1. AC Circuits PH 203 Professor Lee Carkner Lecture 23

2. Alternating Current Issues  Voltage and current vary sinusoidally with time   Voltage and current will have a frequency and angular frequency    in radians per second   Need to create a more general form of resistance  Circuits have natural oscillation frequencies  May get resonance

3. Generators  We can use induction to produce a continuous source of current   Turn a wire loop in a magnetic field with an external source of work to make a generator  Produces alternating current   Thus the current flows in one direction and then the other  Characterized with angular frequency  d

4. Alternating Current   =  max  sin  d t  As the loop makes one complete rotation (  t goes from 0 to 2  radians) the emf goes from 0, to maximum +, to maximum -, and back to zero again   The current through the loop goes one way and then the other, sometimes is weak and sometimes is strong

5. Frequency   The number of these cycles made per second is the frequency f =  d /2    We can also refer to the period, the number of seconds per cycle  T = 1/f = 2  d   Note that if  d is similar to the  of the circuit we have resonance and large current amplitudes are possible

6. AC Circuit Elements   Resistors (Resistance, R)  Capacitors (Reactance, X C )  Inductors (Reactance X L )   Current and voltage may not be in phase

7. Resistors and AC  Resistor connected to an AC generator    Voltage through the circuit varies as the emf of the generator does v R = V R  sin  d t   We can then find the maximum current with Ohm’s Law  V R = I R R

8. Resistors and Phase   When v is max, i is max  i R = I R sin  d t

9. Capacitors and AC   As charge builds up on the capacitor, the potential difference across it increases, decreasing the current   The capacitor is constantly being charged and discharged   In a AC circuit the current will vary with some average rms value that depends on the voltage and the capacitance

10. Capacitive Reactance   We define the capacitive reactance to symbolize this “resistance”: X C = 1/(  d C)  V C = I C X C  Note that the current depends on the frequency  At high frequency the capacitor never gets much charge on it

11. Capacitors and Phase   When the voltage is zero, the current is a maximum   As voltage increases current decreases   We say the voltage lags the current by 90 degrees or ¼ cycle  The equation for current is then i C = I C sin (  d t +  /2)

12. Capacitor Power   Since P = vi, we can see if the power is positive or negative based on the sign of i and v  P is positive half the time and negative half the time   The capacitor draws energy from and returns energy to the generator in equal measure

13. Inductive Reactance  X L =  d L  The inductor is most “effective” at high frequency due to the rapid current changes   The maximum voltage is again the generator emf and is related to the maximum current by: V L = I L X L

14. Inductors and Phase   look at the slope of the current sine wave   The induced voltage is zero when the current is a maximum (since that is where the current is not changing)   The current at any time is: i L = I L sin (  d t –  /2)

15. Reactance and Frequency  Resistor   Capacitor  Low current at low frequency  Inductor 

16. Next Time  Read 31.9-31.11  Problems: Ch 31, P: 32, 33, 34, 41, 53

17. For an LC oscillator when the current through the inductor is zero, the charge on the capacitor is, A)Maximum B)Zero C)½ maximum D)  maximum E)2  maximum

18. For an LC oscillator the direction of current in the circuit is, A)Always in one direction B)In one direction for one complete cycle and then the other direction for the next complete cycle C)In one direction for ½ of the cycle and then the other direction for the other ½ of the cycle D)Changing direction 2  times per cycle E)Fluctuating unpredictably

19. For an LC oscillator when the energy in the capacitor is ½ maximum the energy in the inductor is, A)Maximum B)Negative maximum C)Zero D)½ maximum E)2  maximum