If the diode in the circuit shown in Figure P8. 15 is fabricated from silicon and:
$$
i_D=I_{\Delta}\left[e^{v_D / V_y}-1\right]
$$
where at $T=300 \mathrm{~K}$ :
$$
\begin{aligned}
& I_s=250 \times 10^{-12} \mathrm{~A} \quad V_T=\frac{k T}{q} \approx 26 \mathrm{mV} \\
& v_S=4.2 \mathrm{~V}+110 \mathrm{cos}(\omega t) \mathrm{mV} \\
& \omega=377 \mathrm{rad} / \mathrm{s} \quad R=7 \mathrm{k} \Omega
\end{aligned}
$$
and the DC operating point or quiescent point ( $Q$ point) is:
$$
I_{D Q}=0.5458 \mathrm{~mA} \quad V_{D Q}=379.5 \mathrm{mV}
$$
determine the equivalent small-signal $A C$ resistance of the diode at room temperature at the $Q$ point given.