Hello, I have a problem with powering a cicuit.
I need something to be able to power the circuit both with the battery and via a cable, also when i am using the cable to power, i need to be able to charge the battery and when the battery is full i need to stop charging.

 

You need to ensure that powering the circuit and charging the battery are done separately. In some cases, the battery charging voltage will exceed the safe operating level for the circuit and that would be a bad bad thing.

 

A Resistor feeding 2 shunt-Regulators in series,
with one Shunt-Regulator across each Cell of the Battery would work.

The Shunt-Regulators will need to be accurately set
between ~4-Volts and 4.1-Volts for better Battery-Life

The Resistor size will depend upon the Voltage and Current capacity of the Power-Supply.

The Switch in the Power-Supply-Jack must bypass the Current-Limiting-Resistor
when the Power-Supply is un-plugged.

A Diode from the Power-Supply-Jack directly to the Regulator will
automatically bypass the Battery when the Power-Supply is plugged-in.
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A Resistor feeding 2 shunt-Regulators in series,
with one Shunt-Regulator across each Cell of the Battery would work.

The Shunt-Regulators will need to be accurately set
between ~4-Volts and 4.1-Volts for better Battery-Life

The Resistor size will depend upon the Voltage and Current capacity of the Power-Supply.

The Switch in the Power-Supply-Jack must bypass the Current-Limiting-Resistor
when the Power-Supply is un-plugged.

A Diode from the Power-Supply-Jack directly to the Regulator will
automatically bypass the Battery when the Power-Supply is plugged-in.
.
.
.

Thx for the help,
could you send me a circuit to be clearer, which I don't understand well .

 

The Output-Voltage, and Output-Current of your Power-Supply must be known first.
Measuring it while under a Load is best,
but at the very least,
You need to provide the Specification-Ratings printed on the outside of your Power-Supply.

Your Load is most likely less than 1-Amp,
but You gave no Information on the Load, except that it's 5-Volts.
The Load-Current needs to be estimated, or preferably, actually measured.

Also, what is the mAh rating of your Battery ?
.
.
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