Designing a current limiting circuit for my project
Your first circuit appears to be a current limiter. If the resistor values are properly chosen, the circuit will clamp the collector current (the current through the transistor and thus your load) at some value. It will not cut power.

The second circuit image you posted is not a complete circuit. The box labelled "Drive Circuit" represents some logic block that you would have to design. It takes feedback and directly turns power on and off to the load. That could be done any number of ways.

If you want something that acts more like a fuse that can be easily reset, something like a latching relay in series with the load could work. I'd probably use a comparator to trigger the relay when the voltage across a shunt resistor went above a threshold.







simulate this circuit &ndash; Schematic created using CircuitLab

The relay is a latching type. Rshunt is an appropriately chosen shunt resistor. R1 and R2 are chosen such that they divide to the voltage that triggers the comparator when the current through the load is 1.5A or higher:
Vtrigger = 1.5A * Rshunt = Vcc * R2/(R1+R2)

Here are some considerations:
1. Rshunt should be small so it does not steal too much power from the drive circuit.
2. This circuit assumes Vcc is a stable voltage source. If it's weak and changes voltage under load, the comparator circuit will not trigger correctly.
3. If you're driving a motor, there might be a temporary current surge on start up that exceeds 1.5A for a short period of time. If that's allowable, you may need to build a low-pass filter into the non-inverting input of the comparator.
4. If you choose a double-coil latching relay (not shown), you can rig a button up to the second coil to reset the relay after it triggers.
5. The coil of the relay may not be compatible with Vcc.