There is not much difference between the two circuits except one transistor and a 2.2K resistor. The circuit shown in the figure 1 requires a negative pulse to latch the output of the 555 IC, once it received the pulse the output at pin3 goes high and it will remain high until the power to the 555 timer is interrupted. Whereas the circuit used in the figure 2 requires a positive pulse to latch the output of the 555 IC, both the circuits can provide 200mA output current that can easily drive a relay switch and can also be used as an input to an electronic application. Operating voltage of both the circuits are 5V to 12V DC.
A latch circuit can be built by many ways for example it can be built by using transistors or ICs, latch circuits are used in electronic applications where the continuation of output is required whether the input signal goes off. The figures below shows two simple latch circuits built with 555 timer IC.
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