Consider the common source circuit shown in Figure 12.11(a) with a transistor that has output curves in Figure P12.12, and (a) determine a new value for $R_2$ that will place the $Q$-point on the $V_{G S}=2.5 \mathrm{~V}$ curve. (b) Plot the dc load line to locate the $Q$-point. (c) Compute an approximate value for $g_m$ at this $Q$-point. (d) Draw a small-signal equivalent circuit for this amplifier. (e) Using the equivalent circuit, calculate the small-signal voltage gain.