Power in an ac circuit, $$P = V_{rms}I_{rms}cos varphi$$ As rms values of current and voltage are also called effectivevalues i.e. $$P = V_{eff}I_{eff} cos varphi$$ But $$cos varphi = ext{power factor} = dfrac{R}{Z}$$ In a purely resistive circuit $$Z=R, cos varphi = 1$$ and $$i_{eff} = dfrac{V_{eff}}{Z} = dfrac{V_{eff}}{R}$$ Substituting these values in (i), we get $$P = V_{eff}cdot dfrac{V_{eff}}{R} imes 1 = dfrac{{V_{eff}}^{2}}{R}$$.