Generators and Transformers

1. Generators and Transformers Physics 102: Lecture 11 Verify ‘EX’ grades for Exam #1!

2. Review: Magnetic Flux B f normal A • = B A cos(f) Units is T m2 = Wb f is angle between normal and B

3. 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

4. Review: Rotation Variablesv, , f, T w v v • Velocity (v): • How fast a point moves. • Units: usually m/s • Angular Frequency (): • How fast something rotates. • Units: radians / sec 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/  10

5. Generators and EMF 1 w • q v v r 2 x e wAB t -wAB EMF is voltage! •  = B A cos() = B A cos(t) eloop= -/t = w B A sin() = w B A sin(wt) eloop = w B A sin(wt)  = BA cos(wt) 13

6. Generators and EMF 1 w • q v v r 2 x e  wAB AB t t -wAB -AB EMF is voltage!  = B A cos() = B A cos(t) eloop= -/t= w B A sin(wt) flux is maximum when emf is 0 And vice versa 13

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

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 18

9. w • v v r x • = 30 e q Preflights 11.1, 11.2, 11.3 q = 30 Flux is decreasing at moment shown. 54% got correct. When q=30°, the EMF around the loop is: increasing decreasing not changing 53% 30% 18% EMF is increasing! 19

10. 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 22

11. 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) (0.2)2 (0.15) (2.5) = 0.6 Volts v q x t = NI A B sin(q) Note: Emf is maximum at q=90 = N2w A2 B2 sin2(q)/R = (40)2 (2.5) (0.2)4 (0.15)2/4 = 0.036 Newton-meters Note: Torque is maximum at q=90 25

12. 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? Example P = IV Power delivered by generator through lines I = P/V = 1.2x109 W/120 V = 10,000,000 Amps in lines! P = I2R Power lost in lines = 10,000,0002 (.01) = 1.0 Giga Watt Lost in Lines! 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! 30

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

14. 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 36

15. NP NS (secondary) (primary) 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? iron 1) 50 2) 100 3) 200 58% 13% 29% R ~ Vp e Vs By halving the number of turns around the secondary you decrease the voltage in the secondary by half. 40

16. NP NS (secondary) (primary) ACT: Transformers iron Transformers depend on a change in flux so they only work for alternating currents! 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? Vp Vs R 1) Vs = 0 2) Vs = 6 3) Vs = 12 4) Vs = 24 45

17. Questions to Think About • 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. True False (has smaller current) False (equal) All of them will!

18. See You Monday 50