Lecture 24. Impedance of AC Circuits.

Size: px
Start display at page:

Download "Lecture 24. Impedance of AC Circuits."

Transcription

1 Lecture 4. Impedance of AC Circuits. Don t forget to complete course evaluations: Post-test. You are required to attend one of the lectures on Thursday, Dec. 7 when the post test will be given. If you do not take the post test, you will get a zero for % of your grade. Post-on-line survey. Please take the end-of-semester on-line survey at your earliest convenience but not later than midnight on Friday, December 5th 07. The link is We ask you to take this survey seriously because it helps us make improvements to this course and future courses.

2 Response of L-C-R Circuits to Alternating Currents So far we have considered transient processes in R-C and R-L circuits: the approach to the stationary (time-independent) state after some perturbation (e.g., switch on / off). Today we ll discuss the AC (cos ) driven circuits, e.g. the circuits driven by an AC power source. We disregard all transient processes and instead consider the steady-state AC currents: currents and voltages vary with time as ccc + φ, but their amplitudes are t-independent.

3 Amplitudes, rms Values, and Average Power in AC Circuits V t I t RLC Instantaneous values: Instantaneous power: V t = V 0 cos I t = I 0 cos + φ P t = V t I t Currents and voltages are NOT necessarily in phase, φ is the phase shift between V and I (the phase angle ). P t = V 0 cos I 0 cos + φ = V 0I 0 cos + φ + cos φ Average power: P aa P t = V 0I 0 cos φ Root mean square (rms): the square root of the average of the square of the quantity: a rrr = a t V rrr = V 0 I rrr = I 0 P aa = V rrr I rrr cos φ ccc φ - the power factor 3

4 Examples Average power: P aa P t = V 0I 0 cos φ Resistive loads φ = 0 I t V t R Capacitive and inductive loads φ = ± π Active (average) power: I V P (see below) P = RR S = V rrr I rrr cos φ = 0 φ = ± π π π phase ωt 4

5 Phasors / Complex Number Representation Problem: To find current/voltage in R-L-C circuits, we need to solve differential equations. Solution: The use of complex numbers / phasors allows us to replace linear differential equations with algebraic ones, and reduce trigonometry to algebra. Instantaneous value phasor We represent voltages and currents in the R-L-C circuits as the phase vectors (phasors) on the D plane. Quantity: A t = A 0 cos ωt. Corresponding phasor: a vector of length A 0 rotating counterclockwise with the angular frequency ω. Instantaneous value of A t is the projection of the phasor onto the horizontal axis. φ φ If all the quantities oscillate with the same ω, we can get rid of the term by using the rotating ( merry-goaround ) reference frame. We ll consider the steady state of AC circuits, when all amplitudes (the phasor lengths) are t-independent, and the only time dependence remaining is in the single frequency sinusoidal oscillation of voltages and currents. The t-independent angle between different phasors represents their relative phase. 5

6 b b φ φ Z a + ii = RR Z + i II Z RR Z = r cccφ II Z = r sssφ a Z = re iφ Z a ii = RR Z i II Z complex conjugate of Z Complex Numbers, Phasors Imaginary unit: Z Z Z i e iφ = cos φ + i sin φ e iπ = i A ccc ωt + φ = A A sss ωt + φ = A e iπ = i Z = i = ei +φ + ei +φ i = i Euler s relationship i +φ e e i i +φ The absolute value (or modulus or magnitude): = RR A ei +φ = II A ei +φ r cccc + i ssss r cccc i ssss = r ccc φ + sss φ = r Phasor: refer to either A e i +φ or just A e i φ. In the latter case, it is understood to be a shorthand notation: all phasors rotate with the same angular frequency and the time-independent angle φ between different phasors represents their relative phases. 6

7 Complex Numbers, Phasors (cont d) The use of complex numbers / phasors allows us to replace linear differential equations with algebraic ones, and reduce trigonometry to algebra: Addition: a + ii + c + ii = a + c + i b + d Multiplication: Differentiation: Ae iω t Be iω t = AAe i ω +ω t d dd AAiii = iωaa iii 7

8 V t Complex Power, Active Power and Reactive Power I t P t = V 0 cos I 0 cos + φ = V 0I 0 cos + φ + cos φ RLC P aa = V rrr I rrr cos φ Complex power: S = V t I t = V rrr e iii i +φ I rrr e = V rrr I rrr e ii = V rrr I rrr cos φ i sin φ = P + ii Average (active, real) power Reactive power P = RR S = V rrr I rrr ccc φ Apparent power: S = P + Q cos φ = P S 8

9 V t I t Resistor AC current through a resistor and AC voltage across the resistor are always in phase. Power dissipated in a resistor: P aa = V 0I 0 cccc = V 0I 0 = V rrr I rrr φ = 0 Active (average) power: P = RR S = V rrr I rrr cos φ = V rrr I rrr φ = 0 Q = II S = 0 If the load is purely resistive, both the current and voltage reverse their polarity at the same time. At every instant the product of voltage and current is positive or zero, with the result that the direction of energy flow (recall Poynting vector) does not reverse: only the active power is transferred from the power source to the load. 9

10 V t I t RLC Reactance and Impedance Both Reactance and Impedance are measures of how much the circuit impedes the flow of current. Units: Ohms. Impedance relates the time-independent phasors that represent the instantaneous values of voltage and current in the circuit: V rrr e iωt i φ = I rrr e Z V t = I t Z V rrr = I rrr X e ii all terms are real! Z = Z e ii The impedance is a complex number; it is a time-independent phasor, in contrast to V(t) and I(t). Reactance is the length of the impedance phasor, it is a real number. X Z V t I t V rrr = I rrr e ii Z e ii II I φ φ V RR Z V is the reference phasor 0

11 Reference Phasors II I φ φ V RR Z V is the reference phasor V rrr e iωt i +φ = I rrr e Z V rrr = I rrr e ii Z e iφ e iφ Since V rrr is real, φ must be the same as φ. II φ φ Z I RR V I is the reference phasor V rrr = I rrr e ii Z e ii I rrr = V rrre ii Z e ii = V rrre ii Z eii

12 I t Resistor Reactance and Impedance V t Resistor: V = IR = IX R Z R = X R = R Impedance and Reactance for a resistor are the same as its resistance, they are frequencyindependent.

