Given data

• Resistance: $R = 4\,\Omega$
• Capacitive reactance: $X_C = 4\sqrt{3}\,\Omega$
• Peak voltage: $V_0 = 8\sqrt{2}\,\text{V}$

Find the rms voltage For an AC source, $V_{\text{rms}} = \frac{V_0}{\sqrt{2}} = \frac{8\sqrt{2}}{\sqrt{2}} = 8\,\text{V}$

Find the impedance of the series RC circuit Magnitude of impedance: $Z = \sqrt{R^2 + X_C^2}$ $Z = \sqrt{4^2 + (4\sqrt{3})^2} = \sqrt{16 + 48} = \sqrt{64} = 8\,\Omega$

Find the rms current $I_{\text{rms}} = \frac{V_{\text{rms}}}{Z} = \frac{8}{8} = 1\,\text{A}$

Compute power dissipation In an RC circuit, only the resistor dissipates power: $P = I_{\text{rms}}^2 R$ $P = (1)^2 \cdot 4 = 4\,\text{W}$

Final answer $\boxed{4}$

Comparison with stored answer Stored correct answer = $4$

My derived answer matches the stored answer.