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1. Generators Physics 1161: Lecture 16 • Textbook Sections 23-6 – 23-10 http://www.walter-fendt.de/ph14e/electricmotor.htm http://www.walter-fendt.de/ph14e/generator_e.htm

2. v + + + + Review: Two uses of RHR’s B • Force on moving charge in Magnetic field • Thumb: v (or I) • Fingers: B • Palm: F on + charge I F Palm: out of page. • Magnetic field produced by moving charges • Thumb: I (or v for + charges) • Fingers: curl along B field I

3. Review: Induction • Lenz’s Law • If the magnetic flux (B) through a loop changes, an EMF will be created in the loop to oppose the change in flux • EMF current (V=IR) additional B-field. • Flux decreasing => B-field in same direction as original • Flux increasing => B-field in opposite direction of original • Faraday’s Law • Magnitude of induced EMF given by:

4. Review: Rotation Variablesv, , f, T w • Velocity (v): • How fast a point moves. • Units: usually m/s • Angular Frequency (): • How fast something rotates. • Units: radians / sec v v r v= r • Frequency ( f ): • How fast something rotates. • Units: rotations / sec = Hz • Period (T): • How much time one full rotation takes. • Units: usually seconds f = / 2 T = 1 /f = 2/ 

5. v = wr 1 w • q v v r 2 x e wAB t -wAB Generators and EMF EMF is voltage! eside 1 = v B L sin(q) 2rL = A eside 1 = wr B L sin(q) eside 2 = wr B L sin(q) eloop = eside 1 + eside 2 = 2wr B L sin(q) eloop = w A B sin(q) eloop = w A B sin(wt)

6. At which time does the loop have the greatest emf (greatest / t)? • 1 • 2 • 3

7. At which time does the loop have the greatest emf (greatest / t)? • 1 • 2 • 3 1) Has greatest flux, but q = 0 so e = 0. 2) (Preflight example) q 30 so ewAB/2. 3) Flux is zero, but q = 90 so e = wAB.

8. Flux is maximum Most lines thru loop EMF is minimum Just before: lines enter from left Just after: lines enter from left No change! Flux is minimum Zero lines thru loop EMF is maximum Just before: lines enter from top. Just after: lines enter from bottom. Big change! • • x x Comparison:Flux vs. EMF

9. w • v v r x • = 30 e q Preflights16.1, 16.2, 16.3 q = 30 Flux is _________ at moment shown. Increasing decreasing not changing When q=30°, the EMF around the loop is: increasing decreasing not changing EMF is increasing!

10. w • v v r x • = 30 e q Preflights16.1, 16.2, 16.3 q = 30 Flux is decreasing at moment shown. When q=30°, the EMF around the loop is: increasing decreasing not changing EMF is increasing!

11. Voltage! Generators and Torque • = w A B sin(q) Connect loop to resistance R use I=V/R: I = w A B sin(q) / R w • q v v r Recall: t = A B I sin(q) = w A2 B2 sin2(q)/R x Torque, due to current and B field, tries to slow spinning loop down. Must supply external torque to keep it spinning at constant w

12. Example Generator A generator consists of a square coil of wire with 40 turns, each side is 0.2 meters long, and it is spinning with angular velocity w = 2.5 radians/second in a uniform magnetic field B=0.15 T. Determine the direction of the induced current at instant shown. Calculate the maximum emf and torque if the resistive load is 4W. • = NA B w sin(q) Units? w • v v t = NI A B sin(q) Units? x

13. Example Generator A generator consists of a square coil of wire with 40 turns, each side is 0.2 meters long, and it is spinning with angular velocity w = 2.5 radians/second in a uniform magnetic field B=0.15 T. Determine the direction of the induced current at instant shown. Calculate the maximum emf and torque if the resistive load is 4W. • = NA B w sin(q) w • v = (40) (0.2m)2 (0.15T) (2.5 radians/s) = 0.6 Volts v q x t = NI A B sin(q) Note: Emf is maximum at q=90 t = 40*I0.15A*(0.2m)2 * 0.15 T* 1 = 0.036 Newton-meters Note: Torque is maximum at q=90

14. Power Transmission,Preflight 16.5 Example A generator produces 1.2 Giga watts of power, which it transmits to a town 10 km away through copper power lines. How low does the line resistance need to be in order to consume less than 10% of the power transmitted from the generator at 120 Volts? I = Current leaving/returning to the generator Find I? R = Line resistance for 12 Megawatt loss in lines So why use high voltage lines?

15. Power Transmission,Preflight 16.5 Example A generator produces 1.2 Giga watts of power, which it transmits to a town 10 km away through copper power lines. How low does the line resistance need to be in order to consume less than 10% of the power transmitted from the generator at 120 Volts? I = 107 P = IV so 1.2109 = 120 I or I = 107 amps  of Cu = 10-8-m R = 1.210-6 P = I2 R so 1.2108 = (107)2 R or R = 1.210-6 1 inch square copper wire has about 0.1 ohm resistance in 7 km This would require a cable more than 40 feet in diameter!! Large current is the problem. Since P=IV, use high voltage and low current to deliver power.

16. NP NS (secondary) (primary) Transformers Key to efficient power distribution Increasing current in primary creates an increase in flux through primary and secondary. iron R ~ Vp e Vs Same DF/Dt Energy conservation! IpVp = IsVs

17. NP NS (secondary) (primary) Preflight 13.6 The good news is you are going on a trip to France. The bad news is that in France the outlets have 240 volts. You remember from Phy1152 that you need a transformer, so you wrap 100 turns around the primary. How many turns should you wrap around the secondary if you need 120 volts out to run your hair dryer? iron 1) 50 2) 100 3) 200 R ~ Vp e Vs

18. NP NS (secondary) (primary) Preflight 13.6 The good news is you are going on a trip to France. The bad news is that in France the outlets have 240 volts. You remember from Phy1161 that you need a transformer, so you wrap 100 turns around the primary. How many turns should you wrap around the secondary if you need 120 volts out to run your hair dryer? iron 1) 50 2) 100 3) 200 R ~ Vp e Vs

19. A 12 Volt battery is connected to a transformer that has a 100 turn primary coil, and 200 turn secondary coil. What is the voltage across the secondary after the battery has been connected for a long time? • Vs = 0 • Vs = 6 • Vs = 12 • Vs = 24

20. A 12 Volt battery is connected to a transformer that has a 100 turn primary coil, and 200 turn secondary coil. What is the voltage across the secondary after the battery has been connected for a long time? • Vs = 0 • Vs = 6 • Vs = 12 • Vs = 24 Transformers depend on a change in flux so they only work for alternating currents!

21. Transformers • Key to Modern electrical system • Starting with 120 volts AC • Produce arbitrarily small voltages. • Produce arbitrarily large voltages. • Nearly 100% efficient

22. In a transformer the side with the most turns always has the larger peak voltage. (T/F) • True • False

23. In a transformer the side with the most turns always has the larger peak current. (T/F) • True • False

24. In a transformer the side with the most turns always dissipates the most power. (T/F) • True • False