For the DC analysis, the capacitors can be replaced by open circuits.
Since \(I_G \simeq 0\ A\), the voltage across \(R_G\) is equal to \(0\ V\).
\(V_{GG} + V_{GS} = 0\)
\(\boxed{V_G = V_{GS} = -V_{GG}}\)
Drain current \(I_D\) can be found using Shockley’s equation:
\(\boxed{I_D = I_{DSS} \left( 1 - V_{GS} / V_P \right) ^ 2}\)
\(-V_{DD} + I_D R_D + V_{DS} = 0\)
\(\boxed{V_D = V_{DS} = V_{DD} - I_D R_D}\)
\(\boxed{V_S = 0\ V}\)