The Series RLC Circuit — Question 1

Question 1

A series RLC voltage sum is a phasor sum rather than a sum of amplitudes

A series circuit has R=40.0 ohms, L=.0500 H, and C=50.0 microfarads. It is driven at $\omega=1000$ radians per second by 100 V rms. All components are ideal.

1. Find impedance magnitude, rms current, and current lag.

2. Find each component rms voltage and verify the source voltage.

Question 1 - Solution

A series RLC voltage sum is a phasor sum rather than a sum of amplitudes

(a) Method and calculation

$$X_L=50.0\,\Omega,\quad X_C=20.0\,\Omega,\quad Z=\sqrt{40^2+30^2}=50.0\,\Omega.$$$$\boxed{I=2.00\,A,\quad\phi=\tan^{-1}(30/40)=36.8699^\circ\ \text{lag}}.$$

(b) Interpretation and further calculation

$$V_R=80.0\,V,\quad V_L=100\,V,\quad V_C=40.0\,V.$$$$\boxed{V=\sqrt{V_R^2+(V_L-V_C)^2}=100\,V}.$$

Physical check

Inductor and capacitor voltage phasors point in opposite quadrature directions.