, the player can cycle between 1, 2, 4, and 8 Redstone ticks worth of power before switching to Alt mode.
A Battery in Alt mode carries a 1 Redstone tick charge. However, only the charge will leave an output. This means that in order for the Battery to output a signal in Alt mode, it must be powered and then de-powered.
What problem does it solve?
First, a Battery can be used as a pulse extender. Chaining batteries together can indefinitely extend an output.
Second, a Battery can be used as a pulse shortener. These are essential to circuits T Flip Flops, but they require a fairly large amount of room to create.
Additionally, for pulse extender, the red stone repeater can extend any pulse to up to 4 ticks (with a 4 tick delay) already,
For pulse shortener, the smallest design is 1 wide, 3 long, and 3 tall
For pulse extender, the fader pulse extender can generate a minimum pulse length of 28 ticks (more if you add more comparator to the circuit).
For Extenders under 28 ticks, Repeaters take up an incredibly long amount of vertical space to use. You can get up to
Extenders using the fade method are better with space, but they have issues with getting exact timings.
Using a mere 4 Batteries, you could get a 25/26/28/32 tick extender without having to factor in the button.
The smallest pulse shortener is flawed in that it's inverted. You can't make a T-Flip Flop out of it.
My goal behind this suggestion was to get better support for smaller Monostable circuits.
For instance, take a look at the Alt Mode Battery. Button +-> Block +-> Redstone Torch -> AM Battery. It's a falling edge detector that can be created with 4 blocks and zero pistons. A lone Alt Mode Battery and a Button can create a rising edge detector with 2 blocks.
Pistons are useful but when it comes to circuits, they're not very good at blending in. They have a mandatory 3 block requirement with limitations going upwards and they're loud.
Sometimes, I'd like to be able to build a fully horizontal T-Flip Flop within a straight 1-block high tunnel so that wire can run seamlessly on top of it.
Other times, I simply want to build a door that opens up for 3 seconds before closing again without having to build a block chain of Repeaters. I've never understood why something so simple has to be so difficult.
I see your point and I think it would be a fine addition to the game. I would like to point out a few things.
1. The component description you're describing seems to be more like a "Capacitor" instead of a battery, especially with regards to its Alt mode. Capacitor, when placed in between circuit, act as a form of high pass filter (essentially, it lets fast transitioning signal, such as a pulse, to go through and blocks DC, a constant). So a better term might be a Capacitor. A battery doesn't have the behavior of an Alt mode. Do note that a capacitor's pulsing behavior would be the inverse of your description (the output pulses on the rising edge and not on the falling edge). Technically in circuit, a capacitor do generate a "negative" pulse (in term of a sharp drop in voltage on the other side).
2. Given that you already have a pulse extension mechanism, perhaps have it also define the pulse length of the output.