13 V t I t Phase Shift in Capacitive Circuits V t V t = V 0 e iii i +φ I t = I 0 e Q t C = 0 dv t dd I t = dq t dd = C dd t dd = ii V 0 e iii I 0 e i(+φ) = iicv 0 e iii i = e iπ φ = π/ For a capacitor, voltage LAGS current by V t I t Current (reference phasor) 3

14 I t Phase Shift in Capacitive Circuit (cont d) V t V t I t Active (average) power: P = RR S = V rrr I rrr cos φ = 0 Current (reference phasor) φ = π π I V P π phase ωt If the loads are purely reactive (capacitors and/or inductors, no resistive elements), then the voltage and current are 90 0 out of phase. For half of each cycle, V I is positive, but on the other half of the cycle, the product is negative - on average, exactly as much energy flows toward the load as flows back. There is no net transfer of energy to the load - only reactive power flows back and forth. 4

15 Capacitor Reactance and Impedance I t V t V t I t Current (reference phasor) V t = I t Z Z = Z e ii V t I t iicv 0 e iii = I 0 e i +π V 0 e iii = I 0 e i +π iic Z C = i = i V 0 = I 0 V rrr = I rrr X C = 5

16 V t I t Phase Shift in Inductive Circuits V t L V t = V 0 e iii i +φ I t = I 0 e dd t dd dd t dd = 0 V t = L i +φ = ii I 0 e dd t dd V 0 e iii i +φ = iωli 0 e i = e iπ V 0 e iii = ω LL 0 e i +φ+π φ = π/ In an inductor, current LAGS voltage by

17 I t Phase Shift in Inductive Circuit (cont d) V t Active (average) power: P = RR S = V rrr I rrr cos φ = 0 φ = π π I V P π time t phase ωt Again, the power IS NOT dissipated in an inductor: it is stored in the magnetic field of the inductor for half a period, and returned to the power source for another half. 7

18 I t Inductor Reactance and Impedance V t V t = I t Z Z = Z e ii V t I t V 0 e iii = iωl I 0 e i π Z L = i V 0 = ωl I 0 V rrr = I rrr V rrr = I rrr X L X L = ωl 8

19 Reactances and Impedances: Summary Resistor Z R = X R = R V rrr = I rrr R V t = I t R Capacitor X C = Z C = i = i V rrr = I rrr X C V t = I t Z C Inductor X L = ωl Z L = i V rrr = I rrr X L V t = I t Z L The impedance reflects the phase shift between V and I. In general, the impedance is a complex number (in contrast to reactance, which is real). 9

20 Impedance of Series and Parallel circuits I For R, C, and L in series: Z = Z + Z + Z 3 + = R + ix L ix c = R + i For R, C, and L in parallel: Z = Z + Z + Z 3 + = R + i

21 Low-Pass Filter Goal: to suppress high-frequency (f > f 0 ) components in the spectrum of a signal. Spectral power 0 3 f, khz 0 3 f, khz Qualitatively: V ii drops across R and C, current is the same through both R and C. At high ω the reactance of the capacitor is small, and the rms value of the output voltage will also be small. Spectral power High-Pass Filter: Spectral power 0 3 f, khz 0 3 f, khz Spectral power 3

22 Low-Pass Filter V ii = I R ix c Total impedance: Z = Z R + Z C = R ix c Z = R + X c V ii0 = I 0 R + X c V ooo = I ix c V ooo0 = I 0 X c I V R V ii Z V C = V ooo V ooo0 V ii0 = X c R + X c = ωc R + = ωrc + = ωτ RR + Output power: V ooo0 V ii0 = ωτ RR + ωτ RR ω τ RR ω τ RR / Cutoff frequency: ω 0 = πf 0 = RR We want to suppress the high-frequency (f > 0kkk) components in the output of an audio amplifier with the output resistance 00 Ω. What capacitance do you need? C = πf 0 R = π F = 60nn 4

23 Problem : R-C circuit II I φ φ φ V R R V ii V C = V ooo Z Z RR A voltage V ii = V 0 ccc from an AC power supply with ω = 0 3 rrr/s is applied across a resistor with R = 00 Ω in series with a capacitor with C = 0. μμ. The current in the circuit is I = I 0 ccc + φ. The phase angle φ is given by ttt φ = A. 50 B. 50 C. 0 6 D. 0 6 tan φ = V ii t = I t Z = I 0 e iφ Z e iφ Z Z e ii = R i φ = aaaaaa III RRR = aaaaaa X C R R = 0 3 = Note that φ is positive (as it should be for the RC circuits, CIVIL). 5

24 I Impedance of Series R-L-C Circuits For R, C, and L in series: Z = R + ix L ix c = R + i V V t = I t R + i V L = iωll Z = Z Z = R + V R V I t Current (reference phasor) V rrr = I rrr R + V C = i I 6

25 Resonance in the L-C I I(ii L ) II I I( ii C ) Condition for the Resonance: reactances for L and C are of the same magnitude: X C = = X L = ωl f 0 = ω 0 π ω 0 C = ω 0L ω 0 = LL At ω =ω 0 minimum (real) impedance max current. 7

26 I Resonance in Series R-L-C circuits For R, C, and L in series: Z = Z Z = R + I = V Z = V Z = R + ix L ix c = R + i R + Resonance condition: = ω 0 = LL - resonance frequency At ω =ω 0 minimum (real) impedance, max current. Note that at ω =ω 0, V C and V L can be greater than V. ω > ω 0 ω < ω 0 ω = ω 0 8

27 Problem : Series R-L-C circuits V L = iωll V rrr L =. 80 = 76V V R V rrr R =. 40 = 88V V V rrr C =. 0 = 4V V C = i I V rrr = I rrr Z = I rrr R + V rrr = = 0V 9

