Lab 9 AC FILTERS AND RESONANCE

Size: px
Start display at page:

Download "Lab 9 AC FILTERS AND RESONANCE"

Transcription

1 09-1 Name Date Partners ab 9 A FITES AND ESONANE OBJETIES OEIEW To understand the design of capacitive and inductive filters To understand resonance in circuits driven by A signals In a previous lab, you explored the relationship between impedance (the A equivalent of resistance) and frequency for a resistor, capacitor, and inductor. These relationships are very important to people designing electronic equipment. You can predict many of the basic characteristics of simple A circuits based on what you have learned in previous labs. ecall that we said that it can be shown that any periodic signal can be represented as a sum of weighted sines and cosines (known as a Fourier series). It can also be shown that the response of a circuit containing resistors, capacitors, and inductors (an circuit) to such a signal is simply the sum of the responses of the circuit to each sine and cosine term with the same weights. ecall further that if there is a current of the form I ( t) = I sin ωt (1) ( ) flowing through a circuit containing resistors, capacitors and/or inductors, then the voltage across the circuit will be of the form ( ) sin( ω ϕ ) t = I Z t +. (2) Z is called the impedance (and has units of resistance, Ohms) and φ is called the phase shift (and has units of angle, radians). The peak voltage will be given by = I Z. (3)

2 09-2 ab 9 - A Filters & esonance Figure 1 shows the relationship between and I for an example phase shift of +20. We say that leads I in the sense that the voltage rises through zero a time t before the current. When the voltage rises through zero after the current, we say that it lags the current. Figure 1 The relationship between ϕ and t is given by t ϕ = 2π or ϕ = 360 f t T where T is the period and f is the frequency. For a resistor, Z (4) = and there is no phase shift ( ϕ = 0 ). For a capacitor, Z = X = 1 ω and ϕ = 90 while for an inductor, Z = X = ω and ϕ = In other words: = I sin( ωt) (5) = I X cos( ωt) (6) and = I X cos( ωt) (7) X is called the capacitive reactance and X is called the inductive reactance. et us now consider a series combination of a resistor, a capacitor and an inductor shown in Figure 2. To find the impedance and phase shift for this combination we follow the procedure we established before. Figure 2

3 ab 9 - A Filters & esonance 09-3 From Kirchhoff s loop rule we get: = + + (8) Adding in Kirchhoff s junction rule and Equations (2), (5), (6), and (7) yields sin ( ωt + ϕ ) = I sin ( ωt ) + ( X X ) cos ( ωt ) Once again using a trigonometric identity 1 and equating the sin t cos ω t, we get coefficients of ( ω ) and ( ) and cos( φ ) = I sin ( φ ) = ( ) I X X Hence the phase shift is given by X X tan ( ϕ ) = (9) and the impedance of this series combination of a resistor, an inductor, and a capacitor is given by: ( ) 2 Z = I = + X X (10) 2 The magnitudes of the voltages across the components are then and = I = (11) Z X = I X = (12), Z X = I X = (13), Z Explicitly considering the frequency dependence, we see that = ( ω 1 ω ) (14) and,, = = ω ( ω 1 ω ) ω ( ω 1 ω ) (15) (16) 1 sin( α + β ) = sin( α )cos( β ) + cos( α )sin( β )

4 09-4 ab 9 - A Filters & esonance This system has a lot in common with the forced mechanical oscillator that we studied in the first semester. ecall that the equation of motion was F = ma + bv + kx = mx ɺɺ + bxɺ + kx (17) Similarly, Equation (8) can be written as 1 = qɺɺ + qɺ + q (18) We see that charge separation plays the role of displacement, current the role of velocity, inductance the role of mass (inertia), capacitance (its inverse, actually) the role of the spring constant, and resistance the role of friction. The driving voltage plays the role of the external force. As we saw in the mechanical case, this electrical system displays the property of resonance. It is clear that when the capacitive and inductive reactances are equal, the impedance is at its minimum value,. Hence, the current is at a imum and there is no phase shift between the current and the driving voltage. Denoting the resonant frequency as ω and the common reactance of the capacitor and inductor at resonance as X, we see that, at resonance so and ( ω ) ( ω ) X X = X ω = 1 (19) X = (20) At resonance the magnitude of the voltage across the capacitor is the same as that across the inductor (they are still 180 out of phase with each other and ±90 out of phase with the voltage across the resistor) and is given by X, ( ω ) =, ( ω ) = (21)

