Low battery indicators with LED

For a transistor to conduct, it requires a voltage of about 0.6 between its base and emitter. This voltage is applied from the wiper of the 47K pot. Now if the pot is at minimum, this voltage is across the 22K, so the 47K will have about 1.28v across it - or 1.88 across the pair. Add the 3V9 from the zener: this will require a battery voltage of 5.78v to just turn on the first transistor. Above 5.78 the right hand transistor is turned on, the left hand is therefore off and the LED is also off. Below 5.78v the LED will therefore come on.
Low battery indicators with LED - schematic

Low battery indicators with LED - img1

A green LED has around 2.0v on it when it is illuminated. This value varies a bit with different manufacturers, but is usually pretty well matched within any batch. Add the base emitter voltage and you need 2.6v on the base of right transistor (i.e. across the 3K3) to turn on the transistor. 2.6v across 3K3 needs 9.1 across the supply rail. The two transistors form a current source. R2 conducts via Zd and supplies base current to Tr2. Tr2's collector current flows through R1 developing a voltage which turns Tr1 on. As Tr1 starts to conduct it pinches current that would otherwise turn Tr2 harder on, so the circuit balances at the correct current to just develop 0.6v across R1. So the current is 0.6/R1. You chose R1 for the correct discharge currrent. Remember that to discharge a 9v battery at 100mA, Tr2 will dissipate 9 x 0.1, or 900 milliwatts. Choose a suitable transistor with a suitable heatsink! The current through R2 is defined by the battery voltage less the zener voltage so as the battery discharges, there will eventually come a voltage where the battery has fallen to the zener voltage (plus 0.6v across Tr2's base-emitter. The circuit is now completely off and the battery is discharged to the end level. Below this threshold voltage the transistor is off and the RED LED is on. Above this voltage the red LED is off. The threshold can be altered by altering the three resistors.

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