1. 11/13/2018

2. LECTURE 19 AC Generators AC Circuits
Start by considering simple circuits with one element (R, C, or L) in addition to the driving emf.
It will lead to Oscillations and Driven RLC circuits

3. Alternating Current Generators (DEMO)
(N = 2 for this coil)
DEMO: New AC Motor – coil, magnetic & light bulb – faster I crank the brighter the bulb
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4. Phasors for R
V in phase with I
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5. Power Dissipated in a Resistor
Peak value
Average value
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6. Standard Alternating Voltage in the US
+peak
-peak
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7. Using rms values: summary
Using rms values of current and voltage allows you to use the familiar dc formulas, such as V = IR and P = I 2 R.
One ac ampere is said to flow in a circuit if it produces the same joule heating as one ampere of dc current under the same conditions.
At your house the peak voltage will be 170 V
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8. What is the rms value of an AC voltage whose maximum value is 141 V?
QUIZ lecture 19
What is the rms value of an AC voltage whose maximum value is 141 V?
zero
70.7 V
100 V
141 V
240 V
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9. Inductors in AC Circuits
900
Potential drop, VL(t), leads the current, I(t) by 900
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10. Relationship between Irms & Vrms
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11. Phasors for L V leads I by 90
90 degrees out of phase…..if I and V 90 out of phase no power loss
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12. Quiz Questions
If we increase the driving frequency in a circuit with a purely inductive load does IL
Decrease
Increase
Remain the Same
VL remains the same
IL decreases
If we increase the driving frequency in a circuit with a purely inductive load does VL
Decrease
Increase
Remain the Same
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13. Capacitors in AC Circuits
900
Potential drop, VC(t), lags the current, I(t), by 900
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14. Relationship between Irms & VC,rms
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15. Phasors for C
V lags I by 90
Conventions….most important 90 degrees out of phase
But capacitors and inductors are 180 out of phase with each other
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16. Summary Symbol Reactance X C L L R IC current leads VC IL
current lags VL
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17. Impedances for L, C, R R is resistance is capacitive reactance
For high , XC goes to zero, C acts like a wire.
For low , XC grows larger and at DC, C acts like an open switch
XL = L is inductive Reactance
For high , XL grows large and L acts like an open switch.
For low , XL grows small and at DC, L acts like a conducting wire.
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18. Phasors for R
V in phase with I
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19. Phasors for C
V lags I by 90
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20. Phasors for L
V leads I by 90
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21. AC Power Distribution
AC power can travel at high voltages and low amps, therefore smaller power loss
Tesla liked 60 Hz and 240 V
Standard in Europe was defined by a German company AEG ( monopoly) who chose 50Hz (20% less efficient in generation, 10-15% less efficient in transmission)
Originally Europe was also 110V, but they changed to reduce power loss and voltage drop for the same copper diameter
Nikola Tesla
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22. The Power Grid
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23. Example If 735 kV line is used to transmit electric energy 1000 km.
I = 500 A and R = W/km
Energy is supplied at a rate of
Energy dissipated from resistance of wires
If you doubled the current and halved the voltage, energy dissipated
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24. LC Circuits
++++ R C L C
++++
Consider the LC and RC series circuits shown:
Suppose that at t=0 the capacitor is charged to a value of Q.
Is there is a qualitative difference in the time development of the currents produced in these two cases. Why??
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25. LC Oscillations L C I
++++
Kirchoff’s loop rule
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26. LC Oscillations Q V C I V t L dI dt t
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27. Example 1 (a) Vab < 0 (b) Vab = 0 (c) Vab > 0 L C t=0 L C t=t1+ - Q Qo = L C
t=t1 Q =
At t=0, the capacitor in the LC circuit shown has a total charge Q0. At t = t1, the capacitor is uncharged.
What is the value of Vab, the voltage across the inductor at time t1?
(a) Vab < 0
(b) Vab = 0
(c) Vab > 0
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28. Example 2 (a) I2 = I0 (b) I2 = 2I0 (c) I2 = 4I0 t=0+ - Q Qo =
At t=0 the capacitor has charge Q0; the resulting oscillations have frequency 0. The maximum current in the circuit during these oscillations has value I0.
What is the relation between I0 and I2 , the maximum current in the circuit when the initial charge = 2Q0?
(a) I2 = I0
(b) I2 = 2I0
(c) I2 = 4I0
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29. Example 3 (a) 2 = 1/2 0 (b) 2 = 0 (c) 2 = 20 t=0+ - Q Qo =
At t=0 the capacitor has charge Q0; the resulting oscillations have frequency 0. The maximum current in the circuit during these oscillations has value I0.
What is the relation between 0 and 2, the frequency of oscillations when the initial charge = 2Q0?
(a) 2 = 1/2 0
(b) 2 = 0
(c) 2 = 20
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