The Series RLC Circuit — Question 2

Question 2

Three component voltmeters can reconstruct the source phase

In a series RLC circuit, ideal rms meters read $V_R=60.0$ V, $V_L=120$ V, and $V_C=40.0$ V. R=30.0 ohms and $\omega=500$ radians per second.

1. Find source rms voltage and current phase.

2. Infer L and C.

Question 2 - Solution

Three component voltmeters can reconstruct the source phase

(a) Method and calculation

$$I=V_R/R=2.00\,A,\quad V=\sqrt{60^2+(120-40)^2}.$$$$\boxed{V=100\,V,\quad\phi=\tan^{-1}(80/60)=53.1301^\circ\ \text{lag}}.$$

(b) Interpretation and further calculation

$$L=V_L/(\omega I)=120/(500\cdot2).$$$$\boxed{L=.120\,H,\quad C=I/(\omega V_C)=100\,\mu F}.$$

Physical check

The component readings determine both the net reactive sign and the element values.