When the rms voltages $$V_L$$, $$V_C$$ and $$V_R$$ are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio $$V_L : V_C : V_R = 1 : 2 : 3$$. If the rms voltage of the AC source is 100 V, then $$V_R$$ is close to:

$$V = \sqrt{V_R^2 + (V_C - V_L)^2}$$

The given ratio of the RMS voltages is $$V_L : V_C : V_R = 1 : 2 : 3$$.

$$V_L = \frac{1}{3}V_R$$ and $$V_C = \frac{2}{3}V_R$$

$$V = \sqrt{V_R^2 + \left(\frac{2}{3}V_R - \frac{1}{3}V_R\right)^2}$$

$$V = \sqrt{V_R^2 + \frac{1}{9}V_R^2} = \sqrt{\frac{10}{9}V_R^2} = \frac{\sqrt{10}}{3}V_R$$

$$100 = \frac{\sqrt{10}}{3}V_R$$

$$V_R = 30 \times 3.162 \approx 94.86\text{ V}$$ (close to 95 V)