1. Sinusoidal Sources Voltage or Current Sin or Cos
In our case, choose cos and write in general
ECE 201 Circuit Theory I

2. Graphically
ECE 201 Circuit Theory I

3. Vm = amplitude, or maximum value of the signal (volts)
T = period of the signal (seconds)
f = 1/T = frequency of the signal (Hertz)
ω = 2πf = angular frequency of the signal (radians/sec)
Φ = phase angle (radians)
ECE 201 Circuit Theory I

4. Average value of a sinusoid
ECE 201 Circuit Theory I

5. rms value of a sinusoid
ECE 201 Circuit Theory I

6. Detailed calculation of rms
ECE 201 Circuit Theory I

7. What does rms mean?
Determine the average power delivered to the resistor by the sinusoidal voltage source +
Vmcos(ωt+θv) -
ECE 201 Circuit Theory I

8. If Vrms = 100V, it delivers the same amount of power to the resistor as a 100V DC source, or it is effectively equivalent to a DC source of the same magnitude.
ECE 201 Circuit Theory I

9. Rms and “Effective Value”
rms value and “effective value” are used interchangeably
ECE 201 Circuit Theory I

10. Practical Example Consider the voltage at a standard household outlet
The rms voltage is 120 Volts
The peak voltage Vm is determined as
ECE 201 Circuit Theory I