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

Size: px
Start display at page:

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

Transcription

1 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 ) which produces a sinusoidally varying emf. A rotating coil in a magnetic field gives an important example; another is the sinusoidally varying potential across the inductor in an L- oscillator, used in many situations to provide an emf for another circuit. This kind of oscillating source is called an A (alternating current) generator. Its output is described by E = E max sinωt. Here E max is the maximum emf during a cycle of the oscillation. Shown here is a prototype A generator ( alternator ). The rotating coil ( armature ) has contact with two slip rings, which in turn pass the current to the load through conducting brushes that the rings slide across. The alternator used in most automobiles is a somewhat more sophisticated version of this device. Meters to measure the strength of sinusoidally varying voltages and currents do not usually measure the maximum value. Instead they measure the (root-mean-square) value. This is a statistical measure, defined for any varying quantity by: The value of a quantity f that varies over a MS values distribution is given by f = ( f 2 ) av, where the average is taken over the distribution. In words: square the quantity, take the average of that, then take the square root. In the case of sinusoidal time variation, the average is taken over the time for one cycle. Since the average of sin 2 ωt over a cycle is 1/2, we find a simple rule: E = E max / 2. This is what an A voltmeter, placed across the generator s terminals, will read. For example, the ordinary household outlets in the USA deliver an A voltage with maximum about 170 V, oscillating at frequency 60 Hz. What a voltmeter will read, placed across the terminals, is about 120 V. This is the value.

2 Physics 142 A ircuits Page 2 Example: the series L circuit We will analyze a circuit containing a capacitor, an inductor, a resistor and an A generator, in series as shown. We apply the loop rule at an instant when the current is running clockwise, putting positive charge on the lower capacitor plate. Then we find E L di Q/ I = 0. dt Using I = dq/dt and rearranging, we have L E d 2 Q dt 2 + L dq dt + 1 L Q = 1 L E max sinωt. This differential equation has the same mathematical form as the equation describing a driven oscillator with damping, so its solutions have the same form. The "steady-state" solution (describing the situation where the energy dissipated per cycle is exactly replaced by the energy input per cycle) has the form Q(t) = Q max cos(ωt φ ) where Q max and φ are determined by requiring Q(t) to satisfy the differential equation. We choose the cosine here so that the current, like the emf, will involve the sine. After substitution into the equation and much algebra we find the answer. It is conventionally written in te of quantities determined by the parameters of the circuit, all of which have the dimensions of resistance and are measured in ohms: 1. apacitive reactance: X = 1/ω eactances and impedance for series L circuit 2. Inductive reactance: X L = ωl 3. Impedance: = 2 + (X L X ) 2 In te of these quantities the constants in the solution we seek are: Q max = E max /ω, tanφ = X L X We are usually more interested in the current in the circuit than the capacitor s charge; taking the time derivative of Q we find: urrent in series L circuit I(t) = E max sin(ωt φ) The relations among these quantities is conveniently displayed in the impedance triangle shown. The current "lags" the emf (its peak occurs later in time) by the phase angle φ. If X L > X then φ is positive and the φ X L X

3 Physics 142 A ircuits Page 3 current lags behind the generator voltage; if X L < X then φ is negative and the current leads the generator voltage. The current and the generator voltage are exactly in phase (φ = 0 ) if X L = X. Voltage drops and power in the circuit elements We now examine the voltage drops across the elements and the power delivered to them. The instantaneous voltage drops are obtained from the expressions for I and Q: esistor:! V (t) = I(t) = E max sin(ωt φ) apacitor:v (t) = Q(t) = E max X cos(ωt φ) Inductor:! V L (t) = L di dt = E X L max cos(ωt φ) Note that the capacitor and inductor voltage drops are of opposite sign (i.e., are out of phase with each other by π ), and that they are out of phase with the current by ±π /2 [since cosθ = sin(θ + π /2)]. The values are relatively simple, and all take the form of Ohm s law:!!!! urrent:! I = E /!!!! esistor:! V!!!! apacitor:! V L!!!! Inductor:! V = I = I X = I X L An value is always positive, so the sum of the voltages around the circuit is not zero. (The sum of all the instantaneous potential differences around the circuit at any given time is zero, of course.) Indeed, there are situations where one or more of the voltages across an element exceeds the generator emf. Now we look at the power delivered to each element. Instantaneously, this is the product of the current into the element and the voltage drop across it. This product varies during a cycle, usually being sometimes positive and sometimes negative. We are ordinarily interested in the average power over a cycle. Take as an example the power delivered by the generator. Instantaneously it is P gen (t) = E(t)I(t) = E max 2 sinωt sin(ωt φ) To find the average of this over a cycle we integrate it with respect to t from 0 to T = 2π /ω (the period of the oscillation) and then divide the result by T. We find from this calculation:

