Argh, I followed that perfect circuit design from alsetalokin but I think all my MOSFETs are messed up. I tried a 2nd one and it didn't work either. Only thing i can think of.
Only thing I did different was use 270 Ohm resistors in place of the 220 and 100 Ohm resistors in Alsetalokin's circuit. They were the closest values I had on hand to 220 and 100
Even tried with a LED for visual indication. Nothing.
Attached pictures
Well, that may be easy to fix. Note that your actual breadboard might have the power busses broken into left and right halves. See the breaks in the Red and Blue lines just up and to the left of your mosfet? Bridge those gaps with jumpers and let's see what happens. (Actually you only need to bridge the negative (blue) rail for your particular circuit, but do them both for completeness sake anyhow. See the image below.)
Also make sure you have the LED the right way around, with Cathode to the mosfet Drain and Anode to the resistor>positive rail.
Also, resistors can be used in parallel. If you put 2, 270 ohm resistors in parallel you get 135 ohms. But in your case it probably doesn't matter, the 270R for the mosfet gate series resistor will still work OK, and the 270 ohm for the LED current-limiting resistor will just make the LED a little bit dimmer.
To confirm, I just tried it on my breadboard with a 330 ohm series gate resistor, 100k gate pulldown, and a bog-standard IRF530n mosfet and it still works fine.
Although with a 530n mosfet, I'd suggest using a heatsink on the mosfet if you are using a heavier load like a light bulb or a low-resistance heating resistor, as the 530n mosfet will dissipate some power in its internal Rdss resistance under these conditions of low gate voltage and higher current draw. With the IRF3205 I didn't need a heatsink since it has such a low Rdss and it works fine with about 5V at the gate at these slow switching speeds.
ETA: When using the heating resistor as the load, don't use the 220 (or 270) ohm current-limiting resistor, this is just for the LED. Remove it and put a jumper there instead.
You can use another PWM output line from the Arduino , with its own LED+resistor, to monitor the state of the circuit if you want. Just add the appropriate statements in your sketch code for another PWM pin. And you won't need a separate switching transistor, you can just run the monitor LED+resistor directly from the second PWM output pin.
Or, if you need to know the actual state of the mosfet switching the heating load, you can put an LED+resistor in parallel with the heater resistor load.
By now it should be easy to wire it up and program it!
(ETA2: I see in the Fritzing program, the breadboard type "full" has the power rails split into left and right halves like your breadboard (but doesn't have the red and blue lines.) The breadboard type "full+" has the power rails continuous all the way across and has the red and blue lines. I have both types of breadboards on my bench, and this gave me fits too when I first used one with the split L and R rails.)