In the given L-C-R circuit the value of rms current through the a. c. source is

$$\begin{gathered} V_1^2+V_2^2=V^2 \\ \frac{V_1}{X_L}-\frac{V_1}{X_C}=i \\ {V}_1(\frac{1}{\omega L}-\omega C)=i \end{gathered}$$

$$\begin{gathered} V_1=\frac{\omega Li}{1-{\omega }^{2}LC} \\ {V}_2=iR \\ \frac{{\omega }^2{L}^2}{{(1-{\omega }^{2}LC)}^2}+R^2=\frac{V^2}{i^2} \\ i=\frac{V}{\sqrt{R^2+\frac{{\omega }^2{L}^2}{{(1-{\omega }^{2}LC)}^2}}} \end{gathered}$$