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Case \(I:\) \(P=V_{\text {rms }} I_{\text {rms }}\)

\(=V_{\mathrm{rms}} \times \frac{V_{\mathrm{rms}}}{R}\)

\(P=\frac{V_{\mathrm{rms}}^{2}}{R} \Rightarrow V_{\mathrm{ms}}^{2}=P R \ldots .(\mathrm{i})\)

Case \(II :\) Power drawn in \(L R\) circuit

\(P^{\prime}=V_{\mathrm{rms}} I_{\mathrm{rms}} \cos \phi=V_{\mathrm{rms}} \times \frac{V_{\mathrm{rms}}}{Z} \times \frac{R}{Z}\)

\(=V_{\mathrm{rms}}^{2} \frac{R}{Z^{2}}=P R \times \frac{R}{Z^{2}}\)

[Using eqn \((\mathrm{i})]\)

\(P^{\prime}=P \frac{R^{2}}{Z^{2}}\)