GATE 2026 EC – Question 60
An $n$-channel MOSFET is connected as shown in the Figure. Assume $V_{TH}=1$ V, $V_{DD}=5$ V, and $\mu C_{ox}(W/L)=2$ mA V$^{-2}$ and neglect channel length modulation effects. The gate voltage ($V_G$) of the $n$-channel MOSFET (in Volt) is ________. (rounded off to two decimal places)
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Correct answer: 2.55 to 2.57
Explanation
With gate tied to drain the device is saturated: $I_D=\tfrac12(2\text{ mA/V}^2)(V_G-1)^2=(5-V_G)/1\text{k}$. So $(V_G-1)^2=5-V_G$, i.e. $u^2+u-4=0$ with $u=V_G-1=(-1+\sqrt{17})/2=1.56$, giving $V_G\approx2.56$ V.