4 Physics 142 A ircuits Page 4 Average power from generator P av (from generator) = E 2 cosφ = E I cosφ The last expression shows that the average power supplied by the generator is the product of the readings of an A voltmeter and an A ammeter, multiplied by the power factor cosφ. Applying this procedure to the other elements, we find that P av = I 2, while the average power to the capacitor and inductor are both zero. The capacitor and inductor take in power during half of the cycle and return it to the circuit in the other half, so the average is zero. The net power supplied by the generator thus goes entirely to the resistor, where it is converted to heat. Although the capacitor and inductor consume no net power themselves, they play roles in determining the power actually supplied by the generator, because they help determine the value of, which in turn determines the strength of the current. Series resonance: tuning to a frequency Since the series L circuit is mathematically analogous to a driven mechanical oscillator, there is a resonance phenomenon in it as well. The power supplied to the circuit is a maximum when is a minimum. This happens when X L = X. In this case φ = 0 so the current is exactly in phase with the generator voltage; there is never a time during the cycle when the generator is taking power out of the circuit. This is why the power supplied is as large as possible. The resonance condition is usually written in te of ω: esonant frequency ω = ω 0 = 1/ L The resonant frequency is thus equal to the "free" oscillation frequency of an L- oscillator without resistance. If is small then the average power to the resistor is small except at frequencies near ω 0. This is a "sharp" resonance, corresponding to a high Q-value for the circuit. This kind of resonance is used by the tuner sections of radios and TV sets to select one channel or station and reject others. P av = 10Ω Shown are curves of P av vs. ω for a series L circuit. Two values of are plotted to show its effect on the sharpness and height of the peak. ω 0 = 40Ω ω

5 Physics 142 A ircuits Page 5 Passive filters as A circuits A common use of the elements we have been discussing is in construction of passive filters. (A passive element is one that has in it no sources of e-m energy.) An A input voltage is passed into the device by a pair of terminals. On the other side of the filter are two other terminals, across which is the output voltage. The situation is drawn schematically as shown. V in Filter V out Here V in is an A voltage, which can be considered to be that of an A generator of frequency ω, and V out is also an A voltage at the same frequency, usually the voltage across some circuit element in the filter. Our interest is in the ratio V out /V in, sometimes called the attenuation factor. onsider as an example the circuit shown. Let the instantaneous input voltage be V 0 sinωt. Then V in = V 0 / 2. The impedance of the circuit containing and is = 2 + (1/ω) 2. The V V in out voltage across (which is V out ) is given by V out = I = V in, so we find for this filter V out V in = 2 + (1/ω) 2 = ω. (ω) We see that as ω 0 the ratio goes to zero, while as ω the ratio approaches 1. This type of filter is called high-pass since it leaves high frequency voltages unaffected and suppresses low frequency voltages. If we reverse the locations of and we have V out = I (1/ω) = V in from which we find (1/ω) 2 + (1/ω) 2, V out V in = (1/ω) = (1/ω) 2 (ω) Now the ratio approaches 1 for low frequencies, and it approaches zero for high frequencies. This configuration is a low-pass filter. One can also use inductors and resistors, or combinations of L, and, to make filters. Filters are very common in electronic circuits and in audio systems. The attenuation ratio is often measured in te of db differences.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Alternating Current. Symbol for A.C. source. A.C.

Alternating Current. Symbol for A.C. source. A.C. Alternating Current Kirchoff s rules for loops and junctions may be used to analyze complicated circuits such as the one below, powered by an alternating current (A.C.) source. But the analysis can quickly

More information

Lecture 21. Resonance and power in AC circuits. Physics 212 Lecture 21, Slide 1

Lecture 21. Resonance and power in AC circuits. Physics 212 Lecture 21, Slide 1 Physics 1 ecture 1 esonance and power in A circuits Physics 1 ecture 1, Slide 1 I max X X = w I max X w e max I max X X = 1/w I max I max I max X e max = I max Z I max I max (X -X ) f X -X Physics 1 ecture

More information

Physics 2112 Unit 20. Outline: Driven AC Circuits Phase of V and I Conceputally Mathematically With phasors

Physics 2112 Unit 20. Outline: Driven AC Circuits Phase of V and I Conceputally Mathematically With phasors Physics 2112 Unit 20 Outline: Driven A ircuits Phase of V and I onceputally Mathematically With phasors Electricity & Magnetism ecture 20, Slide 1 Your omments it just got real this stuff is confusing