5 ab 9 - A Filters & esonance 09-5 In analogy with the mechanical case, we call the ratio of the amplitude of the voltage across the capacitor (which is proportional to q, our displacement ) at resonance to the driving amplitude the resonant amplification, which we denote as Q, Q ω (22) Hence, ( ), Q = X = (23) Figure 3 (below) shows the voltage across a capacitor (normalized to the driving voltage) as a function of frequency for various values of Q. Figure 3 In this lab you will continue your investigation of the behavior of resistors, capacitors and inductors in the presence of A signals. In Investigation 1you will explore the relationship between peak current and peak voltage for a series circuit composed of a resistor, inductor, and capacitor. You will also explore the phase difference between the current and the voltage. This circuit is an example of a resonant circuit. The phenomenon of resonance is a central concept underlying the tuning of a radio or television to a particular frequency. INESTIGATION 1: THE SEIES ESONANT (TUNE) IUIT In this investigation, you will use your knowledge of the behavior of resistors, capacitors and inductors in circuits driven by various A signal frequencies to predict and then observe the behavior of a circuit with a resistor, capacitor, and inductor connected in series.

6 09-6 ab 9 - A Filters & esonance The series circuit you will study in this investigation exhibits a resonance behavior that is useful for many familiar applications such a tuner in a radio receiver. You will need the following materials: oltage probes Multimeter 510 Ω resistor test leads 800 mh inductor 820 nf capacitor onsider the series circuit shown in Figure 4 (below). [For clarity, we don t explicitly show the voltage probes.] Figure 4 Prediction 2-1: At very low signal frequencies (less than 10 Hz), will I and be relatively large, intermediate or small? Explain your reasoning. Prediction 2-2: At very high signal frequencies (well above 3,000 Hz), will the values of I and be relatively large, intermediate or small? Explain your reasoning.

7 ab 9 - A Filters & esonance On the axes below, draw qualitative graphs of X vs. frequency and X vs. frequency. learly label each curve. X and X Frequ ency 2. On the axes above (after step 1) draw a curve that qualitatively represents X X vs. frequency. Be sure to label it. 3. ecall that the frequency at which Z is a minimum is called the resonant frequency, f and that the common reactance of the inductor and the capacitor is axes above, mark and label f and X. X. On the Question 2-1 At f will the value of the peak current, I, in the circuit be a imum or minimum? What about the value of the peak voltage,, across the resistor? Explain. 4. Measure the 510 Ω resistor (you have already measured the inductor and the capacitor): 5. Use your measured values to calculate the resonant frequency, the reactance of the capacitor (and the inductor)

8 09-8 ab 9 - A Filters & esonance at resonance, and the resonant amplification factor. Show your work. [Don t forget the units!] f X Q Activity 2-1: The esonant Frequency of a Series ircuit. 1. Open the experiment file 09A2-1 Filter. 2. onnect the circuit with resistor, capacitor, inductor and signal generator shown in Figure 4. [Use the internal generator.] 3. Adjust the generator to make a 50 Hz signal with amplitude of onnect voltage probe P A across the resistor, P B across the inductor, and P across the capacitor. 5. Use the Smart Tool to determine the peak voltages (,,, and, ). Enter the data in the first row of Table epeat for the other frequencies in Table 2-1. Table 2-1 f (Hz) (), (), ()

9 ab 9 - A Filters & esonance Measure the resonant frequency of the circuit to within a few Hz. To do this, slowly adjust the frequency of the signal generator until the peak voltage across the resistor is imal. [Use the results from Table 2-1 to help you locate the resonant frequency.] f, exp Question 2-2: Discuss the agreement between this experimental value for the resonant frequency and your calculated one. 8. Use the Smart Tool to determine the peak voltages at resonance.,, Question 2-3: From these voltages, calculate Q and discuss the agreement between this experimental value and your calculated one.

