The component values are way off and won't give a delay anywhere near 2.2s.
How much current does the circuit draw? drive to turn on with a low enough collector-emitter voltage.
+1, good points.
If the load draws more than a few mA I don't think its possible to build a single BJT power on delay circuit with reasonable timing circuit component values. You want to use a large resistor to avoid the need for a high value physically large capacitor, but that will starve the switching transistor of base current, which means it needs a very high gain. However you cant cheat
* and use a single-package Darlington because Darlington's have much higher Vce_sat voltage drop when on.
So whatever you do, you'll need an extra transistor to drive the base of the switching transistor, and it + a current limiting resistor (so you aren't relying on its H
FE to set the base current) need to go between the base and ground. However the turn-on will still be pretty mushy as the voltage across the capacitor slowly increases through the region around 2x 0.65V Vbe where the transistors start to pass significant base current. See lower circuit.
Add another transistor of the opposite type, connected b to c, c to b to effectively form a
SCR (or even replace the driver transistor with a very small SCR or a
Programmable UJT if you can get one), and you get 'snap-action' switching. See upper circuit.
There are a few more refinements needed:
- In both circuits, there is a reverse biassed diode across the timing resistor to discharge the timing capacitor quickly if the input power is removed - without it there is a risk of the circuit switching back on immediately if power is only briefly removed. The lower circuit uses a Schottky diode because it needs to discharge the timing capacitor more completely due to its lower threshold voltage.
. - In the top circuit, to avoid the constructed SCR triggering due to transistor leakage currents or noise, there is a 1Meg resistor across each b-e junction to help keep the transistors off.
. - It also has a 3.3V Zener in series with the base connected to the timing circuit to increase the threshold to around 3.15V (as the Zener current is *much* lower than the current required for its nominal voltage), which makes far better use of the timing capacitor. Without it, you'd need an order of magnitude bigger timing capacitor.
.
- Due to the snap-action switching, the switching transistor in the upper circuit has to pass a very high current surge at switch-on to quickly charge all the reservoir capacitors downstream of it. C3 connected b-e slows down its switch-on to limit the peak charging current.
.
- In both circuits, if there is any risk of the input being shorted to ground, and there is significant reservoir capacitance downstream of the switching transistor, and the supply voltage is greater than its reverse Vbe rating, (not a problem at 5V), you should add a beefy diode across the transistor, cathode towards the supply to divert the reservoir capacitor discharge current around the transistor, away from the b-e junction.
Neither circuit is a good way to do this - you should be using a P channel MOSFET as MOSFETs draw negligible gate current so you can use high vaue timing resistors without any problems, and their Vds_on drop can be far far lower than a similar current rating BJT.
LTspice sim with approx 200mA load current attached. Vce_sat for both sims at under 0.1V.
* Cheating: a single-package Darlington actually contains two transistors. 
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