More information

General Physics (PHY 2140)

General Physics (PHY 2140) General Physics (PHY 40) eminder: Exam this Wednesday 6/3 ecture 0-4 4 questions. Electricity and Magnetism nduced voltages and induction Self-nductance Circuits Energy in magnetic fields AC circuits and

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

8.1 Alternating Voltage and Alternating Current ( A. C. )

8.1 Alternating Voltage and Alternating Current ( A. C. ) 8 - ALTENATING UENT Page 8. Alternating Voltage and Alternating urrent ( A.. ) The following figure shows N turns of a coil of conducting wire PQS rotating with a uniform angular speed ω with respect to

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

ELECTROMAGNETIC INDUCTION

ELECTROMAGNETIC INDUCTION ELECTROMAGNETIC INDUCTION 1. Magnetic Flux 2. Faraday s Experiments 3. Faraday s Laws of Electromagnetic Induction 4. Lenz s Law and Law of Conservation of Energy 5. Expression for Induced emf based on

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

Get Discount Coupons for your Coaching institute and FREE Study Material at ELECTROMAGNETIC INDUCTION

Get Discount Coupons for your Coaching institute and FREE Study Material at  ELECTROMAGNETIC INDUCTION ELECTROMAGNETIC INDUCTION 1. Magnetic Flux 2. Faraday s Experiments 3. Faraday s Laws of Electromagnetic Induction 4. Lenz s Law and Law of Conservation of Energy 5. Expression for Induced emf based on

More information

Chapter 28: Alternating Current

Chapter 28: Alternating Current hapter 8: Alternating urrent Phasors and Alternating urrents Alternating current (A current) urrent which varies sinusoidally in tie is called alternating current (A) as opposed to direct current (D).

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

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

Chapter 31: RLC Circuits. PHY2049: Chapter 31 1

Chapter 31: RLC Circuits. PHY2049: Chapter 31 1 hapter 31: RL ircuits PHY049: hapter 31 1 L Oscillations onservation of energy Topics Damped oscillations in RL circuits Energy loss A current RMS quantities Forced oscillations Resistance, reactance,

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

Chapter 3: Capacitors, Inductors, and Complex Impedance

Chapter 3: Capacitors, Inductors, and Complex Impedance hapter 3: apacitors, Inductors, and omplex Impedance In this chapter we introduce the concept of complex resistance, or impedance, by studying two reactive circuit elements, the capacitor and the inductor.

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

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

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

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

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

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

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

Module 4. Single-phase AC Circuits. Version 2 EE IIT, Kharagpur 1

Module 4. Single-phase AC Circuits. Version 2 EE IIT, Kharagpur 1 Module 4 Single-phase A ircuits ersion EE IIT, Kharagpur esson 4 Solution of urrent in -- Series ircuits ersion EE IIT, Kharagpur In the last lesson, two points were described:. How to represent a sinusoidal

More information

Physics 4 Spring 1989 Lab 5 - AC Circuits

Physics 4 Spring 1989 Lab 5 - AC Circuits Physics 4 Spring 1989 Lab 5 - AC Circuits Theory Consider the series inductor-resistor-capacitor circuit shown in figure 1. When an alternating voltage is applied to this circuit, the current and voltage

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

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

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

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

INTC 1307 Instrumentation Test Equipment Teaching Unit 6 AC Bridges

INTC 1307 Instrumentation Test Equipment Teaching Unit 6 AC Bridges IHLAN OLLEGE chool of Engineering & Technology ev. 0 W. lonecker ev. (8/6/0) J. Bradbury INT 307 Instrumentation Test Equipment Teaching Unit 6 A Bridges Unit 6: A Bridges OBJETIVE:. To explain the operation

More information

The simplest type of alternating current is one which varies with time simple harmonically. It is represented by

The simplest type of alternating current is one which varies with time simple harmonically. It is represented by ALTERNATING CURRENTS. Alternating Current and Alternating EMF An alternating current is one whose magnitude changes continuously with time between zero and a maximum value and whose direction reverses

More information

ECE2262 Electric Circuits. Chapter 6: Capacitance and Inductance

ECE2262 Electric Circuits. Chapter 6: Capacitance and Inductance ECE2262 Electric Circuits Chapter 6: Capacitance and Inductance Capacitors Inductors Capacitor and Inductor Combinations Op-Amp Integrator and Op-Amp Differentiator 1 CAPACITANCE AND INDUCTANCE Introduces

More information

Impedance. Reactance. Capacitors

Impedance. Reactance. Capacitors Impedance Ohm's law describes the relationship between current and voltage in circuits that are in equilibrium- that is, when the current and voltage are not changing. When we have a situation where the