10 09-10 ab 9 - A Filters & esonance Question 2-4: alculate your experimental value of X and discuss the agreement between this value and your calculated one. Prediction 2-5: What will we get for Q if we short out the resistor? Show your work. 9. Short out the resistor. 10. Measure Q. [You may have to lower the signal voltage to 0.5.] Show your work. Explicitly indicate what you had to measure. Q Question 2-6: Discuss the agreement between this experimental value and your predicted one.

11 ab 9 - A Filters & esonance Activity 2-2: Phase in an ircuit In previous labs, you investigated the phase relationship between the current and voltage in an A circuit composed of a signal generator connected to one of the following circuit elements: a resistor, capacitor, or an inductor. You found that the current and voltage are in phase when the element connected to the signal generator is a resistor, the current leads the voltage with a capacitor, and the current lags the voltage with an inductor. You also discovered that the reactances of capacitors and inductors change in predictable ways as the frequency of the signal changes, while the resistance of a resistor is constant independent of the signal frequency. When considering relatively high or low signal frequencies in a simple circuit, the circuit element (either capacitor or inductor) with the highest reactance is said to dominate because this element determines whether the current lags or leads the voltage. At resonance, the reactances of capacitor and inductor cancel, and do not contribute to the impedance of the circuit. The resistor then is said to dominate the circuit. In this activity, you will explore the phase relationship between the applied voltage (signal generator voltage) and current in an circuit. onsider again our circuit (it is the same as Figure 4). Figure 5 Question 2-7: Which circuit element (the resistor, inductor, or capacitor) dominates the circuit at frequencies well below the resonant frequency? Explain.

12 09-12 ab 9 - A Filters & esonance Question 2-8: Which circuit element (the resistor, inductor, or capacitor) dominates the circuit at frequencies well above the resonant frequency? Explain. Question 2-9a: In the circuit in Figure 5, will the current through the resistor always be in phase with the voltage across the resistor, regardless of the frequency? Explain your reasoning. Question 2-9b: If your answer to Question 2-9a was no, then which will lead for frequencies below the resonant frequency (current or voltage)? Which will lead for frequencies above the resonant frequency (current or voltage)? Question 2-10a: In the circuit in Figure 5, will the current through the resistor always be in phase with applied voltage from the signal generator? Explain your reasoning. Question 2-10b: If your answer to Question 2-10a was no, then which will lead for frequencies below the resonant

13 ab 9 - A Filters & esonance frequency (current or voltage)? Which will lead for frequencies above the resonant frequency (current or voltage)? 1. ontinue to use 09A2-1 Filter. 2. econnect the circuit shown in Figure 5. onnect voltage probe P A across the resistor, P B across the inductor, and P across the capacitor. 3. Start the scope and set the signal generator to a frequency 20 Hz below the resonant frequency you measured in Investigation 2, and set the amplitude of the signal to 2. Question 2-11: Which leads applied voltage, current or neither when the A signal frequency is lower than the resonant frequency? Discuss agreement with your prediction. 4. Set the signal generator to a frequency 20 Hz above the resonant frequency. Question 2-12: Which leads applied voltage, current or neither when the A signal frequency is higher than the resonant frequency? Discuss agreement with your prediction.

14 09-14 ab 9 - A Filters & esonance Question 2-13: At resonance, what is the phase relationship between the current and the applied voltage? 5. Use this result to find the resonant frequency. f, phase Question 2-14: Discuss how this experimental value compares with your calculated one. Question 2-15: How does this experimental value for the resonant frequency compare with the one you determined by looking at the amplitude? omment on the relative sensitivities of the two techniques.

