Impedance of an RLC Circuit

In this simulation, a 100 W resistor, a 50 mH inductor, and a 20 microF capacitor are connected in series with a 10-Volt (maximum) AC source. The graph shows the voltage across each of the components as function a of time in different colors, and the source voltage in black. Vary the value of the source's angular frequency (5 rad/s < w < 5000 rad/s ) using the slider. What is the impedance of the circuit?  How do the voltages across the components add up?

Hints:

  1. At one frequency, use the cursor to measure the maximum voltage across each component.  Do they add up to the maximum source voltage?
  2. At one frequency and one time, use the cursor to measure the voltage across each component.  Do they add up to the source voltage?
  3. Why don't both approaches work?  Does one take something else into account?  What?
  4. What is the relationship between the times at which the maximum voltages occur?  
  5. Is there a way to "add" the maximum voltages so that they add to the maximum source voltage?  Refer to the calculation of impedance for an example.

Reference

See Serway and Beichner, Physics For Scientists and Engineers 5th Edition, Section 33.5

Illustration written by Chuck Niederriter