28 Next time: post-test! me your questions for the review session on Monday, //07! 30

29 Problem 3: Series R-L-C circuits An R-L-C series circuit with an inductance of 0.9H, a resistance of 44 Ω, and a capacitance of 7.7 µf carries an rms current of 0.446A with a frequency of 39Hz.. What is the impedance of the circuit? ω = 455 rrr/s Z = R + ix L ix c = R + i. What is the phase angle? Z 0 = R + = 339Ω II φ φ Z V RR tan φ = ωl ωc R = arctan rrr I 3. What is the rms voltage of the source? V rrr = I rrr Z 0 = 0.446A 339Ω = 5V 4. What average power is delivered by the source? cos 0.77 = power factor for this circuit P aa = V rrr I rrr cos φ = 5V 0.446A 0.7 = 48.6W - average rate at which electrical energy is converted to thermal energy in the resistor 3

30 Appendix : R-L-C circuits P aa = V rrr I rrr cos φ = V 0 I 0 cos φ cos φ = P aa V 0 I 0 = arccos W 00V 0.5A = 0.6 3

31 Appendix : Transformer Φ B - the flux per turn ℇ p = N p dφ B dd ℇ s = N s dφ B dd For an ideal transformer (R s = R p = 0): Energy conservation: ℇ p ℇ s = N p N s V p V s = N p N s V p I p = V s I s I s I p = N p N s V p V s I p = N p N s V s I s V p I p = N p N s R - as if the source had been connected directly to a resistance N p N s R impedance transformation Using mutual inductance M = L p L s : M Φ s I p = N sφ B I p M di p dd = N dφ B s dd ℇ s = M di p dd 33

32 Sloppy formulation Example ℇ s = M di p dd = I sr s M = I sr s di p dd = 0.4 cos 377t cos 377t =.55mm ℇ s = M di p dd = M 6t = = 0.8V 34

33 Parallel R-L-C Circuit: Example P aa = V rrr I rrr cos φ I rrr = V rrr Z Z = R + i Z = R + tan φ = /R = 3 4 II φ φ I Z V RR I rrr = V rrr Z = V rrr R + cos φ = = 0 + ttt φ = = 50 A P aa = V rrr I rrr cos φ = = 00W 35

34 I Parallel Resonance in the R-L-C circuits Z = R + iii + ωc i = R i + i = X L X C R + i Z = R + ωc ωl At the resonance frequency ω 0 = LL Z is at its minimum ω 0 L is a short ω C is a short I = V Z = V R + min at = or ω 0 = LL Note that at ω =ω 0, I C and I L can be greater than I. R = Ω, C = F, L = H, and V = V 36

1 Phasors and Alternating Currents

1 Phasors and Alternating Currents Physics 4 Chapter : Alternating Current 0/5 Phasors and Alternating Currents alternating current: current that varies sinusoidally with time ac source: any device that supplies a sinusoidally varying potential

More information

Handout 11: AC circuit. AC generator

Handout 11: AC circuit. AC generator Handout : AC circuit AC generator Figure compares the voltage across the directcurrent (DC) generator and that across the alternatingcurrent (AC) generator For DC generator, the voltage is constant For

More information

Chapter 33. Alternating Current Circuits

Chapter 33. Alternating Current Circuits Chapter 33 Alternating Current Circuits 1 Capacitor Resistor + Q = C V = I R R I + + Inductance d I Vab = L dt AC power source The AC power source provides an alternative voltage, Notation - Lower case

More information

Announcements: Today: more AC circuits

Announcements: Today: more AC circuits Announcements: Today: more AC circuits I 0 I rms Current through a light bulb I 0 I rms I t = I 0 cos ωt I 0 Current through a LED I t = I 0 cos ωt Θ(cos ωt ) Theta function (is zero for a negative argument)

More information

ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT

ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT Chapter 31: ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT 1 A charged capacitor and an inductor are connected in series At time t = 0 the current is zero, but the capacitor is charged If T is the

More information

Alternating Current Circuits

Alternating Current Circuits Alternating Current Circuits AC Circuit An AC circuit consists of a combination of circuit elements and an AC generator or source. The output of an AC generator is sinusoidal and varies with time according

More information

RLC Circuit (3) We can then write the differential equation for charge on the capacitor. The solution of this differential equation is

RLC Circuit (3) We can then write the differential equation for charge on the capacitor. The solution of this differential equation is RLC Circuit (3) We can then write the differential equation for charge on the capacitor The solution of this differential equation is (damped harmonic oscillation!), where 25 RLC Circuit (4) If we charge

More information

Supplemental Notes on Complex Numbers, Complex Impedance, RLC Circuits, and Resonance

Supplemental Notes on Complex Numbers, Complex Impedance, RLC Circuits, and Resonance Supplemental Notes on Complex Numbers, Complex Impedance, RLC Circuits, and Resonance Complex numbers Complex numbers are expressions of the form z = a + ib, where both a and b are real numbers, and i

More information

Course Updates. Reminders: 1) Assignment #10 due Today. 2) Quiz # 5 Friday (Chap 29, 30) 3) Start AC Circuits

Course Updates. Reminders: 1) Assignment #10 due Today. 2) Quiz # 5 Friday (Chap 29, 30) 3) Start AC Circuits ourse Updates http://www.phys.hawaii.edu/~varner/phys272-spr10/physics272.html eminders: 1) Assignment #10 due Today 2) Quiz # 5 Friday (hap 29, 30) 3) Start A ircuits Alternating urrents (hap 31) In this

More information

AC Circuits Homework Set

AC Circuits Homework Set Problem 1. In an oscillating LC circuit in which C=4.0 μf, the maximum potential difference across the capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 ma.

More information

SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS

SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS 1. Introduction A sinusoidal current has the following form: where I m is the amplitude value; ω=2 πf is the angular frequency; φ is the phase shift. i (t )=I m.sin

More information

Electromagnetic Oscillations and Alternating Current. 1. Electromagnetic oscillations and LC circuit 2. Alternating Current 3.