Lab 9 AC FILTERS AND RESONANCE

Lab 9 AC FILTERS AND RESONANCE 151 Name Date Partners ab 9 A FITES AND ESONANE OBJETIES OEIEW To understand the design of capacitive and inductive filters To understand resonance in circuits driven by A signals In a previous lab, you

More information

Lab 9 - AC Filters and Resonance

Lab 9 - AC Filters and Resonance Lab 9 AC Filters and Resonance L9-1 Name Date Partners Lab 9 - AC Filters and Resonance OBJECTIES To understand the design of capacitive and inductive filters. To understand resonance in circuits driven

More information

INTRODUCTION TO AC FILTERS AND RESONANCE

INTRODUCTION TO AC FILTERS AND RESONANCE AC Filters & Resonance 167 Name Date Partners INTRODUCTION TO AC FILTERS AND RESONANCE OBJECTIVES To understand the design of capacitive and inductive filters To understand resonance in circuits driven

More information

Lab 10 - INTRODUCTION TO AC FILTERS AND RESONANCE

Lab 10 - INTRODUCTION TO AC FILTERS AND RESONANCE 159 Name Date Partners Lab 10 - INTRODUCTION TO AC FILTERS AND RESONANCE OBJECTIVES To understand the design of capacitive and inductive filters To understand resonance in circuits driven by AC signals

More information

AC CURRENTS, VOLTAGES, FILTERS, and RESONANCE

AC CURRENTS, VOLTAGES, FILTERS, and RESONANCE July 22, 2008 AC Currents, Voltages, Filters, Resonance 1 Name Date Partners AC CURRENTS, VOLTAGES, FILTERS, and RESONANCE V(volts) t(s) OBJECTIVES To understand the meanings of amplitude, frequency, phase,

More information

Lab 8 - INTRODUCTION TO AC CURRENTS AND VOLTAGES

Lab 8 - INTRODUCTION TO AC CURRENTS AND VOLTAGES 08-1 Name Date Partners ab 8 - INTRODUCTION TO AC CURRENTS AND VOTAGES OBJECTIVES To understand the meanings of amplitude, frequency, phase, reactance, and impedance in AC circuits. To observe the behavior

More information

Experiment VI: The LRC Circuit and Resonance

Experiment VI: The LRC Circuit and Resonance Experiment VI: The ircuit and esonance I. eferences Halliday, esnick and Krane, Physics, Vol., 4th Ed., hapters 38,39 Purcell, Electricity and Magnetism, hapter 7,8 II. Equipment Digital Oscilloscope Digital

More information

LRC Circuit PHYS 296 Your name Lab section

LRC Circuit PHYS 296 Your name Lab section LRC Circuit PHYS 296 Your name Lab section PRE-LAB QUIZZES 1. What will we investigate in this lab? 2. Figure 1 on the following page shows an LRC circuit with the resistor of 1 Ω, the capacitor of 33

More information

Resonance in Circuits

Resonance in Circuits Resonance in Circuits Purpose: To map out the analogy between mechanical and electronic resonant systems To discover how relative phase depends on driving frequency To gain experience setting up circuits

More information

Study of Inductive and Capacitive Reactance and RLC Resonance

Study of Inductive and Capacitive Reactance and RLC Resonance Objective Study of Inductive and Capacitive Reactance and RLC Resonance To understand how the reactance of inductors and capacitors change with frequency, and how the two can cancel each other to leave

More information

The RLC Series Circuit with an AC Source

The RLC Series Circuit with an AC Source The R Series ircuit with an A Source Introduction Ohm s law and R circuit labs use a steady current. However, this lab uses a different power supply, which is alternating current (A). The previous electronics

More information

Experiment 18: Driven RLC Circuit

Experiment 18: Driven RLC Circuit MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8. Spring 3 Experiment 8: Driven LC Circuit OBJECTIVES To measure the resonance frequency and the quality factor of a driven LC circuit INTODUCTION

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring Experiment 11: Driven RLC Circuit

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring Experiment 11: Driven RLC Circuit MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.2 Spring 24 Experiment 11: Driven LC Circuit OBJECTIVES 1. To measure the resonance frequency and the quality factor of a driven LC circuit.

