Physics 2420 In-Class Problems: Complex Impedance

Complex Number Exercises

1. Verify

   (a)     (b)     (c)

2. Convert the following to the form re^j:

   (a)     (b)     (c)

3. Express the following in the form a+jb:

   (a)     (b)     (c)

   (d)     (e)     (f)
   

Complex Impedance

1. Calculate the equivalent impedance for the circuit in the diagram below at a frequency of 100 Hz. Repeat for 1000 Hz.
   

2. Determine the current and RMS voltages across each component in the series LCR circuit shown below at a frequency of 900 Hz. Show that, considering the phase angles of the voltages, Kirchhoff's rule concerning voltages about a loop is valid.
   

3. Determine the RMS current in the 1000 Ω resistor in the circuit below. Is the current inductive or capacitive?
   

4. The diagram below represents a real inductor, i.e. one with a small resistance, in parallel with a capacitor. Obtain an expression for the complex impedance as a function of Ω. Plot 1/Z versus Ω to determine the resonance frequency. What is the impedance at resonance?
   

Questions? mike.coombes@kwantlen.ca