Electromagnetic Oscillations and Alternating Current. 1. Electromagnetic oscillations and LC circuit 2. Alternating Current 3. Electromagnetic Oscillations and Alternating Current 1. Electromagnetic oscillations and LC circuit 2. Alternating Current 3. RLC circuit in AC 1 RL and RC circuits RL RC Charging Discharging I = emf R

More information

REACTANCE. By: Enzo Paterno Date: 03/2013

REACTANCE. By: Enzo Paterno Date: 03/2013 REACTANCE REACTANCE By: Enzo Paterno Date: 03/2013 5/2007 Enzo Paterno 1 RESISTANCE - R i R (t R A resistor for all practical purposes is unaffected by the frequency of the applied sinusoidal voltage or

More information

Sinusoidal Steady-State Analysis

Sinusoidal Steady-State Analysis Chapter 4 Sinusoidal Steady-State Analysis In this unit, we consider circuits in which the sources are sinusoidal in nature. The review section of this unit covers most of section 9.1 9.9 of the text.

More information

Physics 115. AC: RL vs RC circuits Phase relationships RLC circuits. General Physics II. Session 33

Physics 115. AC: RL vs RC circuits Phase relationships RLC circuits. General Physics II. Session 33 Session 33 Physics 115 General Physics II AC: RL vs RC circuits Phase relationships RLC circuits R. J. Wilkes Email: phy115a@u.washington.edu Home page: http://courses.washington.edu/phy115a/ 6/2/14 1

More information

Physics 115. AC circuits Reactances Phase relationships Evaluation. General Physics II. Session 35. R. J. Wilkes

Physics 115. AC circuits Reactances Phase relationships Evaluation. General Physics II. Session 35. R. J. Wilkes Session 35 Physics 115 General Physics II AC circuits Reactances Phase relationships Evaluation R. J. Wilkes Email: phy115a@u.washington.edu 06/05/14 1 Lecture Schedule Today 2 Announcements Please pick

More information

Oscillations and Electromagnetic Waves. March 30, 2014 Chapter 31 1

Oscillations and Electromagnetic Waves. March 30, 2014 Chapter 31 1 Oscillations and Electromagnetic Waves March 30, 2014 Chapter 31 1 Three Polarizers! Consider the case of unpolarized light with intensity I 0 incident on three polarizers! The first polarizer has a polarizing

More information

EM Oscillations. David J. Starling Penn State Hazleton PHYS 212

EM Oscillations. David J. Starling Penn State Hazleton PHYS 212 I ve got an oscillating fan at my house. The fan goes back and forth. It looks like the fan is saying No. So I like to ask it questions that a fan would say no to. Do you keep my hair in place? Do you

More information

Driven RLC Circuits Challenge Problem Solutions

Driven RLC Circuits Challenge Problem Solutions Driven LC Circuits Challenge Problem Solutions Problem : Using the same circuit as in problem 6, only this time leaving the function generator on and driving below resonance, which in the following pairs

More information

EE292: Fundamentals of ECE

EE292: Fundamentals of ECE EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 18 121025 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review RMS Values Complex Numbers Phasors Complex Impedance Circuit Analysis

More information

EE292: Fundamentals of ECE

EE292: Fundamentals of ECE EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 20 121101 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Chapters 1-3 Circuit Analysis Techniques Chapter 10 Diodes Ideal Model

More information

CHAPTER 22 ELECTROMAGNETIC INDUCTION

CHAPTER 22 ELECTROMAGNETIC INDUCTION CHAPTER 22 ELECTROMAGNETIC INDUCTION PROBLEMS 47. REASONING AND Using Equation 22.7, we find emf 2 M I or M ( emf 2 ) t ( 0.2 V) ( 0.4 s) t I (.6 A) ( 3.4 A) 9.3 0 3 H 49. SSM REASONING AND From the results

More information

Alternating Current Circuits. Home Work Solutions

Alternating Current Circuits. Home Work Solutions Chapter 21 Alternating Current Circuits. Home Work s 21.1 Problem 21.11 What is the time constant of the circuit in Figure (21.19). 10 Ω 10 Ω 5.0 Ω 2.0µF 2.0µF 2.0µF 3.0µF Figure 21.19: Given: The circuit

More information

Lecture 4: R-L-C Circuits and Resonant Circuits

Lecture 4: R-L-C Circuits and Resonant Circuits Lecture 4: R-L-C Circuits and Resonant Circuits RLC series circuit: What's V R? Simplest way to solve for V is to use voltage divider equation in complex notation: V X L X C V R = in R R + X C + X L L

More information

ELEC ELE TRO TR MAGNETIC INDUCTION

ELEC ELE TRO TR MAGNETIC INDUCTION ELECTRO MAGNETIC INDUCTION Faraday Henry 1791-1867 1797 1878 Laws:- Faraday s Laws :- 1) When ever there is a change in magnetic flux linked with a coil, a current is generated in the coil. The current

More information

Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current

Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current People of mediocre ability sometimes achieve outstanding success because they don't know when to quit. Most men succeed because

More information

I. Impedance of an R-L circuit.

I. Impedance of an R-L circuit. I. Impedance of an R-L circuit. [For inductor in an AC Circuit, see Chapter 31, pg. 1024] Consider the R-L circuit shown in Figure: 1. A current i(t) = I cos(ωt) is driven across the circuit using an AC

More information

Chapter 10: Sinusoids and Phasors

Chapter 10: Sinusoids and Phasors Chapter 10: Sinusoids and Phasors 1. Motivation 2. Sinusoid Features 3. Phasors 4. Phasor Relationships for Circuit Elements 5. Impedance and Admittance 6. Kirchhoff s Laws in the Frequency Domain 7. Impedance

More information

Part 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is

Part 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is 1 Part 4: Electromagnetism 4.1: Induction A. Faraday's Law The magnetic flux through a loop of wire is Φ = BA cos θ B A B = magnetic field penetrating loop [T] A = area of loop [m 2 ] = angle between field

More information

Sinusoidal Response of RLC Circuits

Sinusoidal Response of RLC Circuits Sinusoidal Response of RLC Circuits Series RL circuit Series RC circuit Series RLC circuit Parallel RL circuit Parallel RC circuit R-L Series Circuit R-L Series Circuit R-L Series Circuit Instantaneous

More information

Yell if you have any questions

Yell if you have any questions Class 31: Outline Hour 1: Concept Review / Overview PRS Questions possible exam questions Hour : Sample Exam Yell if you have any questions P31 1 Exam 3 Topics Faraday s Law Self Inductance Energy Stored

More information

SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING. Self-paced Course

SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING. Self-paced Course SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING Self-paced Course MODULE 26 APPLICATIONS TO ELECTRICAL CIRCUITS Module Topics 1. Complex numbers and alternating currents 2. Complex impedance 3.