More information

Lab 9 - INTRODUCTION TO AC CURRENTS AND VOLTAGES

Lab 9 - INTRODUCTION TO AC CURRENTS AND VOLTAGES 145 Name Date Partners Lab 9 INTRODUCTION TO AC CURRENTS AND VOLTAGES V(volts) t(s) OBJECTIVES To learn the meanings of peak voltage and frequency for AC signals. To observe the behavior of resistors in

More information

LCR CIRCUITS Institute of Lifelong Learning, University of Delhi

LCR CIRCUITS Institute of Lifelong Learning, University of Delhi L UTS nstitute of Lifelong Learning, University of Delhi L UTS PHYSS (LAB MANUAL) nstitute of Lifelong Learning, University of Delhi PHYSS (LAB MANUAL) L UTS ntroduction ircuits containing an inductor

More information

DC and AC Circuits. Objective. Theory. 1. Direct Current (DC) R-C Circuit

DC and AC Circuits. Objective. Theory. 1. Direct Current (DC) R-C Circuit [International Campus Lab] Objective Determine the behavior of resistors, capacitors, and inductors in DC and AC circuits. Theory ----------------------------- Reference -------------------------- Young

More information

Alternating current circuits- Series RLC circuits

Alternating current circuits- Series RLC circuits FISI30 Física Universitaria II Professor J.. ersosimo hapter 8 Alternating current circuits- Series circuits 8- Introduction A loop rotated in a magnetic field produces a sinusoidal voltage and current.

More information

AC Circuits INTRODUCTION DISCUSSION OF PRINCIPLES. Resistance in an AC Circuit

AC Circuits INTRODUCTION DISCUSSION OF PRINCIPLES. Resistance in an AC Circuit AC Circuits INTRODUCTION The study of alternating current 1 (AC) in physics is very important as it has practical applications in our daily lives. As the name implies, the current and voltage change directions

More information

Experiment 7: Undriven & Driven RLC Circuits

Experiment 7: Undriven & Driven RLC Circuits MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2006 OBJECTIVES Experiment 7: Undriven & Driven RLC Circuits 1. To explore the time dependent behavior of RLC Circuits, both driven

More information

EXPERIMENT 8: LRC CIRCUITS

EXPERIMENT 8: LRC CIRCUITS EXPERIMENT 8: LRC CIRCUITS Equipment List S 1 BK Precision 4011 or 4011A 5 MHz Function Generator OS BK 2120B Dual Channel Oscilloscope V 1 BK 388B Multimeter L 1 Leeds & Northrup #1532 100 mh Inductor

More information

ωc ωc sin(wt 90o ) (for a capacitance) (4)

ωc ωc sin(wt 90o ) (for a capacitance) (4) Physics'241'Signal'Processing:'Lab'3' Sinusoidal esponse of, L ircuits In the previous lab, we studied the behavior of series combinations of and L circuits with input square and triangular waveforms.

More information

Lab 4: Transmission Line

Lab 4: Transmission Line 1 Introduction Lab 4: Transmission Line In this experiment we will study the properties of a wave propagating in a periodic medium. Usually this takes the form of an array of masses and springs of the

More information

Chapter 6: Alternating Current

Chapter 6: Alternating Current hapter 6: Alternating urrent 6. Alternating urrent.o 6.. Define alternating current (A) An alternating current (A) is the electrical current which varies periodically with time in direction and magnitude.

More information

PHASES IN A SERIES LRC CIRCUIT

PHASES IN A SERIES LRC CIRCUIT PHASES IN A SERIES LRC CIRCUIT Introduction: In this lab, we will use a computer interface to analyze a series circuit consisting of an inductor (L), a resistor (R), a capacitor (C), and an AC power supply.

