Engr 16 Todays Topics Sinusoidal Voltages Currents Instantaneous

Engr 16 Today’s Topics Sinusoidal Voltages & Currents Instantaneous Power Average Power RMS (Root Mean Squared) Complex Numbers Phasor Representation

Sinusoids Angular frequency w=2 pf (rad/sec or /sec) Frequency f = w/2 p (Hz) Period T=1/f (sec) Phase Shift q (in degrees or radians) Offset = DC = Average Voff = Vave = 1/T ∫v(t)dt Amplitude (magnitude) Peak-to-Peak RMS Root Mean Squared Vp = 1/2 Vp-p = 2 Vp Vrms = sqrt(1/T ∫v(t)^2 dt)

Power (Watts) Average Power Pave = 1/T ∫p(t)dt = 1/T ∫v(t)i(t)dt for a resistor… Pave = 1/T ∫v(t)^2/Rdt =1/T ∫v(t)^2 dt /R =Vrms^2/R or Irms^2*R or Irms. Vrms RMS Shortcuts (no DC Offsets) Sinusoids Vrms = 1/√ 2 Vp Triangle Vrms = 1/√ 3 Vp Square Vrms = Vp DC only Vrms = Vp

Complex Number Review Complex numbers work like vectors Use for impedances and phasors Calculator uses () for complex

Homework Hints Prob 6. 4: The phase can be entered in degrees, if the ° symbol is put in the units section Prob 6. 6: The phase shift needs to be entered in radians, i. e. 15° is 15π/180 Prob 6. 11: Vince no like their units… they give credit for just V when the correct units need to be Vrms. And Vrms is wrong!? ! Prob 6. 13: The phase shift is 1/6 of a cycle, figure out the radians and the +/-.

Phasors V=VR+VL+VC