More information

Physics 9 Friday, April 18, 2014

Physics 9 Friday, April 18, 2014 Physics 9 Friday, April 18, 2014 Turn in HW12. I ll put HW13 online tomorrow. For Monday: read all of Ch33 (optics) For Wednesday: skim Ch34 (wave optics) I ll hand out your take-home practice final exam

More information

12 Chapter Driven RLC Circuits

12 Chapter Driven RLC Circuits hapter Driven ircuits. A Sources... -. A ircuits with a Source and One ircuit Element... -3.. Purely esistive oad... -3.. Purely Inductive oad... -6..3 Purely apacitive oad... -8.3 The Series ircuit...

More information

ALTERNATING CURRENT. with X C = 0.34 A. SET UP: The specified value is the root-mean-square current; I. EXECUTE: (a) V = (0.34 A) = 0.12 A.

ALTERNATING CURRENT. with X C = 0.34 A. SET UP: The specified value is the root-mean-square current; I. EXECUTE: (a) V = (0.34 A) = 0.12 A. ATENATING UENT 3 3 IDENTIFY: i Icosωt and I I/ SET UP: The specified value is the root-mean-square current; I 34 A EXEUTE: (a) I 34 A (b) I I (34 A) 48 A (c) Since the current is positive half of the time

More information

Lectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits. Nov. 7 & 9, 2011

Lectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits. Nov. 7 & 9, 2011 Lectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits Nov. 7 & 9, 2011 Material from Textbook by Alexander & Sadiku and Electrical Engineering: Principles & Applications,

More information

Circuit Analysis-II. Circuit Analysis-II Lecture # 5 Monday 23 rd April, 18

Circuit Analysis-II. Circuit Analysis-II Lecture # 5 Monday 23 rd April, 18 Circuit Analysis-II Capacitors in AC Circuits Introduction ü The instantaneous capacitor current is equal to the capacitance times the instantaneous rate of change of the voltage across the capacitor.

More information

Single Phase Parallel AC Circuits

Single Phase Parallel AC Circuits Single Phase Parallel AC Circuits 1 Single Phase Parallel A.C. Circuits (Much of this material has come from Electrical & Electronic Principles & Technology by John Bird) n parallel a.c. circuits similar

More information

Consider a simple RC circuit. We might like to know how much power is being supplied by the source. We probably need to find the current.

Consider a simple RC circuit. We might like to know how much power is being supplied by the source. We probably need to find the current. AC power Consider a simple RC circuit We might like to know how much power is being supplied by the source We probably need to find the current R 10! R 10! is VS Vmcosωt Vm 10 V f 60 Hz V m 10 V C 150

More information

Sinusoidal Steady-State Analysis

Sinusoidal Steady-State Analysis Sinusoidal Steady-State Analysis Almost all electrical systems, whether signal or power, operate with alternating currents and voltages. We have seen that when any circuit is disturbed (switched on or

More information

Exam 3 Topics. Displacement Current Poynting Vector. Faraday s Law Self Inductance. Circuits. Energy Stored in Inductor/Magnetic Field

Exam 3 Topics. Displacement Current Poynting Vector. Faraday s Law Self Inductance. Circuits. Energy Stored in Inductor/Magnetic Field Exam 3 Topics Faraday s Law Self Inductance Energy Stored in Inductor/Magnetic Field Circuits LR Circuits Undriven (R)LC Circuits Driven RLC Circuits Displacement Current Poynting Vector NO: B Materials,

More information

Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance

Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Lesson 7 Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Oscillations in an LC Circuit The RLC Circuit Alternating Current Electromagnetic

More information

R-L-C Circuits and Resonant Circuits

R-L-C Circuits and Resonant Circuits P517/617 Lec4, P1 R-L-C Circuits and Resonant Circuits Consider the following RLC series circuit What's R? Simplest way to solve for is to use voltage divider equation in complex notation. X L X C in 0

More information

Physics 142 AC Circuits Page 1. AC Circuits. I ve had a perfectly lovely evening but this wasn t it. Groucho Marx

Physics 142 AC Circuits Page 1. AC Circuits. I ve had a perfectly lovely evening but this wasn t it. Groucho Marx Physics 142 A ircuits Page 1 A ircuits I ve had a perfectly lovely evening but this wasn t it. Groucho Marx Alternating current: generators and values It is relatively easy to devise a source (a generator

More information

University of California, Berkeley Physics H7B Spring 1999 (Strovink) SOLUTION TO PROBLEM SET 11 Solutions by P. Pebler

University of California, Berkeley Physics H7B Spring 1999 (Strovink) SOLUTION TO PROBLEM SET 11 Solutions by P. Pebler University of California Berkeley Physics H7B Spring 999 (Strovink) SOLUTION TO PROBLEM SET Solutions by P. Pebler Purcell 7.2 A solenoid of radius a and length b is located inside a longer solenoid of

More information

P441 Analytical Mechanics - I. RLC Circuits. c Alex R. Dzierba. In this note we discuss electrical oscillating circuits: undamped, damped and driven.

