Topic 4: AC Waveforms

Sine Wave (Degrees and Radians)

• Circumference of a Circle: ( C = 2\pi )
  • For a circle with radius = 1 unit, the circumference ( C = 2\pi )
• Conversions:
  • 360° = 2π radians
  • 180° = π radians
  • 1° = ( \frac{\pi}{180} ) radians
  • Sine wave rotates 360 degrees or 2π radians per cycle

Sine Wave (Angular Velocity)

• Definitions:
  • Frequency = 10 Hz
  • Period = ( \frac{1}{f} ) seconds
  • Angular velocity ( \omega = 2\pi f )
  • Total angle in 1 second = ( 2\pi f ) radians

Examples

• Example 4.1: Convert angles from degrees to radians
  • 30°, 45°, 420°, 77°
• Example 4.2: Convert radians to degrees
  • 3π, ( \frac{5\pi}{4} ), 1 rad, 0.32 rad

Sine Wave (General Form)

• General equation: ( V = V_m \sin(\omega t + \phi) )
• Phase Relations:
  • Positive phase shift: waveform shifts left
  • Negative phase shift: waveform shifts right

Practical Applications

• Example 4.3: Frequency and time relations for sinusoidal waveforms
  • Given f = 50 Hz
  • Calculate time for 1 cycle, angular velocity, time for 60°
• Example 4.4: Sinusoidal voltage waveform ( v = 325 \sin(628t) )
  • Find period, sketch waveform, and degrees per second

Average / Effective (RMS) Values

• Definitions:
  • RMS value is the DC equivalent power value
  • ( V_{rms} = \frac{V_{peak}}{\sqrt{2}} )
• Examples
  • Example 4.9: Calculate RMS and equivalent DC voltage
  • Example 4.10: Compare DC and AC power delivery

Summary

• Sine waveforms are periodic and have specific angular velocity and frequency characteristics
• Conversion between degrees and radians is crucial in AC waveform analysis
• RMS values provide a basis for comparing AC and DC power delivery