1. Cleaning Up
November 28, 2005

2. 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 !

3. THE TEST

4. 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)

5. 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.

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

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

8. 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!)

9. 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.

10. 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)

11. 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.

12. Some math …. (sorry!)
Check Graph

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

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

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

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

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

18. VR
wt-f VL VT f
900-f wt

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

20. Resonance Curve

21. What about power??

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

23. That's All Folks!