P441 Analytical Mechanics - I. RLC Circuits. c Alex R. Dzierba. In this note we discuss electrical oscillating circuits: undamped, damped and driven. Lecture 10 Monday - September 19, 005 Written or last updated: September 19, 005 P441 Analytical Mechanics - I RLC Circuits c Alex R. Dzierba Introduction In this note we discuss electrical oscillating

More information

Electronics. Basics & Applications. group talk Daniel Biesinger

Electronics. Basics & Applications. group talk Daniel Biesinger Electronics Basics & Applications group talk 23.7.2010 by Daniel Biesinger 1 2 Contents Contents Basics Simple applications Equivalent circuit Impedance & Reactance More advanced applications - RC circuits

More information

Schedule. ECEN 301 Discussion #20 Exam 2 Review 1. Lab Due date. Title Chapters HW Due date. Date Day Class No. 10 Nov Mon 20 Exam Review.

Schedule. ECEN 301 Discussion #20 Exam 2 Review 1. Lab Due date. Title Chapters HW Due date. Date Day Class No. 10 Nov Mon 20 Exam Review. Schedule Date Day lass No. 0 Nov Mon 0 Exam Review Nov Tue Title hapters HW Due date Nov Wed Boolean Algebra 3. 3.3 ab Due date AB 7 Exam EXAM 3 Nov Thu 4 Nov Fri Recitation 5 Nov Sat 6 Nov Sun 7 Nov Mon

More information

Chapter 32A AC Circuits. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 32A AC Circuits. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Chapter 32A AC Circuits A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should be able to: Describe

More information

Circuit Analysis-III. Circuit Analysis-II Lecture # 3 Friday 06 th April, 18

Circuit Analysis-III. Circuit Analysis-II Lecture # 3 Friday 06 th April, 18 Circuit Analysis-III Sinusoids Example #1 ü Find the amplitude, phase, period and frequency of the sinusoid: v (t ) =12cos(50t +10 ) Signal Conversion ü From sine to cosine and vice versa. ü sin (A ± B)

More information

General Physics (PHY 2140)

General Physics (PHY 2140) General Physics (PHY 2140) Lecture 10 6/12/2007 Electricity and Magnetism Induced voltages and induction Self-Inductance RL Circuits Energy in magnetic fields AC circuits and EM waves Resistors, capacitors

More information

z = x + iy ; x, y R rectangular or Cartesian form z = re iθ ; r, θ R polar form. (1)

z = x + iy ; x, y R rectangular or Cartesian form z = re iθ ; r, θ R polar form. (1) 11 Complex numbers Read: Boas Ch. Represent an arb. complex number z C in one of two ways: z = x + iy ; x, y R rectangular or Cartesian form z = re iθ ; r, θ R polar form. (1) Here i is 1, engineers call

More information

20. Alternating Currents

20. Alternating Currents University of hode sland DigitalCommons@U PHY 204: Elementary Physics Physics Course Materials 2015 20. lternating Currents Gerhard Müller University of hode sland, gmuller@uri.edu Creative Commons License

More information

To find the step response of an RC circuit

To find the step response of an RC circuit To find the step response of an RC circuit v( t) v( ) [ v( t) v( )] e tt The time constant = RC The final capacitor voltage v() The initial capacitor voltage v(t ) To find the step response of an RL circuit

More information

CLUSTER LEVEL WORK SHOP

CLUSTER LEVEL WORK SHOP CLUSTER LEVEL WORK SHOP SUBJECT PHYSICS QUESTION BANK (ALTERNATING CURRENT ) DATE: 0/08/06 What is the phase difference between the voltage across the inductance and capacitor in series AC circuit? Ans.

More information

ELEC 2501 AB. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.

ELEC 2501 AB. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work. It is most beneficial to you to write this mock midterm UNDER EXAM CONDITIONS. This means: Complete the midterm in 3 hour(s). Work on your own. Keep your notes and textbook closed. Attempt every question.

More information

AC Circuits III. Physics 2415 Lecture 24. Michael Fowler, UVa

AC Circuits III. Physics 2415 Lecture 24. Michael Fowler, UVa AC Circuits III Physics 415 Lecture 4 Michael Fowler, UVa Today s Topics LC circuits: analogy with mass on spring LCR circuits: damped oscillations LCR circuits with ac source: driven pendulum, resonance.

More information

Electrical Circuits Lab Series RC Circuit Phasor Diagram

Electrical Circuits Lab Series RC Circuit Phasor Diagram Electrical Circuits Lab. 0903219 Series RC Circuit Phasor Diagram - Simple steps to draw phasor diagram of a series RC circuit without memorizing: * Start with the quantity (voltage or current) that is

More information

Chapter 31 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively

Chapter 31 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively Chapter 3 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively In the LC circuit the charge, current, and potential difference vary sinusoidally (with period T and angular

More information

Physics for Scientists & Engineers 2

Physics for Scientists & Engineers 2 Electromagnetic Oscillations Physics for Scientists & Engineers Spring Semester 005 Lecture 8! We have been working with circuits that have a constant current a current that increases to a constant current

More information

Experiment 3: Resonance in LRC Circuits Driven by Alternating Current

Experiment 3: Resonance in LRC Circuits Driven by Alternating Current Experiment 3: Resonance in LRC Circuits Driven by Alternating Current Introduction In last week s laboratory you examined the LRC circuit when constant voltage was applied to it. During this laboratory

More information

Alternating Currents. The power is transmitted from a power house on high voltage ac because (a) Electric current travels faster at higher volts (b) It is more economical due to less power wastage (c)

More information

Assessment Schedule 2015 Physics: Demonstrate understanding of electrical systems (91526)

Assessment Schedule 2015 Physics: Demonstrate understanding of electrical systems (91526) NCEA Level 3 Physics (91526) 2015 page 1 of 6 Assessment Schedule 2015 Physics: Demonstrate understanding of electrical systems (91526) Evidence Q Evidence Achievement Achievement with Merit Achievement

More information

Physics-272 Lecture 20. AC Power Resonant Circuits Phasors (2-dim vectors, amplitude and phase)

Physics-272 Lecture 20. AC Power Resonant Circuits Phasors (2-dim vectors, amplitude and phase) Physics-7 ecture 0 A Power esonant ircuits Phasors (-dim vectors, amplitude and phase) What is reactance? You can think of it as a frequency-dependent resistance. 1 ω For high ω, χ ~0 - apacitor looks

