This shortcircuit indicator circuit is very simple and uses few electronic components. This indicator circuit can be used as the optical indication at voltage stabilizers.
To obtain a constant bright of the LED, the LED current must be made independent of output voltage. So, current limiting , must be done using a current power source, no with a resistor connected in series. Such a source can be build using one additional component: T1 from the circuit diagram.
Available reference voltage across R1 is generated by the LM317 and serves in the first instance, with R1, R2 and P1, the output voltage stabilization.
The indicator circuit, reference voltage is used to maintain constant voltage drop on R3:
UR3 = 1.25 V - EUB = 1.25 - 0.65 = 0.6 V. The current through D3 is then 0.6 / 180 = 3.3 mA, which is more than enough power for an LED small as the one used here.
T1's base current is only 15 nA, so stabilizer operation is unaffected by connecting it to the reference voltage.
T1 dissipates only 100mW when its collector-emitter voltage is 25 V.