MOSFET Circuit Analysis Gate Drain shorted

[hioyo]

Below is my circuit and its DC simulation result are shown below. The mosfet datasheet is available here.

May I know how to find the voltage across the 1k resistor mathematically?

I know that the MOSFET is operating in saturation region. Vgs>Vth

My approach is equating Vgs to Vth.

Vg-Vs = Vth

Vg- Voltage drop across 1K = 3.38

Therefore Voltage across 1K = Vg-3.38 = 36.62V

May I know this approach is correct or not

 

[FvM]

May I know this approach is correct or not

Not exactly. Vgs in operation point is > Vth. You can calculate according to idealized quadratic MOSFET characteristic or by reading actual Vgs from datasheet curves.