More information

Chapter 10: Sinusoidal Steady-State Analysis

Chapter 10: Sinusoidal Steady-State Analysis Chapter 10: Sinusoidal Steady-State Analysis 1 Objectives : sinusoidal functions Impedance use phasors to determine the forced response of a circuit subjected to sinusoidal excitation Apply techniques

More information

Module 25: Outline Resonance & Resonance Driven & LRC Circuits Circuits 2

Module 25: Outline Resonance & Resonance Driven & LRC Circuits Circuits 2 Module 25: Driven RLC Circuits 1 Module 25: Outline Resonance & Driven LRC Circuits 2 Driven Oscillations: Resonance 3 Mass on a Spring: Simple Harmonic Motion A Second Look 4 Mass on a Spring (1) (2)

More information

Chapter 21: RLC Circuits. PHY2054: Chapter 21 1

Chapter 21: RLC Circuits. PHY2054: Chapter 21 1 Chapter 21: RC Circuits PHY2054: Chapter 21 1 Voltage and Current in RC Circuits AC emf source: driving frequency f ε = ε sinωt ω = 2π f m If circuit contains only R + emf source, current is simple ε ε

More information

2 Signal Frequency and Impedances First Order Filter Circuits Resonant and Second Order Filter Circuits... 13

2 Signal Frequency and Impedances First Order Filter Circuits Resonant and Second Order Filter Circuits... 13 Lecture Notes: 3454 Physics and Electronics Lecture ( nd Half), Year: 7 Physics Department, Faculty of Science, Chulalongkorn University //7 Contents Power in Ac Circuits Signal Frequency and Impedances

More information

Power Factor Improvement

Power Factor Improvement Salman bin AbdulazizUniversity College of Engineering Electrical Engineering Department EE 2050Electrical Circuit Laboratory Power Factor Improvement Experiment # 4 Objectives: 1. To introduce the concept

More information

Lecture 05 Power in AC circuit

Lecture 05 Power in AC circuit CA2627 Building Science Lecture 05 Power in AC circuit Instructor: Jiayu Chen Ph.D. Announcement 1. Makeup Midterm 2. Midterm grade Grade 25 20 15 10 5 0 10 15 20 25 30 35 40 Grade Jiayu Chen, Ph.D. 2

More information

Learnabout Electronics - AC Theory

Learnabout Electronics - AC Theory Learnabout Electronics - AC Theory Facts & Formulae for AC Theory www.learnabout-electronics.org Contents AC Wave Values... 2 Capacitance... 2 Charge on a Capacitor... 2 Total Capacitance... 2 Inductance...

More information

Electric Circuit Theory

Electric Circuit Theory Electric Circuit Theory Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Chapter 11 Sinusoidal Steady-State Analysis Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Contents and Objectives 3 Chapter Contents 11.1

More information

EXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA

EXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA EXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA DISCUSSION The capacitor is a element which stores electric energy by charging the charge on it. Bear in mind that the charge on a capacitor

More information

AC Source and RLC Circuits

AC Source and RLC Circuits X X L C = 2π fl = 1/2π fc 2 AC Source and RLC Circuits ( ) 2 Inductive reactance Capacitive reactance Z = R + X X Total impedance L C εmax Imax = Z XL XC tanφ = R Maximum current Phase angle PHY2054: Chapter

More information

EXP. NO. 3 Power on (resistive inductive & capacitive) load Series connection

EXP. NO. 3 Power on (resistive inductive & capacitive) load Series connection OBJECT: To examine the power distribution on (R, L, C) series circuit. APPARATUS 1-signal function generator 2- Oscilloscope, A.V.O meter 3- Resisters & inductor &capacitor THEORY the following form for

More information

Solutions to these tests are available online in some places (but not all explanations are good)...

Solutions to these tests are available online in some places (but not all explanations are good)... The Physics GRE Sample test put out by ETS https://www.ets.org/s/gre/pdf/practice_book_physics.pdf OSU physics website has lots of tips, and 4 additional tests http://www.physics.ohiostate.edu/undergrad/ugs_gre.php

More information

Laboratory I: Impedance

Laboratory I: Impedance Physics 331, Fall 2008 Lab I - Handout 1 Laboratory I: Impedance Reading: Simpson Chapter 1 (if necessary) & Chapter 2 (particularly 2.9-2.13) 1 Introduction In this first lab we review the properties

More information

Physics 294H. lectures will be posted frequently, mostly! every day if I can remember to do so

Physics 294H. lectures will be posted frequently, mostly! every day if I can remember to do so Physics 294H l Professor: Joey Huston l email:huston@msu.edu l office: BPS3230 l Homework will be with Mastering Physics (and an average of 1 hand-written problem per week) Help-room hours: 12:40-2:40

More information

Assessment Schedule 2016 Physics: Demonstrate understanding electrical systems (91526)

Assessment Schedule 2016 Physics: Demonstrate understanding electrical systems (91526) NCEA evel 3 Physics (91526) 2016 page 1 of 5 Assessment Schedule 2016 Physics: Demonstrate understanding electrical systems (91526) Evidence Statement NØ N1 N 2 A 3 A 4 M 5 M 6 E 7 E 8 0 1A 2A 3A 4A or

More information

RLC Circuits. 1 Introduction. 1.1 Undriven Systems. 1.2 Driven Systems

RLC Circuits. 1 Introduction. 1.1 Undriven Systems. 1.2 Driven Systems RLC Circuits Equipment: Capstone, 850 interface, RLC circuit board, 4 leads (91 cm), 3 voltage sensors, Fluke mulitmeter, and BNC connector on one end and banana plugs on the other Reading: Review AC circuits

More information

RLC Series Circuit. We can define effective resistances for capacitors and inductors: 1 = Capacitive reactance:

RLC Series Circuit. We can define effective resistances for capacitors and inductors: 1 = Capacitive reactance: RLC Series Circuit In this exercise you will investigate the effects of changing inductance, capacitance, resistance, and frequency on an RLC series AC circuit. We can define effective resistances for

More information

Homework 2 SJTU233. Part A. Part B. Problem 2. Part A. Problem 1. Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω.