More information

Basics of Electric Circuits

Basics of Electric Circuits António Dente Célia de Jesus February 2014 1 Alternating Current Circuits 1.1 Using Phasors There are practical and economic reasons justifying that electrical generators produce emf with alternating and

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

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

INDUCTANCE Self Inductance

INDUCTANCE Self Inductance NDUTANE 3. Self nductance onsider the circuit shown in the Figure. When the switch is closed the current, and so the magnetic field, through the circuit increases from zero to a specific value. The increasing

More information

Sinusoidal Steady State Analysis (AC Analysis) Part II

Sinusoidal Steady State Analysis (AC Analysis) Part II Sinusoidal Steady State Analysis (AC Analysis) Part II Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/

More information

C R. Consider from point of view of energy! Consider the RC and LC series circuits shown:

C R. Consider from point of view of energy! Consider the RC and LC series circuits shown: ircuits onsider the R and series circuits shown: ++++ ---- R ++++ ---- Suppose that the circuits are formed at t with the capacitor charged to value. There is a qualitative difference in the time development

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

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

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

mywbut.com Lesson 16 Solution of Current in AC Parallel and Seriesparallel

mywbut.com Lesson 16 Solution of Current in AC Parallel and Seriesparallel esson 6 Solution of urrent in Parallel and Seriesparallel ircuits n the last lesson, the following points were described:. How to compute the total impedance/admittance in series/parallel circuits?. How

More information

Physics 11b Lecture #15

Physics 11b Lecture #15 Physics 11b ecture #15 and ircuits A ircuits S&J hapter 3 & 33 Administravia Midterm # is Thursday If you can t take midterm, you MUST let us (me, arol and Shaun) know in writing before Wednesday noon

More information

DOING PHYSICS WITH MATLAB

DOING PHYSICS WITH MATLAB DOING PHYSIS WITH MATAB THE FINITE DIFFERENE METHOD FOR THE NUMERIA ANAYSIS OF IRUITS ONTAINING RESISTORS, APAITORS AND INDUTORS MATAB DOWNOAD DIRETORY N01.m Voltage and current for a resistor, capacitor

More information

CHEM*3440. Current Convention. Charge. Potential Energy. Chemical Instrumentation. Rudimentary Electronics. Topic 3

CHEM*3440. Current Convention. Charge. Potential Energy. Chemical Instrumentation. Rudimentary Electronics. Topic 3 urrent onvention HEM*3440 hemical nstrumentation Topic 3 udimentary Electronics ONENTON: Electrical current flows from a region of positive potential energy to a region of more negative (or less positive)

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

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

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

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

Inductance. Slide 2 / 26. Slide 1 / 26. Slide 4 / 26. Slide 3 / 26. Slide 6 / 26. Slide 5 / 26. Mutual Inductance. Mutual Inductance.

Inductance. Slide 2 / 26. Slide 1 / 26. Slide 4 / 26. Slide 3 / 26. Slide 6 / 26. Slide 5 / 26. Mutual Inductance. Mutual Inductance. Slide 1 / 26 Inductance 2011 by Bryan Pflueger Slide 2 / 26 Mutual Inductance If two coils of wire are placed near each other and have a current passing through them, they will each induce an emf on one

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

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur Module 4 Single-phase circuits ersion EE T, Kharagpur esson 6 Solution of urrent in Parallel and Seriesparallel ircuits ersion EE T, Kharagpur n the last lesson, the following points were described:. How

More information

Physics 2B Winter 2012 Final Exam Practice

Physics 2B Winter 2012 Final Exam Practice Physics 2B Winter 2012 Final Exam Practice 1) When the distance between two charges is increased, the force between the charges A) increases directly with the square of the distance. B) increases directly

More information

Notes on Electric Circuits (Dr. Ramakant Srivastava)

Notes on Electric Circuits (Dr. Ramakant Srivastava) Notes on Electric ircuits (Dr. Ramakant Srivastava) Passive Sign onvention (PS) Passive sign convention deals with the designation of the polarity of the voltage and the direction of the current arrow

More information

PH 222-2C Fall Electromagnetic Oscillations and Alternating Current. Lectures 18-19

PH 222-2C Fall Electromagnetic Oscillations and Alternating Current. Lectures 18-19 H - Fall 0 Electroagnetic Oscillations and Alternating urrent ectures 8-9 hapter 3 (Halliday/esnick/Walker, Fundaentals of hysics 8 th edition) hapter 3 Electroagnetic Oscillations and Alternating urrent

