Discussion
At \( V_{GS} = -2 \ \mathrm{V} \) that device's transconductance falls to
Answer: C
Transconductance falls linearly towards pinch-off:
\[ \begin{aligned} g_{m} &= g_{m0}\left(1 - \tfrac{-2}{-4}\right) \\ &= 4 \times 0.5 \\ &= 2 \ \mathrm{mS} \end{aligned} \]
so 2 millisiemens. Halving is right here because the transconductance is the derivative of a square and so is linear in gate voltage, even though the current itself falls to a quarter. Knowing which quantity is linear and which is squared avoids applying the wrong factor.
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