Discussion
In a JFET, the amplification factor \(\mu\), transconductance \(g_{m}\), and the dynamic drain resistance (\(r_{d}\)) are related as
Answer: C
The three JFET parameters are related by \(\mu = r_{d} \times g_{m}\), which is option (C). The amplification factor is the ratio of a change in drain-source voltage to the change in gate-source voltage that keeps the drain current constant, so
\[ \begin{aligned} \mu &= -\frac{\Delta V_{DS}}{\Delta V_{GS}} \\ &= \frac{\Delta V_{DS}}{\Delta I_{D}} \cdot \frac{\Delta I_{D}}{\Delta V_{GS}} \\ &= r_{d}\, g_{m} \end{aligned} \]
Options (A) and (B) are ratios, which have the wrong units for a dimensionless factor, and (D) squares the drain resistance, so the dimensions do not match either.
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