More information

ELECTROMAGNETIC INDUCTION AND FARADAY S LAW

ELECTROMAGNETIC INDUCTION AND FARADAY S LAW ELECTROMAGNETIC INDUCTION AND FARADAY S LAW Magnetic Flux The emf is actually induced by a change in the quantity called the magnetic flux rather than simply py by a change in the magnetic field Magnetic

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

L L, R, C. Kirchhoff s rules applied to AC circuits. C Examples: Resonant circuits: series and parallel LRC. Filters: narrowband,

L L, R, C. Kirchhoff s rules applied to AC circuits. C Examples: Resonant circuits: series and parallel LRC. Filters: narrowband, Today in Physics 1: A circuits Solving circuit problems one frequency at a time. omplex impedance of,,. Kirchhoff s rules applied to A circuits. it V in Examples: esonant circuits: i series and parallel.

More information

Circuits Advanced Topics by Dr. Colton (Fall 2016)

Circuits Advanced Topics by Dr. Colton (Fall 2016) ircuits Advanced Topics by Dr. olton (Fall 06). Time dependence of general and L problems General and L problems can always be cast into first order ODEs. You can solve these via the particular solution

More information

PHYSICS. Chapter 30 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT

PHYSICS. Chapter 30 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 30 Lecture RANDALL D. KNIGHT Chapter 30 Electromagnetic Induction IN THIS CHAPTER, you will learn what electromagnetic induction is

More information

Lecture 24. Impedance of AC Circuits.

Lecture 24. Impedance of AC Circuits. Lecture 4. Impedance of AC Circuits. Don t forget to complete course evaluations: https://sakai.rutgers.edu/portal/site/sirs Post-test. You are required to attend one of the lectures on Thursday, Dec.

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

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

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

Chapter 30 Inductance

Chapter 30 Inductance Chapter 30 Inductance In this chapter we investigate the properties of an inductor in a circuit. There are two kinds of inductance mutual inductance and self-inductance. An inductor is formed by taken

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

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

Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits

Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits Self-inductance A time-varying current in a circuit produces an induced emf opposing the emf that initially set up the timevarying

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

Ch. 23 Electromagnetic Induction, AC Circuits, And Electrical Technologies

Ch. 23 Electromagnetic Induction, AC Circuits, And Electrical Technologies Ch. 23 Electromagnetic Induction, AC Circuits, And Electrical Technologies Induced emf - Faraday s Experiment When a magnet moves toward a loop of wire, the ammeter shows the presence of a current When

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

AP Physics C - E & M

AP Physics C - E & M Slide 1 / 27 Slide 2 / 27 AP Physics C - E & M Current, Resistance & Electromotive Force 2015-12-05 www.njctl.org Slide 3 / 27 Electric Current Electric Current is defined as the movement of charge from

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

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

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

BME/ISE 3511 Bioelectronics - Test Six Course Notes Fall 2016

BME/ISE 3511 Bioelectronics - Test Six Course Notes Fall 2016 BME/ISE 35 Bioelectronics - Test Six ourse Notes Fall 06 Alternating urrent apacitive & Inductive Reactance and omplex Impedance R & R ircuit Analyses (D Transients, Time onstants, Steady State) Electrical

More information

RMS values. Book page

RMS values. Book page RMS values Book page 443-444 cgrahamphysics.com 015 Review When angle between normal to loop and field lines is θ = 90 0 max flux, Φ = NAB cos θ min emf, emf = ωnab sin ωt θ = 0 0 min flux, max emf cgrahamphysics.com

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

Physics 102 Spring 2007: Final Exam Multiple-Choice Questions

Physics 102 Spring 2007: Final Exam Multiple-Choice Questions Last Name: First Name: Physics 102 Spring 2007: Final Exam Multiple-Choice Questions 1. The circuit on the left in the figure below contains a battery of potential V and a variable resistor R V. The circuit

More information

ELECTRO MAGNETIC INDUCTION

ELECTRO MAGNETIC INDUCTION ELECTRO MAGNETIC INDUCTION 1) A Circular coil is placed near a current carrying conductor. The induced current is anti clock wise when the coil is, 1. Stationary 2. Moved away from the conductor 3. Moved

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

Chapter 28. Direct Current Circuits

Chapter 28. Direct Current Circuits Chapter 28 Direct Current Circuits Circuit Analysis Simple electric circuits may contain batteries, resistors, and capacitors in various combinations. For some circuits, analysis may consist of combining

More information

PHYSICS NOTES ALTERNATING CURRENT

PHYSICS NOTES ALTERNATING CURRENT LESSON 7 ALENAING CUEN Alternating current As we have seen earlier a rotating coil in a magnetic field, induces an alternating emf and hence an alternating current. Since the emf induced in the coil varies

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