The problem is, enhancement mode MOSFETs have a Vgs threshold, below which they basically don't conduct. The threshold varies with part number, and even quite a bit among individual units of the same part number, but it is always on the order of volts - not millivolts. Below is the V-I curve of a diode-connected (Vgs=Vds) IRF530, which I picked at random from the LTspice model collection that I have. The IRF530 is spec'ed at Rds=0.11 ohms max with Vgs=10V. However, it's maximum threshold voltage (Vgs=Vds, Id=250uA) is 4 volts. The curve below is actually a plot of that worst-case part. The minimum threshold voltage is 2 volts.What I mean is with an RDSon of less than an ohm and a current of, say, 1 amp, the voltage drop across the mosfet will be less than 1V. That means, the Vgs (if the gate is tied to Vcc) will also be less than a volt. At least that is the way it is explained in the IR literature.
I think we are saying the same thing, namely that Vgs need to be 10V for regular mosfets. If you notice the times on our posts, I was writing while you were posting. I don't think mine adds anything to your post, except introduction of the term Vds. John
Edits: I mean Vgs not Vds
Edit#2: BTW, I notice the OP wants something on the order of a 60 second delay. The left circuit works fine for a few hundred ms, but would keep the mosfet in the linear region for a relatively long time , if one had it set for a 60 second delay. For such long delays, I would consider something like a comparator between the switching transistor and the RC timer to give a rapid turn-on/turn-off period.
In the plot below, you can see that, with Vds=5V, Id~2.5A (Pdiss=12.5W). With a 12V supply, this would occur with Rload~2.8 ohms. You only get 7V across that load.
However, if Vgs=10V (Rds=0.11 ohms), Vds would only be about 450mV, and Id~4.1A (Pdiss=1.9W).
I have included the LTspice .asc file, in case anyone wants to play with the sim.
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