1. ENGS2613 Intro Electrical Science Week 15 Dr. George Scheets
Read: 10.1 – 10.4, 10.6
Problems: 10.2, 4, 5, 6, 11, 12, 18, 41, & 43
Quiz 8 Results Hi = 10, Lo = 1.5, Ave = 7.29, Deviation = 2.04 Versions A & B +1 point
Take Home Project Results Hi = 30, Lo = 0, Ave = 28.67, Deviation = 2.34

2. Final Exam Closed Book & Neighbor
Up to 4 unattached sheets of notes OK Keep on your desk Have them on hand before you start
No Textbooks
Calculator OK
Smart Phones NOT OK
Reaching down for something in backpack?
Get permission first

3. Final Exam
Friday, 12 May, 1000 – 1150
4 pages, comprehensive, 1 hour & 50 minutes
R circuit, Opamp, Phasor, Something Else
10 pt Extra Credit Thevenin Equivalent of Circuit with Dependent Source
No TA Office Hours during Finals Week
Though they will respond to ed questions
Final Exam Review Session Wednesday, 10 May, 7:00 – 9:00 pm ES 317
Instructor Available Thursday, 11 May, 10:00 am – 5:00 pm

4. What to Study? Electrical Science Notes & Homework Power Point
Problems
Readings
Anything in the
circles is fair game.
Overlaps more
likely.

5. Calculus You Might Need on Final
Integrals or Derivatives (with respect to time t) of…
time raised to some power (i.e. tα)
sines or cosines; e.g. sin(2πft)
et raised to some power (i.e. eαt)
integral of form 1/x = ln(x)

6. Quiz 7A Transfer Function H(f)
Vout = VinH(360) = (8∟328º)∙ (1.299∟-1.52º) = 10.39∟326.5 º

7. Quiz 7B Transfer Function H(f)
Vout = VinH(300) = (4∟21º)∙ (0.181∟74.21º) = 0.724∟95.21 º

8. Quiz 7C Transfer Function H(f)
Vout = VinH(400) = (6∟101º)∙ (0.786∟38.18º) = 4.716∟139.2 º
Null occurs when Zeq denominator = 0 at f = Hz
Here jωL || 1/(jωC) = ∞

9. Increasing R

10. RLC Bandstop Filter Vout/Vin ≡ H(f) H(f) = R/(L||C + R) EKG or EEG
Weak Signals contaminated by 60 Hz
Run thru Narrow Bandstop to eliminate 60 Hz

11. Eyeballing Filter Type
Examine at ω = 0 & ω = ∞ rads/sec
Output at ω = 0 > Output at ω = ∞ Probably Low Pass
Output at ω = 0 < Output at ω = ∞ Probably High Pass
Output at ω = 0 close or equal to zero Output at ω = ∞ close or equal to zero Probably Band Pass
Output at ω = 0 ≈ Output at ω = ∞ both > 0 Probably Band Reject

12. 2R & 2C Circuit
Vout = VinH(350) = (5∟239º)∙ (0.15∟-51.65º) = 0.75∟187.4 º

13. What kind of volts? Have a Time Varying Signal? Specify type of volts.
Vrms
Take square root of time average of waveform squared
Delivers same average power as DC Voltage of same value
Vpeak
Max + or – swing from average voltage
Average Voltage = Volts DC
Vpeak-to-peak
Max + swing minus Max - swing

14. Power P = VI (for DC) p = vi (for a time varying signal)
p = Vpcos(ωt + θv)Ipcos(ωt + θi) = [VpIp/2]{cos(θv - θi) + cos(2ωt + θv + θi)}
for a sinusoid waveform
Power Factor
Average Power
Instantaneous Power

15. Power in a Resistor p = vi (for a time varying signal)
p = Vpcos(ωt + θv)Ipcos(ωt + θi) = [VpIp/2]{cos(0) + cos(2ωt + 2θv)}
for a sinusoid waveform
Power Factor
Average Power
Instantaneous Power

16. 100 Hz Cosine thru Capacitor
v = C (dv/dt)
Current leads Voltage by 90º
=1/4 wavelength
= (1/4)(1/100)
= 1/400 second

17. ELI the ICE man. E = IR Voltage leads current Inductor
E = voltage here
Voltage leads current
Inductor
Current leads voltage
Capacitor

18. Capacitor Current, Voltage, & Power+ -
On 1st Power 1/2 cycle, v and i are positive, and capacitor is absorbing power.
On the 2nd Power 1/2 cycle, i goes negative and the current direction flips. The capacitor is now releasing the absorbed power.

19. Power in a Capacitor p = vi (for a time varying signal)
p = Vpcos(ωt + θv)Ipcos(ωt + θi) = [VpIp/2]{cos(-90º) + cos(2ωt + 2θv + 90º)}
for a sinusoid waveform
Power Factor
Average Power
Instantaneous Power

20. Power p = vi (for a time varying signal)
p = Vpcos(ωt + θv)Ipcos(ωt + θi) = [VpIp/2]{cos(-90º) + cos(2ωt + 2θv + 90º)}
for a sinusoid waveform
0 < Power Factor < 1
Current can't lead or lag voltage by more than 90º
Power Company wants this = 1
Power Factor
Average Power
Instantaneous Power

21. Maximizing Power Delivered to Load
Both Adjustable
Decrease Rsource & Rload as much as possible
Cancel Reactive Component
Neither Adjustable
Use Capacitance or Inductance & Cancel Reactive Component
Source Impedance Adjustable, Load Not?
Decrease Rsource as much as possible
Load Impedance Adjustable, Source Not?
Set Zload = Z*source

22. Reducing Line Impedance to 0
250/0ᵒ
Load
39 + j26
46.87/33.69ᵒ
Power to load was watts
When Zline = 1 + j4
Average load power now = watts
Power to load was watts
When Zline+capacitor = 1 – j26

23. Reducing Line Resistance to 0 & Canceling Reactance
0 - j26
250/0ᵒ
Load
39 + j26
46.87/33.69ᵒ
Power to load = watts when Zline = 1 + j4
Power to load = watts when Zline = 0
Power to load was watts Zline+capacitor = 1 – j26
Power to load = watts when Zline = -j26