Since the drain voltage is lower than the gate voltage by 4.9 V and $V_t=1 \mathrm{~V}$, the MOSFET is operating in the triode region. Thus the current $I_D$ is given by

$$
\begin{aligned}
I_D & =k_n^{\prime} \frac{W}{L}\left[\left(V_{G S}-V_l\right) V_{D S}-\frac{1}{2} V_{D S}^2\right] \\
I_D & =1 \times\left[(5-1) \times 0.1-\frac{1}{2} \times 0.01\right] \\
& =0.395 \mathrm{~mA}
\end{aligned}
$$

The required value for $R_D$ can be found as follows:

$$
\begin{aligned}
R_D & =\frac{V_{D D}-V_D}{I_D} \\
& =\frac{5-0.1}{0.395}=12.4 \mathrm{k} \Omega
\end{aligned}
$$


In a practical discrete-circuit design problem one selects the closest standard value available for, say, $5 \%$ resistors-in this case, $12 \mathrm{k} \Omega$; see Appendix G. Since the transistor is operating in the triode region with a small $V_{D S}$, the effective drain-to-source resistance can be determined as follows:

$$
\begin{aligned}
r_{D S} & =\frac{V_{D S}}{I_D} \\
& =\frac{0.1}{0.395}=253 \Omega
\end{aligned}
$$