Electricity and Magnetism Transformers and Alternating Current

Transcription

1 Electricity and Magnetism Transformers and Alternating Current Lana Sheridan De Anza College Mar 19, 2018

2 Last time RLC circuits and oscillations alternating current

3 Overview alternating current transformers rectifiers and filters

4 Transformers which is alm Transformers change V rms and I rms simultaneously, while keeping rule: Transm the average power P avg = I rms V rms (resistive load) constant (conservation of energy). Φ B The Ideal S The transm for efficient V N p p V s R and consum N s lower (for u sentially con Primary Secondary by Faraday The ide Fig An ideal transformer (two This works bers of turn coils via mutual wound inductance. on iron core) If thein current a basicin the first coil did not constantly In use, the transformer change circuit. (AC) An this ac would generator not work. produces current in the coil at the left (the primary). The coil v at the s = right v p (the secondary) generator w N s N p is connected to the resistive load R when

5 Transformers The reason for the voltage relation is that the iron core ideally contains all the magnetic flux lines produced. Then the emf per turn E t = dφ dt is the same in both solenoids. v p = N p dφ dt and v s = N s dφ dt v s = v p N s N p

6 Transformers Let V now refer to the rms voltage. Imagine wh age. Energy wou as previously, bu If V s > V p (and therefore N s > N p ), the transformer is which calledis aalmost step-up transformer. rule: Transmit at This is a step up transformer: V p Primary Φ B N p N s Fig An ideal transformer (two coils wound on an iron core) in a basic transformer circuit. An ac generator produces current in the coil at the left (the primary). The coil at the right (the secondary) V s S Secondary R The Ideal Tran The transmission for efficient high and consumption lower (for use) th sentially constan by Faraday s law The ideal tra bers of turns, wo In use, the prim generator whose If V s < V p (and therefore N s < N p ), the transformer is called a step-down transformer.

7 Example from Lecture 21 A power station supplies current I = 5 A and potential difference V = 1200 kv to a particular installation along the electric grid. How much power is supplied to the installation? P = I V = (5 A)( V) = 6 MW Suppose the power station is 1000 km from the installation and delivers the power over copper wires. Assume the resistivity of copper is Ω m and the radius of the high tension wire is 2 cm. What is the resistance of the wire delivering the electricty? R = ρl A = 13.4 Ω

8 Example from Lecture 21 How much power is dissipated as heat in the transmission lines to the installation (current I = 5 A and potential difference V = 1200 kv are supplied to the station)? P = I 2 R = (5 A) 2 (13.4 Ω) = 336 W How much power would be dissipated as heat in the transmission lines to the installation if instead the station supplied 6 MW of power with current I = 500 A and potential difference V = 12 kv? Much more loss! P = I 2 R = (500 A) 2 (13.4 Ω) = 3.36 MW

9 Transformers Transmitting power at very high voltage and low current is much more efficient, though very high voltages are not safe or practical for household use. Transformers allow for the voltage to be adjusted as needed. This is the main reason why alternating current won out over direct current for use as the mains power delivered to consumers.

10 ound a common iron core that is found inside all Transformers The circuit diagram for a transformer looks like: ircuit diarmer. I 1 I 2 v 1 R L v 2 R L is the load resistance. N 1 N 2 The equivalent resistance, as seen by the generator on the primary side (R eq = V p /I p ) is: ( ) 2 Np R eq = R L N s

11 Transformers R eq = ( Np N s ) 2 R L Since the effective resistance is different from the actual load resistance R L, transformers are also used for load matching The Transformer and Power Transmission 101 Maximum power is delivered when the emf source s internal resistance, r = R L. The primary winding in this transformer is attached to the prongs of the plug, whereas the secondary winding is connected to the Figure Electronic devic are often powered by AC adaptor containing transformers such as this one. These adaptors alter the AC voltage. In many applications Sometimes, this is not power possible, cord on the right. but using a transformer we can make R eq = r. the adaptors also convert alterna ing current to direct current.. Cengage Learning/George Semple sformer is smaller than the one in ing photograph of this chapter. In it is a step-down transformer. It. Cengage Learning/George Semple

