1. ECE 201 Circuit Theory I1 Sinusoidal Sources Voltage or Current Sin or Cos In our case, choose cos and write in general

2. ECE 201 Circuit Theory I2 Graphically

3. ECE 201 Circuit Theory I3 V m = 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)

4. ECE 201 Circuit Theory I4 Average value of a sinusoid

5. ECE 201 Circuit Theory I5 rms value of a sinusoid

6. ECE 201 Circuit Theory I6 Detailed calculation of rms

7. ECE 201 Circuit Theory I7 What does rms mean? Determine the average power delivered to the resistor by the sinusoidal voltage source + V m cos(ωt+θ v ) -

8. ECE 201 Circuit Theory I8 If V rms = 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.

9. ECE 201 Circuit Theory I9 Rms and “Effective Value” rms value and “effective value” are used interchangeably

10. ECE 201 Circuit Theory I10 Practical Example Consider the voltage at a standard household outlet –The rms voltage is 120 Volts –The peak voltage V m is determined as