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Physics 102: Lecture 11 Generators and Transformers • Today’s lecture will cover Textbook Sections 20.2, 6 Physics 102: Lecture 11, Slide 1 Review: Two uses of RHR’s • Force on moving charge in Magnetic field + + + +v F I – Thumb: v (or I) – Fingers: B – Palm: F on + charge Palm: out of page. • Magnetic field produced by moving charges – Thumb: I (or v for + charges) – Fingers: where you want to know B – Palm: B Physics 102: Lecture 11, Slide 2 Thumb: out Fingers: up Palm: left. x • Review: Two uses of RHR’s • Force on moving charge in Magnetic field • Magnetic field produced by moving charges – Thumb: I (or v for + charges) – Fingers: curl along B field Physics 102: Lecture 11, Slide 3 F I – Thumb: v (or I) – Fingers: B – Palm: F on + charge + + + +v Palm: out of page. I 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: f i t t f ti Physics 102: Lecture 11, Slide 4 Review: Rotation Variables v, , f, T • Velocity (v): – How fast a point moves. – Units: usually m/s r • Angular Frequency (): – How fast something rotates. – Units: radians / sec v v v= r • Frequency ( f ): – How fast something rotates. – Units: rotations / sec = Hz f = / 2 • Period (T): – How much time one full rotation takes. – Units: usually seconds Physics 102: Lecture 11, Slide 5 T = 1 / f = 2 / Generators and EMF EMF is voltage! side 1 = v B L sin(q) v = r side 1 = r B L sin(q) side 2 = r B L sin(q) loop = side 1 + side 2 2r B L sin(q) 2rL = A loop = A B sin(q) loop = A B sin(t) Physics 102: Lecture 11, Slide 6 1 • v 2 AB x q v r t AB ACT: Generators and EMF = A B sin(q) • q x 1 2 3 At which time does the loop have the greatest emf (greatest / t)? Physics 102: Lecture 11, Slide 7 ACT: Generators and EMF = A B sin(q) • θ x 1 2 3 At which time does the loop have the greatest emf (greatest / t)? 1) Has greatest flux, but q = 0 so = 0. 2) (Preflight example) q 30 so AB/2. 3) Flux is zero, but q = 90 so = AB. Physics 102: Lecture 11, Slide 8 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 Physics 102: Lecture 11, Slide 9 – Just before: lines enter from top. – Just after: lines enter from bottom. – Big change! Preflights 11.1, 11.2, 11.3 • v v Flux is _________ at moment shown. Increasing x q 30 r decreasing not changing When q=30°, the EMF around the loop is: increasing decreasing not changing Physics 102: Lecture 11, Slide 10 q 30 EMF is increasing! q Preflights 11.1, 11.2, 11.3 • Flux is decreasing at moment shown. v v x q 30 r When q=30°, the EMF around the loop is: q 30 increasing decreasing not changing Physics 102: Lecture 11, Slide 11 EMF is increasing! q Generators and Torque = A B sin(q) Voltage! Connect loop to resistance R use I=V/R: I = A B sin(q) / R Recall: t = A B I sin(q) = A2 B2 sin2(q)/R • v x r Torque, due to current and B field, tries to slow spinning loop down. Must supply external torque to keep it spinning at constant Physics 102: Lecture 11, Slide 12 q v 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 = 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 sin(q) Units? v t = NI A B sin(q) Physics 102: Lecture 11, Slide 13 Units? x • v 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 = 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 sin(q) = (40) (0.2)2 (0.15) (2.5) = 0.6 Volts t = NI A B sin(q) = N2 A2 B2 sin2(q)/R = (40)2 (2.5) (0.2)4 (0.15)2/4 = 0.036 Newton-meters Physics 102: Lecture 11, Slide 14 • v v x q Note: Emf is maximum at q=90 Note: Torque is maximum at q=90 Power Transmission, Preflight 11.5 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? Physics 102: Lecture 11, Slide 15 Power Transmission, Preflight 11.5 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 = I V so 1.2 109 = 120 I or I = 107 amps R= P = I2 R so 1.2 108 = (107)2 R or R = 1.2 10-6 W 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. Physics 102: Lecture 11, Slide 16 Transformers Key to efficient power distribution Increasing current in primary creates an increase in flux through primary and secondary. Vp N p t Vs N s t iron ~ Vp V s Same /t Vs N s Vp N p Energy conservation! Physics 102: Lecture 11, Slide 17 I p Vp = I s Vs NP NS (primary) (secondary) R 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 ~ Vp V s Physics 102: Lecture 11, Slide 18 NP NS (primary) (secondary) R 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 Vs N s Vp N p 3) 200 Vs 120 N s N p 100 50 240 Vp Physics 102: Lecture 11, Slide 19 ~ Vp V s NP NS (primary) (secondary) R ACT: Transformers iron Vp V s 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? 1) Vs = 0 2) Vs = 6 Physics 102: Lecture 11, Slide 20 3) Vs = 12 NP NS (primary) (secondary) 4) Vs = 24 R ACT: Transformers Transformers depend on a change in flux so they only work for alternating currents! 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? 1) Vs = 0 2) Vs = 6 Physics 102: Lecture 11, Slide 21 3) Vs = 12 iron Vp V s NP NS (primary) (secondary) 4) Vs = 24 R Transformers • Key to Modern electrical system • Starting with 120 volts AC – Produce arbitrarily small voltages. – Produce arbitrarily large voltages. • Nearly 100% efficient !!!Volt!! Physics 102: Lecture 11, Slide 22 Exam Prep Questions • 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. Physics 102: Lecture 11, Slide 23 See you next time! • Read Sections 20.9, 21.1, 3-4 Physics 102: Lecture 11, Slide 24