1. AC Circuits Physics 102 Professor Lee Carkner Lecture 24

2. PAL #23 Alternating Current  240  lightbulb, V rms = 120 V, 60 Hz  the rms current  V rms = I rms R, I rms = V rms /R = 120/240 =  the maximum current  I max = (2) ½ I rms = (2) ½ (0.5) =  the maximum power  P max = I 2 max R = (0.707) 2 (240) =  the average power  P av = I 2 rms R =(0.5) 2 (240) =  the power at time equals 1/120 second  I = I max sin  t = I max sin(2  ft) = I max sin [(2)(  )(60)(120) -1 ] =  P = 

3. RC Circuits  A capacitor will act like a resistor with reactance:  What if we have a capacitor and a resistor in a circuit together?   The voltages can be thought of as vectors each with its own phase angle  V 2 = V 2 R + V 2 C

4. An AC – RC Circuit

5. Phase Diagram

6. Impedance  We can write the voltages in terms of the currents:    If the resistor and the capacitor are in series they each have the same current, which we can factor out  We can rewrite as:  Where: Z = (R 2 + X 2 C ) ½ 

7. Today’s PAL (Part 1)  Consider a 10  resistor connected to a 1 Hz,  V max = 10 V, AC power source:  What is the rms voltage?  What is the reactance (or resistance)?  What is the rms current?  What is the maximum current?  What is the phase shift between current and voltage?  What is the current when the voltage is zero?

8. Phase Angle   They are separated by a phase angle    If we plot the voltages we see, cos  = IR/IZ = R/Z

9. Vectors and Phase Angle

10. Phase and Power  We know that power can be written P = IV   We can re-write power in terms of  by using:   R = Z cos   P av = I rms V rms cos   The average power depends not just on the magnitude of I and V but also their phase   If they are shifted 90 deg (  /2) they “average” out to zero power

11. Phase and Resistance  Since cos  = R/Z, we can think of cos  as the ratio of resistance to the total impedance   If cos  is small, R is small relative to Z   However, we also know that if cos  is large, power is large  Only the resistor dissipates power in a RC circuit

12. V, I,  and Power

13. Today’s PAL (Part 2)  Consider a 10 F capacitor connected to a 1 Hz,  V max = 10 V, AC power source:  What is the rms voltage?  What is the reactance (or resistance)?  What is the rms current?  What is the maximum current?  What is the phase shift between current and voltage?  What is the current when the voltage is zero?

14. Inductors and AC   The changing current produces an induced back emf in the inductor (  V L )   The induced voltage is maximum when the current is zero (since that is where it is changing the most)   The voltage leads the current by 90 degrees (V is max 1/4 cycle before I)

15. AC Circuit With Inductor

16. Inductive Reactance  We can define the way in which an inductor impedes the current with the inductive reactance: X L =  L   We can relate the current and the potential difference across the inductor with:   Compare to the capacitive reactance: X C = 1/(  C)

17. Reactance and Frequency

18. Phase for R, L and C  The phase angle for a circuit with just one R, L or C is as follows:  For just resistor:   =   For just capacitor:   = -   Voltage is max 1/4 cycle after current  For just inductor   =   Voltage is max 1/4 before current

19. Today’s PAL (Part 3)  Consider a 10  inductor connected to a 1 Hz,  V max = 10 V, AC power source:  What is the rms voltage?  What is the reactance (or resistance)?  What is the rms current?  What is the maximum current?  What is the phase shift between current and voltage?  What is the current when the voltage is zero?

20. RCL and AC   For a series circuit, all elements have a common current  If you combine a resistor, capacitor and an inductor into one series circuit, they all will have the same current but all will have difference voltages at any one time 

21. RLC Circuit

22. RLC Impedance  Z = (R 2 + (X L - X C ) 2 ) ½  The voltages for the inductor and capacitor are 180 degrees opposed and so subtract   V = IZ 

23. Next Time  Read 21.14  Homework Ch 21, P 64, 65, 69, 70