## Exploration 31.6: RLC Circuits and Phasors

Please wait for the animation to completely load.

Assume an ideal power supply. The graph shows the voltage as a function of time across the source **(red)**, the resistor **(blue)**, the capacitor **(green)**, and the inductor **(yellow)**, as well as the current through the circuit **(black) (voltage is given in volts, current is given in milliamperes, angles are given in degrees, and time is given in seconds)**. Restart.

From the vectors on the phasor diagram, we can develop a connection between the peak (or rms) voltage and the peak (or rms) current, where V_{0} = I_{0} Z and the phase difference between the voltage and current is given by φ. On the phasor diagram V_{0} (**the source voltage-red**) is the vector sum of the three voltage vectors (**resistor-blue**, **inductor-yellow**, and **capacitor-green**) and φ is the angle between V_{0} and the resistor phasor (since resistor current and voltage are in phase). The y components of the phasor vectors are the voltages across the various circuit elements. See Illustrations 31.6 and 31.7 as well as Exploration 31.5.

- Explain the phase difference between the blue, yellow, and green vectors in the phasor animation.
- Pick a frequency and pause the animation. Verify that the red vector is the vector sum of the other three vectors.
- Pick a frequency and measure φ on the phasor diagram using the pink protractor.
- Explain how you can tell that the phasor animation matches the voltage and current vs. time graph for the circuit.
- Also measure the phase angle on the voltage and current graphs. To measure the phase angle, since one period (1/ƒ) represents a phase shift of 2π, measure the time difference between the peaks of the voltage and current plots and divide by the period.
- Measure Z for this same frequency (Z = V
_{0}/ I_{0}). - Check your answers by using the equations for impedance and the phase shift between the voltage and the current, Z = (R
^{2}+ (ωL - 1/ωC)^{2})^{1/2}and cosφ = R/Z.

Exploration authored by Anne J. Cox.

Script authored by Wolfgang Christian and Anne J. Cox.