2. GeneratorsGenerators and Transformers Today’s lecture will cover Textbook Sections 20.2, 20.6 Physics 102: Lecture 11

3. Exam I Results Average score 77.5% Nice work!

4. Review: Magnetic Flux  is angle between normal and B B A  normal  = B A cos(  Units is T-m 2

5. Review: Induction Faraday’s Law –Magnitude of induced EMF given by: 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 7

6. ACT: Change B II SNSN Flux from magnet is down. Induced current creates flux up - opposite original. So flux from magnet must be increasing. Magnet must be falling down N S 42 Which way is the magnet moving if it is inducing a current in the loop as shown? 1)Up 2)Down Demo 371

7. Review: Rotation Variables v, , f, T Velocity (v): –How fast a point moves. –Units: usually m/s Angular Frequency (  ): –How fast something rotates. –Units: radians / sec  r v v  = v / r f =  / 2  T = 1 / f = 2  /  Frequency ( f ): –How fast something rotates. –Units: rotations / sec = Hz Period (T): –How much time one full rotation takes. –Units: usually seconds 10

8. Generators and EMF  loop =  B A sin(  t) v v x   r 1 2 13  t  AB  AB EMF is voltage!  = B A cos(  ) =B A cos(  t)  loop = -  /  t =  B A sin(  )  B A sin(  t )

9. ACT: Generators and EMF x  =  A B sin(  ) x x 1 2 3 At which time does the loop have the greatest emf (greatest  /  t)? 1) Has greatest flux, but  = 0 so  = 0. 2) Example we’ve studied,   30 so    AB/2. 3) Flux is zero, but  = 90 so  =  AB. 16 

10. Comparison: Flux vs. EMF 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 18

11. Preflights 11.1, 11.2, 11.3  v v x  r Flux is decreasing at moment shown. 46% got correct. When  =30°, the EMF around the loop is: increasing decreasing not changing 19 EMF is increasing!    48% 32% 20%

12. Generators and Torque v v x   r  =  A B sin(  ) Recall:  = A B I sin(  ) =  A 2 B 2 sin 2 (  )/R Torque, due to current and B field, tries to slow spinning loop down. Must supply external torque to keep it spinning at constant  22 Voltage! Connect loop to resistance R use I=V/R: I =  A B sin(  ) / R

13. Generator v v x  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  = 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 4 .  = NA B  sin(  )  = NI A B sin(  ) 25 Note: Emf is maximum at  =90 Note: Torque is maximum at  =90 = (40) (0.2) 2 (0.15) (2.5) = 0.6 Volts = N 2  A 2 B 2 sin 2 (  )/R = (40) 2 (2.5) (0.2) 4 (0.15) 2 /4 = 0.036 Newton-meters 

14. Power Transmission, Preflight 11.5 A generator produces 1.2 Giga watts of power, which it transmits to a town 7 miles away through power lines with a total resistance 0.01 ohms. How much power is lost in the lines if the energy is transmitted at 120 Volts? P = IV Power delivered by generator through lines I = P/V = 1.2x10 9 W/120 V = 10,000,000 Amps in lines! P = I 2 R Power lost in lines = 10,000,000 2 (.01) = 1.0 Giga Watt Lost in Lines! 30 Large current is the problem. Since P=IV, use high voltage and low current to deliver power. If V = 12,000 Volts, loose 0.0001 Giga Watts!

15. Transformers Key to Modern electrical system Starting with 120 volts AC –Produce arbitrarily small voltages. –Produce arbitrarily large voltages. Nearly 100% efficient 31 !!!Volt!!

16. Transformers Increasing current in primary creates an increase in flux through primary and secondary.   iron VsVs VpVp Same  t Energy conservation! I p V p = I s V s R 36 (primary) (secondary) NSNS NPNP Key to efficient power distribution

17. Preflight 11.6 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 P102 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? 40   iron VsVs VpVp R 1) 502) 1003) 200 (primary) (secondary) NSNS NPNP 49% 16% 35% By halving the number of turns around the secondary you decrease the voltage in the secondary by half.

18. ACT: Transformers iron VsVs VpVp R A 12 Volt battery is connected to a transformer 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? 1) V s = 0 2) V s = 6 3) V s = 12 4) V s = 24 Transformers depend on a change in flux so they only work for alternating currents! 45 (primary) (secondary) NSNS NPNP

19. In a transformer the side with the most turns always has the larger peak voltage. (T/F) In a transformer the side with the most turns always has the larger peak current. (T/F) In a transformer the side with the most turns always dissipates the most power. (T/F) Which of the following changes will increase the peak voltage delivered by a generator –Increase the speed it is spinning. –Increase the area of the loop. –Increase the strength of the magnetic field. Questions to Think About True False (has smaller current) False (equal) All of them will!

20. See You Monday! 50