1. Alternating Current Part 1
6/17/2018
Voltages that Wiggle
PHY-2054
Alternating Current Part 1

2. or
Back to Trigonometry

3. This week We will do the lab session on the inductor’s time constant.
We will discuss what happens when the applied voltage is a sinusoid.
We will do some experiments on AC circuits
We will have a quiz on Friday.
NOTE: Start reading chapter 23! – AC Circuits

4. CALENDAR MONDAY WEDNESDAY FRIDAY 29 AC 5 WAVES EXAM III OPTICS 12 1926
EXAM IV
Date and Time of Final is being investigated.

5. ac generator – Similar to the motor but really different … whatever that means!

6. “Output” from the previous diagram

8. DC /AC

9. AC -All is “in-phase” for R

10. But not always! (capacitor)

11. so, Let’s talk about phase y=f(x)=x2

12. y=f(x-2)=(x-2)2 y x2
(x-2)2 2 x

13. the “rule” f(x-b): shift a distance b in the POSITIVE direction
f(x+b): shift a distance n in the NEGATIVE direction.
The signs switch!

14. The Sine

15. Let’s talk about PHASE f(t)=A sin(wt) A=Amplitude (=1 here)
f(t)=A sin(wt-[p/2])
A=Amplitude (=1 here)

16. A sine wave shifted by P radians is
cosine
- sine
-cosine
sine
tangent

18. For the future

19. AC Applied voltages This graph corresponds to an applied voltage
of V cos(wt).
Because the current
and the voltage are
together (in-phase) this
must apply to a Resistor
for which Ohmmmm said
that I~V.

20. oops – the ac phaser

21. the resistor

22. Phasor diagram
Pretty Simple, Huh??

23. here comes trouble ….
We need the relationship between I (the current through)
and vL (the voltage across) the inductor.

24. From the last chapter:
HUH??*
* unless you have taken calculus.

25. check it out---

26. so-
cancel
When Dt gets very small,
cos (wDt) goes to 1. ??

28. this leaves
The resistor voltage looked like a cosine so we would like the
inductor voltage to look as similar to this as possible. So let’s
look at the following graph again (~10 slides back):
f(t)=A sin(wt)
A=Amplitude (=1 here)
f(t)=A sin(wt-[p/2])
A=Amplitude (=1 here)

29. BREAK

30. AC GENERATION

31. Where bee we?
Equipment didn’t work on Monday but it should be working today. You finished all of the calculations in the previous hand-out.
Today we will begin with a look at LR circuits:
LR with a square wave input so you can determine the time constant.
LR with AC so you can look at phase relationships as well as inductive reactance
Add a capacitor and look at an RLC circuit to determine resonance conditions as well as phase relationships.
The previous will take at least one additional session. Maybe two!

32. Keepeth in Mind START STUDYING FOR EXAM III!!!
Note the appearance of a new WebethAssignment.
Quiz on Friday
Exam Next Wednesday – Magnetism  AC circuits
Monday – we will try to begin optics. Some of the AC may spill over into that session
Starting Monday, Dr. Dubey will take over the class as lead instructor. She is a better teacher than I am.
START STUDYING FOR EXAM III!!!

33. result - inductor
I is the MAXIMUM
current in the
circuit.

34. (wL) looks like a resistance
Resistor
inductor
(wL) looks like a resistance
XL=wL
Reactance - OHMS
comparing

35. Let’s put these together.
For the inductor
FOR THE RESISTOR
Let’s put these together.

36. slightly confusing point
We will always use the CURRENT as the basis for calculations and express voltages with respect to the current.
What that means?

37. the phasor

38. direction wt wt

39. remember for ac series circuits
The current is the
same throughout the
series circuit.
The Maximum Current “I”
is also the same for
all series circuit elements.

40. In the circuit below, R=30 W and L= 30 mH. If the angular frequency
of the 60 volt AC source is is 3 K-Hz
WHAT WE WANT TO DO:
calculate the maximum current in the circuit
calculate the voltage across the inductor
Does Kirchoff’s Law Work?
E=60V
R=30 W
L= 30 mH
w=3 KHZ

41. I wt R=30W w=3 KHZ R=30 W XL=wL=90W E=60V
L= 30 mH
w=3 KHZ
R=30W
XL=wL=90W
The instantaneous voltage across
each element is the PROJECTION
of the MAXIIMUM voltage onto
the horizontal axis!
This is the SAME as the sum of the
maximum vectors projected onto
the horizontal axis. I wt

42. I wt Source voltage leads the current by the angle f. w=3 KHZ R=30 W
L= 30 mH
w=3 KHZ

43. I wt The drawing is obviously NOT to scale. w=3 KHZ R=30 W E=60V
L= 30 mH
w=3 KHZ wt

44. Let’s look
at the
NUMBERS

45. wt
56.7Sin(wt)
18.9 cos(wt)
SUM
18.9
0.2
0.4
0.6
0.8 1
1.2
1.4

46. it does! 2p

47. What about the capacitor??
Without repeating what we did, the question is what function will have
a Df/Dt = cosine? Obviously, the sine! So, using the same process
that we used for the inductor,

48. capacitor phasor diagram

49. NOTICE THAT The voltage lags the current by 90 deg
I and V are represented on the same graph but are different quantities.

50. SUMMARY

51. For AC Circuits

52. Resonance

53. ac circuits look complicated
When you get a chance – check this site out.

54. stoppeth here

55. An AC source with ΔVmax = 125 V and f = 25
An AC source with ΔVmax = 125 V and f = 25.0 Hz is connected between points a and d in the figure.
Calculate the maximum voltages between the following points: (a) a and b V (b) b and c V (c) c and d V (d) b and d V