Cleaning Up November 28, 2005

TODAY Last week’s examination Finish up AC topics Begin Quick Review of Semesters Work Wednesday and Friday … Continue Review and putting things in perspective DO a few typical problems Next Monday … FINAL EXAMINATION !

THE TEST

CURRENT IS THE SAME THROUGHOUT THE CIRCUIT! RLC Circuit Current & Voltage in Phase in R. CURRENT IS THE SAME THROUGHOUT THE CIRCUIT! I=VR/R V=V0Sin(wt)

FOR EACH TYPE OF CIRCUIT ELEMENT, THE VOLTAGE AND CURRENT BEHAVE SOMEWHAT DIFFERENTLY. THE VOLTAGE ACROSS ANY ELEMENT WILL BE OUT OF PHASE WITH THE APPLIED VOLTAGE.

What have we done? We looked at each element (C, R, L) separately and looked at the voltages and currents. The results were-

Look at AC RL Circuit (No C) V=V0Sin(wt)

Remember for a Resistor and an Inductor Current in phase with the voltage. For our circuit, the voltage across the resistor is NOT the applied voltage! It also may be out of phase with the applied voltage. INDUCTOR The current in the inductor LAGS the voltage across the inductor by 900 or p/2. (The voltage also leads the current .. just to confuse matters more!)

Current The current through the circuit is the same throughout the circuit! IL=IR=Icircuit=I The current will not be in phase with the applied voltage so we need to include a phase shift in our calculations.

The RESISTOR Since voltage and current are in phase in a resistor, VR=I(t)R Using the same symbols, we can assume that I=I0Sin(wt-f). f is the phase difference. We chose it to be negative to agree with the textbook. Therefore: VR=I0R0Sin(wt-f)

Notice that plotting a voltage and a current on the same axes is not Phasor Notation VR (and current) wt-f V0 wt Applied Voltage Phasor Notice that plotting a voltage and a current on the same axes is not normally permitted. Watch what is plotted as we go along and be consistent.

Some math …. (sorry!) Check Graph

The Graph - Cos(q) = + Sin(q-900)

So … Graphical identification of f VR (and current) wt-f V0 wt Applied Voltage Phasor f

Moving Along … VR VL wt-f If current lags the voltage in the inductor by 900 then the voltage leads the current by 900. VR is the current.

The Geometry VT VR 900-f f wt VL wt-f

Back to the Loop VT VR 900-f f wt VL wt-f 1800 -(900 +(wt-f))=900-(wt-f)

VR wt-f VL VT f 900-f wt

And … VR wt-f VL VT f 900-f wt RESONANCE: XL=XC

Resonance Curve

What about power??

Continuing VR wt-f VL VT f 900-f wt

That's All Folks!