Homework 2 SJTU233. Part A. Part B. Problem 2. Part A. Problem 1. Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω. Homework 2 SJTU233 Problem 1 Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω. Express Zab in polar form. Enter your answer using polar notation. Express argument in degrees.

More information

Module 4. Single-phase AC Circuits

Module 4. Single-phase AC Circuits Module 4 Single-phase AC Circuits Lesson 14 Solution of Current in R-L-C Series Circuits In the last lesson, two points were described: 1. How to represent a sinusoidal (ac) quantity, i.e. voltage/current

More information

Chapter 31: AC Circuits

Chapter 31: AC Circuits hapter 31: A ircuits A urrents and Voltages In this chapter, we discuss the behior of circuits driven by a source of A. Recall that A means, literally, alternating current. An alternating current is a

More information

Sinusoidal Steady-State Analysis

Sinusoidal Steady-State Analysis Sinusoidal Steady-State Analysis Mauro Forti October 27, 2018 Constitutive Relations in the Frequency Domain Consider a network with independent voltage and current sources at the same angular frequency

More information

SUMMARY Phys 2523 (University Physics II) Compiled by Prof. Erickson. F e (r )=q E(r ) dq r 2 ˆr = k e E = V. V (r )=k e r = k q i. r i r.

SUMMARY Phys 2523 (University Physics II) Compiled by Prof. Erickson. F e (r )=q E(r ) dq r 2 ˆr = k e E = V. V (r )=k e r = k q i. r i r. SUMMARY Phys 53 (University Physics II) Compiled by Prof. Erickson q 1 q Coulomb s Law: F 1 = k e r ˆr where k e = 1 4π =8.9875 10 9 N m /C, and =8.85 10 1 C /(N m )isthepermittivity of free space. Generally,

More information

Self-Inductance. Φ i. Self-induction. = (if flux Φ 1 through 1 loop. Tm Vs A A. Lecture 11-1

Self-Inductance. Φ i. Self-induction. = (if flux Φ 1 through 1 loop. Tm Vs A A. Lecture 11-1 Lecture - Self-Inductance As current i through coil increases, magnetic flux through itself increases. This in turn induces back emf in the coil itself When current i is decreasing, emf is induced again

More information

Inductance, RL and RLC Circuits

Inductance, RL and RLC Circuits Inductance, RL and RLC Circuits Inductance Temporarily storage of energy by the magnetic field When the switch is closed, the current does not immediately reach its maximum value. Faraday s law of electromagnetic

More information

AC analysis. EE 201 AC analysis 1

AC analysis. EE 201 AC analysis 1 AC analysis Now we turn to circuits with sinusoidal sources. Earlier, we had a brief look at sinusoids, but now we will add in capacitors and inductors, making the story much more interesting. What are

More information

ALTERNATING CURRENT

ALTERNATING CURRENT ATENATING UENT Important oints:. The alternating current (A) is generally expressed as ( ) I I sin ω t + φ Where i peak value of alternating current.. emf of an alternating current source is generally

More information

Sinusoids and Phasors

Sinusoids and Phasors CHAPTER 9 Sinusoids and Phasors We now begins the analysis of circuits in which the voltage or current sources are time-varying. In this chapter, we are particularly interested in sinusoidally time-varying

More information

EE221 Circuits II. Chapter 14 Frequency Response

EE221 Circuits II. Chapter 14 Frequency Response EE22 Circuits II Chapter 4 Frequency Response Frequency Response Chapter 4 4. Introduction 4.2 Transfer Function 4.3 Bode Plots 4.4 Series Resonance 4.5 Parallel Resonance 4.6 Passive Filters 4.7 Active

More information

Lecture 11 - AC Power

Lecture 11 - AC Power - AC Power 11/17/2015 Reading: Chapter 11 1 Outline Instantaneous power Complex power Average (real) power Reactive power Apparent power Maximum power transfer Power factor correction 2 Power in AC Circuits

More information

Lecture 9 Time Domain vs. Frequency Domain

Lecture 9 Time Domain vs. Frequency Domain . Topics covered Lecture 9 Time Domain vs. Frequency Domain (a) AC power in the time domain (b) AC power in the frequency domain (c) Reactive power (d) Maximum power transfer in AC circuits (e) Frequency

More information

Inductive & Capacitive Circuits. Subhasish Chandra Assistant Professor Department of Physics Institute of Forensic Science, Nagpur

Inductive & Capacitive Circuits. Subhasish Chandra Assistant Professor Department of Physics Institute of Forensic Science, Nagpur Inductive & Capacitive Circuits Subhasish Chandra Assistant Professor Department of Physics Institute of Forensic Science, Nagpur LR Circuit LR Circuit (Charging) Let us consider a circuit having an inductance

More information

Circuit Q and Field Energy

Circuit Q and Field Energy 1 Problem Circuit Q and Field Energy Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (April 1, 01) In a series R-L-C circuit, as sketched below, the maximum power

More information

Handout 10: Inductance. Self-Inductance and inductors

Handout 10: Inductance. Self-Inductance and inductors 1 Handout 10: Inductance Self-Inductance and inductors In Fig. 1, electric current is present in an isolate circuit, setting up magnetic field that causes a magnetic flux through the circuit itself. This

More information

04-Electric Power. ECEGR 452 Renewable Energy Systems

04-Electric Power. ECEGR 452 Renewable Energy Systems 04-Electric Power ECEGR 452 Renewable Energy Systems Overview Review of Electric Circuits Phasor Representation Electrical Power Power Factor Dr. Louie 2 Introduction Majority of the electrical energy

More information

Refresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas

Refresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas Refresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas A specifically designed programme for Da Afghanistan Breshna Sherkat (DABS) Afghanistan 1 Areas Covered Under this Module

More information

PHYS 241 EXAM #2 November 9, 2006

PHYS 241 EXAM #2 November 9, 2006 1. ( 5 points) A resistance R and a 3.9 H inductance are in series across a 60 Hz AC voltage. The voltage across the resistor is 23 V and the voltage across the inductor is 35 V. Assume that all voltages

More information