Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.
Why not, but in case that you have good quality of PC PSU. If you suspect in PSU quality use 12V output with 7805 or 3,3V regulators to get stable 5V or 3,3V. Some bad quality PSU products have bad noise and voltage variations.
Standard unimer have low sampling speed or bad display refresh time, but if PSU have very bad ripple you can see flickering led 7-seg display digits of your project, or such things. My opinion that is best way in that situation to use 12V from PSU and voltage regulators for 5V and 3,3V with appropriate capacitors in input and output stages, and of course standard usage of 100nF closer as possible to VDD/VSS pins as usually.
I use very often PC PSU when working on various projects.
It's best to use the 12V supply and use a 5V regulator such as the 7805. For 3.3V you can use another regulator. For example you can use an LDO powered off the 5V line. You may use the LM2937.
Like mentioned before the power supply may suffer from noise issues and voltage variations. And obviously you don't want some "small" spike to damage your PIC or the voltage variations to affect the rest of the circuit. Better safe than sorry.
As for the current limiter, there's no need for that.
Boost up the voltage to a level where the battery can be charged. A simple way is to use float/trickle charging. For this you usually need around 13.5V, but do consult the manufacturer's datasheet if available. So you can use a circuit to boost up the voltage to 13.5V and you can keep the battery connected without worrying about damage. You can also implement a multi-step charging algorithm. However if you don't require relatively quick charge, this is unnecessary.
You can use either the 12V or 5V input for the boost converter (just an idea)! Just be careful with the circuit design.