PHYS 219 Spring semester Lecture 16: ac Voltages, ac currents and Transformers. Ron Reifenberger Birck Nanotechnology Center Purdue University

Transcription

1 HYS 9 Spring semester 06 Lecture 6: ac oltages, ac currents and Transformers on eifenberger Birck anotechnology Center urdue University Exam When: Wednesday, May 4, 06 7:00-9:00 M Where: HYS Lecture 6 (t) AC Generators T f T time, t(s) T if T ½T, then f f T 3 Sinusoidal wavefo otation t t sin πft sinπ sin ωt T O t t sin πft sinπ T sinωt o o o if T s ω π radians 60s - f 60s 60Hz - 377rad/ s

2 esistors in AC Circuits Assume a circuit consisting of an AC generator and a resistor The voltage across the output of the AC source varies with time according to (t) sin ( π ƒ t) (or o ) is the amplitude of the AC voltage (t) is the instantaneous potential difference (t ) sin ( π ƒ t ) t 3 What is the Current? Applying Ohm s Law: oltage applied Since the voltage varies sinusoidally, so does the current or sinπƒt where sin πƒt esponse (t) is in-phase with (t) 4

3 hasors: linking a rotating vector to the time-domain representation of the waveform. voltage phasor Θωt rojection of vector onto y-axis The voltage in an AC circuit can be represented by a voltage phasor The current in an AC circuit can also be represented by a current phasor The voltage and current phasors always make the same angle with the horizontal axis as time passes For a circuit with only resistors. the current and voltage are in phase 5 hasor Simulation Θ π ƒ t nstantaneous voltage Θ

4 Specifying the value (effective average) of a sine wave What is the average voltage of an AC source? s there a better way? To specify voltage values varying sinusoidally with time, the value has been universally adopted stands for oot Mean Square: Find average (mean) value of and take square root For a sinusoidally varying voltage sinπft t t sin πft ave t t t 3... t 7 ower lost in a resistor The instantaneous power is the product of the instantaneous voltage and instantaneous current Since both and vary with time, the power also varies with time: sin (πƒt) The instantaneous power varies between 0 and The average power is ½ the imum power ave ½ ( ) Ohm s Law can be used to express the average power in different ways ave 8 4

5 Example: ac circuit analysis 70 f60 Hz 0 Ω What are,, and average power dissipated in load? What are,, and imum power dissipated in load? Average values Maximum values 0 6A 6 A0 70W ave Ω Ω 8.5A 8.5 A W 9 An ac isolator () p t Bt () s () t rimary Secondary The Secondary is electrically isolated from the rimary nput: ac +dc signal () p t offset s Output: ac signal OLY () t Air coupling not very efficient 0 5

6 A ractical Transformer: Trapping Magnetic Flux with an ron Core iron core Coil Coil An ron-core Transformer p s rimary (Coil ) Secondary (Coil ) 6

7 Electric transformer: rimary and Secondary Coils esistive Load nput voltage must vary with time mportant equations for an ideal transformer Δ Δ in out Δ Δ Δ Δ Both input voltage and input current can be transformed " output " " input" Δ Δ 3 Adjusting the Output oltage schematic diagrams rimary Secondary ½ ac 8 turns 4 turns 4 7

8 EXAMLE A transformer has 0 turns on the primary and 00 turns on the secondary. f 0 is applied to the primary, what is the peak-to-peak voltage across the secondary? Δ Δ ptop 0 0 Δ 00 Δ p to p 5 f a 00 Ω load is connected to the secondary, what is the current in the primary? Δ Δ 0 0 Δ 00 Δ Δ 00 A load 00Ω 0 A A0A Ω 6 8

9 Up ext Optics and Optical henomena 7 AEDX: Transformers in the US ower Grid Lost Transmitted Lost line line 34.5Ω Why is power transmitted at such high voltages? 345,000 Typical values 000A Transmitted 345,000000A 345MW SUOSE 0% of power is lost 0% 34. 5MW ow suppose is decreased by 9/0 and is increased by 0/9, so the average power transmitted remains the same: 9 345,000 30, A A 9 Transmitted 30,500 A 345MW (same as before) How much power is now lost? line 34.5Ω (same as before) Lost line A Ω 4.6MW Lost Transmitted 4.6MW power lost increases by.3% 345MW 8 9