GATE 2014 EC (EC1) – Question 46
A depletion N-channel MOSFET is stated to operate in its linear region as a voltage-controlled resistor. Given $V_{TH}=-0.5$ V, $V_{GS}=2.0$ V, $V_{DS}=5$ V, $W/L=100$, $C_{ox}=10^{-8}$ F/cm² and $\mu_n=800$ cm²/(V·s), find its resistance (Ω).
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Correct answer: 499 to 501
Explanation
The intended small-drain-voltage linear-region formula is R≈1/[µnCox(W/L)(VGS−VT)]. Here µnCox(W/L)=800×10⁻⁸×100=8×10⁻⁴A/V² and VGS−VT=2.5V, giving R=1/0.002=**500Ω**, the official answer. However the printed VDS=5V exceeds the2.5V overdrive and violates the stated linear-region condition; it cannot be used as a consistent operating point for this approximation.