1. AC Fundamentals Radians Converting Between Radians and Degrees
Frequency and Period
Angular Velocity
Generated Angle
Instantaneous Current and Voltage
Effective Value of ac Current or Voltage
Capacitance and Inductance

2. Radians
Key Point:
When the length of an arc equals the length of the radius of a circle, the angle is equal to 1 radian.
One radian = 57.3°.

3. Converting Between Radians and Degrees
To convert from radians to degrees:
Convert 85o to radians
Convert 3.42 radians to degrees
angle = 37°

4. Frequency and Period
The frequency (f) is the number of times per second that we generate a sine wave.
The period (T) is the time it takes to generate one complete sine wave.
T = 400 μs. Find f
f = 1/T
T = 1/f
f = 15 kHz. Find T

5. Angular Velocity
Angular velocity, ω, is the angular motion or speed of a rotating vector or phasor.
Angular velocity is measured in radians per second or in degrees per second.
ω = 2πf
ω = 360o f

6. Generated Angle
The generated angle at any instant, t, can be calculated as:
angle in radians = 2πft = ωt angle in degrees = 360° ft = ωt
Self-Test #4, 5, 6
Given: f = 2kHz t = 100 μs
ωt = 1.26 rad ωt = 72.0°

7. Instantaneous Current and Voltage
In ac circuits, instantaneous values of current and voltage may be found using the following equations:
i = Ipk sin ωt
e = Epk sin ωt
Self-Test #1, 2
Let Ipk = 40 mA, Epk = 12 V, and f = 5 kHz
Find i and e after 70 μs
i = 40 mApk sin ωt
= 32.4 mAt
e = 12 Vpk sin ωt
= 9.71 Vt

8. Effective Value of ac Current or Voltage
The rms or effective value of an ac voltage or current is the value that converts the same energy as does a dc value.
The rms value equals of the maximum or peak of a sine wave.
Irms = Ieff = Ipk
Vrms = Veff = Vpk
Ipk = 1/ Ieff = Irms
Vpk = 1/ Veff = Vrms

9. Capacitance and Inductance
Key Point:
Whenever we have capacitance or inductance in an ac circuit, the current and voltage are out of phase. When the phase angle, theta, θ, is known, we can calculate the instantaneous values of current and voltage.
When current is the reference,
i = Ipk sin ωt
e = Epk sin (ωt  )
When voltage is the reference,
e = Epk sin ωt
i = Ipk sin (ωt  )
Self-Test #5