The impedance $Z$ of the circuit is:
\(Z = \sqrt{R^2 + X_C^2} = \sqrt{4^2 + (4\sqrt{3})^2} = \sqrt{16 + 48} = \sqrt{64} = 8 \, \Omega.\)
The RMS voltage is:
\(V_\text{rms} = \frac{V_\text{peak}}{\sqrt{2}} = \frac{8\sqrt{2}}{\sqrt{2}} = 8 \, \text{V}.\)
The RMS current is: \(I_\text{rms} = \frac{V_\text{rms}}{Z} = \frac{8}{8} = 1 \, \text{A}.\)
Power dissipation in the resistor is: \(P = I_\text{rms}^2 R = 1^2 \times 4 = 4 \, \text{W}.\)