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

Graphically ECE 201 Circuit Theory I

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

Average value of a sinusoid ECE 201 Circuit Theory I

rms value of a sinusoid ECE 201 Circuit Theory I

Detailed calculation of rms ECE 201 Circuit Theory I

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

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

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

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