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Given\begin{array}{l}k_{n-}=\operatorname{smnlV^{2}} \\V_{T}=2 \mathrm{~V} \\V_{4 S}=5 \mathrm{~V}\end{array}(a)\begin{aligned}V_{D S}(\text { Sat) }) & =V_{\text {GSS }}-V_{T} \\& =5-2=3 V \\V_{D S} & =3 V \text { Answer. }\end{aligned}(6.) if the morer is operated is the satcosation regran wixd V_{A S}=12 K\begin{aligned}I_{D} & =\frac{1}{2} \mu_{n} C_{0 \times} \frac{w}{L}\left(V_{\left.c_{1 s}-r_{4}\right)^{2}}\right. \\& =\frac{K_{n}}{2}\left(V_{15-4}\right)^{2} \\& =\frac{5}{2}(3)^{2} m A \\& =\frac{5}{2} \times 9 \mathrm{~mA}=22.5 \mathrm{~mA} \\& I_{D}=22.5 \mathrm{~mA} \quad \text { Answer }\end{aligned}(c)\begin{array}{l}g_{m}=\frac{5 I_{D}}{3 V_{M S}}=\mu_{b} c_{0} \frac{N}{L}\left(V_{4 s}-V_{4}\right) \\=k_{n}\left(V_{G S-r_{T}}\right) \\=5 \times 3 \mathrm{~mA} / \mathrm{V} \\=15 \mathrm{~ms} \\g_{m}=15 \mathrm{~ms} \text { AnsweL } \\\end{array}(d) if the moseET is opcuated is the satumation region with r_{\text {ps }}=0.5 \mathrm{~V}\begin{aligned}I_{D} & \left.=k_{n}\left(V_{G S}-V_{T}\right) V_{D S}-\frac{V_{D S}{ }^{2}}{2}\right) \\& =5\left[3 \times 0.8-\frac{(0.8)^{2}}{2}\right] \mathrm{mA}=10.4 \mathrm{~mA} \\& I_{D}=10.4 \mathrm{~mA} \text { Answer }\end{aligned}(e.)\begin{array}{l}g_{m}=\left.\frac{\Delta I_{0}}{\Delta V_{M S}}\right|_{V D=0} 0 \\g_{m}=I_{D} / V_{\text {HS }}=\frac{22.5 \mathrm{~mA}}{5 \mathrm{~V}}=4.5 \\g_{m}=4.5 \text { Answan }\end{array} ...