Chapter Contents

• Complex Numbers
• 1. Basic Definitions
• 2. Basic Operations
• 3. Graphical Representation
• 4. Polar Form
• Convert polar to rectangular using calculator
• 5. Exponential Form
• 6. Products and Quotients
• 7. Powers and Roots
• 8. AC Circuit Definitions
• 9. Impedance and Phase Angle
• 10. Reactance and Angular Velocity
• 11. AC Circuit Exercises
• 12. Parallel AC Circuits
• Vocabulary
• Fractals
• Complex Numbers Problem Solver

• Comments, Questions?

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From the math blog...

10. Reactance and Angular Velocity - Alternating Currents

by M. Bourne

Alternating Currents

An alternating current is created by rotating a coil of wire through a magnetic field. If the angular velocity of the wire is ω, the

capacitive reactance is given by:

`X_C=1/(omegaC)`

inductive reactance is given by:

X_L = ωL

Example

If R = 10 Ω, L = 0.6 H, C = 200 μF and ω = 50 rad/s, find the magnitude of the impedance and the phase difference between the current and the voltage.

Answer

Angular Velocity and Frequency

In this section, recall that angular velocity and frequency are related by the expression:

ω = 2πf