In an L-C-R series circuit, power is dissipated only in the resistor, as the average power over a cycle for pure inductors and capacitors is zero. The average power dissipated is given by $P = I^2 R$, where $I$ is the rms current . The rms current is given by $I = \varepsilon / Z$, where $\varepsilon$ is the rms emf and $Z$ is the impedance. The impedance $Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{R^2 + (L\omega - \frac{1}{C\omega})^2}$ . Substituting $I$ into the power equation: $P = \left( \frac{\varepsilon}{Z} \right)^2 R = \frac{\varepsilon^2 R}{Z^2} = \frac{\varepsilon^2 R}{R^2 + (L\omega - \frac{1}{C\omega})^2}$.