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I need to find the voltage across the 1k resistor in the below circuit.

My approach is given below. I would like to know if the way I am approaching this problem is correct or not.

The gate and drain are shorted so the MOSFET is always in saturation region.

The MOSFET will be on so Vgs>=Vth.

I am equating Vgs to Vth.

Vg-Vs = Vth

Vs is nothing but the voltage across 1k resistor.

Vg- Voltage drop across 1k = 3.38 V

Therefore the voltage across 1k = Vg-3.38 = 36.62 V

enter image description here

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    \$\begingroup\$ How many useful digits do you need on the answer? If you’re asking about practical circuits, then - given the parameter spread of physical mosfets - any theoretical answer would be only accurate to about +/-0.5V. You’d have to grade the mosfets to keep their threshold voltages closer than that. So, that 36.62V is wishful thinking. The last digit will be varying with ambient temperature as well. Eg. if you left this circuit in a hot car for 15 minutes and checked the voltage again, the last modeled digit wouldn’t be meaningful anymore. \$\endgroup\$
    – Kuba hasn't forgotten Monica
    Commented Aug 28, 2022 at 15:46
  • \$\begingroup\$ If all you need is to derive the same answer that SPICE provides: look up the mosfet model used, and do the calculations manually. You’ll get the same 4 digits, but I question the usefulness of doing it - since you won’t be getting that very voltage in practice, not unless you test hundreds or thousands of assembled circuits. \$\endgroup\$
    – Kuba hasn't forgotten Monica
    Commented Aug 28, 2022 at 15:50

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You are close, but if you need the precise answer you'll have to use the MOSFETs square law equations and the transconductance coefficient to calculate the exact VGS.

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