How to increase current while keeping the voltage the same?
How to increase current while keeping the voltage the same?
I = U / R

reduce the resistance!
But you're talking about Arduino outputs.
First: there is a confusion here regarding the power supply of the Arduino itself vs. the load that the pins can drive. What I do is I have my 5 V x 4 A power supply for my circuits, and I do not use the Arduino power supply from the USB plug for that. All you need to do is connect the Arduino ground (GND) pin to the ground of your external power rail. You do not connect the +5V pins with each other, not needed.
Now, to actually switch husky loads with your Arduino pins, you guessed right that you need transistors. Power transistors to be exact, or ideally a MOSFET or a relay. Even for a relay you might need a transistor to drive the current needed for the solenoid.
Using a classic bipolar junction transistor (NPN or PNP) is a problem because you still need current to drive current. So you run out of current from your pin. But there are ways around it, I'm showing below. First the MOSFET.
A MOSFET is a voltage controlled device that requires almost no gate current. You can try a 2N7000 if you're working on breadboards:



simulate this circuit &ndash; Schematic created using CircuitLab
The 2N7000 can switch 200 mA, the BS170 can do 500 mA. You need more? You can do some bigger MOSFET in a TO-220 package. I don't have a standard part number handy right now.
Here is the same with a BJ transistor, can use a BC546/7/8 here instead of 2N2222,



simulate this circuit
but those are medium power, again, only in the few-hundred mA range. They don't get you to amperes ranges, so you can run them in a Darlington configuration:



simulate this circuit
The TIP41 should do a few amps (with heat sink!); or, whatever bigger power transistor you want, maybe even those old fat 2N3055 power transistors with 15A collector current.
There are also Darlington pairs in a single package, like the popular TIP122, it feels as if you were connecting the TIP41 directly, just that there are two transistors inside in the Darlington configuration.



simulate this circuit
You can replace the load with a relay and then you can drive 110/220 V circuits at whatever power you want. I think you might be able to drive a small suitable relay directly off the pin or you might need a little BC247/2N2222 instead as per the second schematic above.