\(P=E_{ rms } I_{ rms } \cos \phi\)
\(\cos \phi=\frac{R}{Z}\)
\(\cos \phi=1 \text { for resistor }\)
\(V_{ rms }=\frac{V_0}{\sqrt{2}}\)
\(P=\frac{V_0}{\sqrt{2}}, \frac{V_0}{R \sqrt{2}}(1) \quad\left(\because I_{ ms }=\frac{V_{ rms }}{R}=\frac{V_0}{R \sqrt{2}}\right)\)
\(P=\frac{V_0^2}{2 R}\)