12 Transformer Question An alternating-current emf device in a certain circuit has a smaller resistance than that of the resistive load in the circuit; to increase the transfer of energy from the device to the load, a transformer will be connected between the two. (i) Should Ns be greater than or less than Np? (ii) Will that make it a step-up or step-down transformer? A (i) greater; (ii) step-up B (i) greater; (ii) step-down C (i) less; (ii) step-up D (i) less; (ii) step-down

13 Transformer Question An alternating-current emf device in a certain circuit has a smaller resistance than that of the resistive load in the circuit; to increase the transfer of energy from the device to the load, a transformer will be connected between the two. (i) Should Ns be greater than or less than Np? (ii) Will that make it a step-up or step-down transformer? A (i) greater; (ii) step-up B (i) greater; (ii) step-down C (i) less; (ii) step-up D (i) less; (ii) step-down

14 Rectifers What if a device needs a DC source, but is powered by the mains supply? Or, how do the lab power supplies work? They take in AC and output DC.

15 The steps most the important voltage down element from 120 in a V rectifier to, typically, circuit 6 V is or a 9 diode, V and a circuit element that con-thaverts alternating current in current one direction to current. but not The the AC DC other. Most converting diodes process used is in called modern conducts electronics rectification, are semiconductor and the converting devices. device The is called circuit a rectifier. symbol for a diode is, The most important element in a rectifier circuit is a diode, a circuit element that where the arrow indicates the direction of the current in the diode. A diode has Rectifers What conducts if a device current in needs one direction a DC but source, not the but other. ismost powered diodes used by the in modern mains low resistance supply? electronics to current in one direction (the direction of the arrow) and high resistance Or, are to current howsemiconductor do in the theopposite labdevices. power The direction. supplies circuit symbol To understand work? for a They diode is how a diode take rectifies in, AC where the arrow indicates the direction of the current in the diode. A diode has and a current, output consider DC. Figure 33.21a, which shows a diode and a resistor connected to low resistance to current in one direction (the direction of the arrow) and high the secondary resistance to of current a transformer. in the opposite The direction. transformer To understand reduces the how voltage a diode from rectifies 120-V AC to a current, the lower consider voltage Figure that is 33.21a, needed which for shows the device a diode having and a a resistor resistance connected R (the to load the secondary of a transformer. The transformer reduces the voltage from 120-V AC to the lower voltage that is needed for the device having a resistance R (the load Diode This is done using a rectifier. Diode C R Primary (input) Primary (input) a C R The diode only allowsa current through in one direction. The solid curve represents the current The solid in curve the represents resistor with the no filter current capacitor, in the resistor and the with dashed no curve filter capacitor, is the current and the when dashed the i R curve is the current when the i circuit includes the capacitor. R circuit includes the capacitor. ve alf-wave r al filter time versus time t t

16 Filters We can also select varying current signals based on their frequencies. A high-pass filter. C V out / V in 1 v in R v out log v a b Only high frequencies (large ω) reach v out.

17 Filters ting-current Circuits We can also select varying current signals based on their frequencies. A low-pass filter. The output voltage of the filter becomes very close to the input voltage as the frequency becomes small. R V out / V in 1 v in C v out log v a Only low frequencies (large ω) reach v out. You may be familiar with crossover networks, which are an important part speaker systems for high-quality audio systems. These networks use low-pa ers to direct low frequencies to a special type of speaker, the woofer, which b

18 Summary transformers filters and rectifiers Collected Homework 4! due Thursday. Final Exam Tuesday, Mar 27, 9:15-11:15am, S35 (here). Homework Serway & Jewett: NEW: Ch 32, Probs: 45, 53, 57, 59 NEW: Ch 33, onward from page Obj. Qs: 12, 13; Conc. Qs.: 8, 9; Probs: 1, 3, 5, 49, 51, 53, 57