Physics 102: Lecture 11 Generators and Transformers

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1 Physics 102: Lecture 11 Generators and Transormers Physics 102: Lecture 11, Slide 1

2 Reiew: Magnetic Flux & Induction B Flux: Induced oltage: = B A cos() is angle between normal and B ε = Φ Δt = Φ Φ i t t i Last lecture Today Physics 102: Lecture 11, Slide 2 3 things can change : 1. Area o loop 2. Magnetic ield B 3. Angle between normal and B

3 Generators and EMF A loop o wire is rotated (ex: by a steam engine turbine) in a uniorm B ield d normal normal a B B c b = B A cos() Loop normal rotates relatie to B ield => changes => changes => em in loop => oltage generated! Physics 102: Lecture 11, Slide 3

4 Reiew (Phys 101): Rotation Variables,,, T Velocity (): How ast a point moes. Units: usually m/s Angular Frequency ( ): How ast something rotates. Units: radians / sec Physics 102: Lecture 11, Slide 4 = / r Frequency ( ): How ast something rotates. Units: rotations / sec = Hz Period (T): How much time one ull rotation takes. Units: usually seconds r = / 2 T = 1 / = 2 /

5 Generator: lux t = 0, = AB (max) n B t > 0, < AB t = T/4, = 0 t > T/4, < 0 t = T/2, = AB (min) AB t -AB = B A cos() = B A cos( t) Physics 102: Lecture 11, Slide 5

6 Generator: EMF t = 0, ~const, e = 0 ε = Φ Δt B n t > 0,, e > 0 t = T/4,, e (max) t > T/4,, e > 0 t = T/2, ~const, e = 0 AB t AB e t -AB T - AB T = B A cos( t) Physics 102: Lecture 11, Slide 6 e = B A sin( t)

7 Comparison: Flux s. EMF Flux is maximum Most lines thru loop EMF is minimum Just beore: lines enter rom let Just ater: lines enter rom let No change! Physics 102: Lecture 11, Slide 7 Flux is minimum Zero lines thru loop EMF is maximum Just beore: lines enter rom top. Just ater: lines enter rom bottom. Big change!

8 ACT: Generators and EMF x A B C At which time does the loop hae the greatest em (greatest / t)? Physics 102: Lecture 11, Slide 8

9 ACT: EMF direction In which direction does the current low in wire a-b at the moment shown? d a Side iew a B B b c n b n A) B) EMF = 0 C) Physics 102: Lecture 11, Slide 9

10 Generators and Torque e = A B sin() F Voltage! Connect loop to resistance R use I=V/R: I = A B sin() / R I t B Recall: t = A B I sin() = A 2 B 2 sin 2 ()/R F Direction: use RHR1 n Torque, due to current and B ield, tries to slow spinning loop down. Must supply external torque to keep it spinning at constant Physics 102: Lecture 11, Slide 10

11 Generator A generator consists o a square coil o wire with 40 turns, each side is 0.2 meters long, and it is spinning with angular elocity = 2.5 radians/second in a uniorm magnetic ield B=0.15 T. Calculate the maximum EMF and torque i the resistie load is 4W. e = NA B sin() = = t = NI A B sin() x = = = Physics 102: Lecture 11, Slide 11 Note: Em is maximum at =90 Note: Torque is maximum at =90

12 In a hydropower plant, that torque is supplied by alling water. The power plant deliers AC (alternating current) power to your house: the oltage and current switch directions at =60 Hz (more next lecture). At your house: 120 V. There is a big challenge getting electric current to your house: P = I 2 R! Physics 102: Lecture 11, Slide 12

Power Transmission A generator produces 1.2 Giga watts o power, which it transmits to a town 7 miles away through power lines with a total resistance 0.01 ohms.

13 Power Transmission A generator produces 1.2 Giga watts o 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 i the energy is transmitted at 120 Volts? P = IV Power deliered 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! Large current is the problem. Since P=IV, use high oltage and low current to delier power. I V = 12,000 Volts, lose Giga Watts! Physics 102: Lecture 11, Slide 13

14 Transormers make it possible to distribute electrical power at high oltage and step-down to low oltage at your house. 500,000 V Low current 240 / 120 V High current Physics 102: Lecture 11, Slide 14

15 Transormers Key to Modern electrical system Transorm between high and low oltages Very eicient Nikola Tesla Physics 102: Lecture 11, Slide 15

16 Transormers Key to eicient power distribution Changing current in primary creates changing lux in primary and secondary. iron V p = N p ΔΦ Δt V s = N s ΔΦ Δt V s V p = N s N p Same / t e ~ N s > N p : V s > V p step up V p N s < N p : V s < V p step down N P (primary) V s N S (secondary) R Energy conseration! Physics 102: Lecture 11, Slide 16 I p V p = I s V s I s I p = N p N s

17 CheckPoint 3.1 The good news is you are going on a trip to France. The bad news is that in France the outlets hae 240 olts. You remember rom P102 that you need a transormer, so you wrap 100 turns around the primary. How many turns should you wrap around the secondary i you need 120 olts out to run your hair dryer? iron 1) 50 2) 100 3) 200 e ~ V p V s R N P (primary) N S (secondary) Physics 102: Lecture 11, Slide 17

18 ACT: Transormers iron V p V s R A 12 Volt battery is connected to a transormer transormer that has a 100 turn primary coil, and 200 turn secondary coil. What is the oltage across the secondary ater the battery has been connected or a long time? N P (primary) N S (secondary) A) V s = 0 B) V s = 6 C) V s = 12 D) V s = 24 Physics 102: Lecture 11, Slide 18

19 Questions to Think About In a transormer the side with the most turns always has the larger peak oltage. (T/F) In a transormer the side with the most turns always has the larger peak current. (T/F) In a transormer the side with the most turns always dissipates the most power. (T/F) Which o the ollowing changes will increase the peak oltage deliered by a generator Increase the speed it is spinning. Increase the area o the loop. Increase the strength o the magnetic ield. Physics 102: Lecture 11, Slide 19

Physics 102: Lecture 10. Faraday s Law. Changing Magnetic Fields create Electric Fields. Physics 102: Lecture 10, Slide 1

Physics 102: Lecture 10. Faraday s Law. Changing Magnetic Fields create Electric Fields. Physics 102: Lecture 10, Slide 1 Physics 102: Lecture 10 Faraday s Law Changing Magnetic Fields create Electric Fields Physics 102: Lecture 10, Slide 1 Last Two Lectures Magnetic fields Forces on moing charges and currents Torques on