More information

Lab 1: Basic RL and RC DC Circuits

Lab 1: Basic RL and RC DC Circuits Name- Surname: ID: Department: Lab 1: Basic RL and RC DC Circuits Objective In this exercise, the DC steady state response of simple RL and RC circuits is examined. The transient behavior of RC circuits

More information

ECE 2006 University of Minnesota Duluth Lab 11. AC Circuits

ECE 2006 University of Minnesota Duluth Lab 11. AC Circuits 1. Objective AC Circuits In this lab, the student will study sinusoidal voltages and currents in order to understand frequency, period, effective value, instantaneous power and average power. Also, the

More information

Chapter 30 Inductance, Electromagnetic. Copyright 2009 Pearson Education, Inc.

Chapter 30 Inductance, Electromagnetic. Copyright 2009 Pearson Education, Inc. Chapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits 30-7 AC Circuits with AC Source Resistors, capacitors, and inductors have different phase relationships between current and voltage

More information

Exercise 9: inductor-resistor-capacitor (LRC) circuits

Exercise 9: inductor-resistor-capacitor (LRC) circuits Exercise 9: inductor-resistor-capacitor (LRC) circuits Purpose: to study the relationship of the phase and resonance on capacitor and inductor reactance in a circuit driven by an AC signal. Introduction

More information

not to be republished NCERT ALTERNATING CURRENT Chapter Seven MCQ 1

not to be republished NCERT ALTERNATING CURRENT Chapter Seven MCQ 1 hapter Seven ALTERNATING URRENT MQ 1 7.1 If the rms current in a 50 Hz ac circuit is 5 A, the value of the current 1/300 seconds after its value becomes zero is (a) 5 2 A (b) 5 3/2 A (c) 5/6 A (d) 5/ 2

More information

EECS40 RLC Lab guide

EECS40 RLC Lab guide EECS40 RLC Lab guide Introduction Second-Order Circuits Second order circuits have both inductor and capacitor components, which produce one or more resonant frequencies, ω0. In general, a differential

More information

RLC Circuits. Centre College. Physics 230 Lab 8

RLC Circuits. Centre College. Physics 230 Lab 8 ircuits entre ollege Phsics 230 ab 8 1 Preliminaries Objective To stud the electrical characteristics of an alternating current circuit containing a resistor, inductor, and capacitor. Equipment Oscilloscope,

More information

#8A RLC Circuits: Free Oscillations

#8A RLC Circuits: Free Oscillations #8A RL ircuits: Free Oscillations Goals In this lab we investigate the properties of a series RL circuit. Such circuits are interesting, not only for there widespread application in electrical devices,

More information

Experiment 9: AC circuits

Experiment 9: AC circuits Experiment 9: AC circuits Nate Saffold nas2173@columbia.edu Office Hour: Mondays, 5:30PM-6:30PM @ Pupin 1216 INTRO TO EXPERIMENTAL PHYS-LAB 1493/1494/2699 Introduction Last week (RC circuit): This week:

More information

I(A) FIGURE 1 - Current vs. Time graph

I(A) FIGURE 1 - Current vs. Time graph ab 7 A ircuits What You Need To Know: The Physics All of the circuit labs you ve been dealing with in this lab course have been using direct current or D. D implies that the current has a constant value

More information

PHY203: General Physics III Lab page 1 of 5 PCC-Cascade. Lab: AC Circuits

PHY203: General Physics III Lab page 1 of 5 PCC-Cascade. Lab: AC Circuits PHY203: General Physics III Lab page 1 of 5 Lab: AC Circuits OBJECTIVES: EQUIPMENT: Universal Breadboard (Archer 276-169) 2 Simpson Digital Multimeters (464) Function Generator (Global Specialties 2001)*

More information

Experiment 1 LRC Transients

Experiment 1 LRC Transients Physics 263 Experiment 1 LRC Transients 1 Introduction In this experiment we will study the damped oscillations and other transient waveforms produced in a circuit containing an inductor, a capacitor,

More information

AC Circuits. "Look for knowledge not in books but in things themselves." W. Gilbert ( )

AC Circuits. Look for knowledge not in books but in things themselves. W. Gilbert ( ) AC Circuits "Look for knowledge not in books but in things themselves." W. Gilbert (1540-1603) OBJECTIVES To study some circuit elements and a simple AC circuit. THEORY All useful circuits use varying

More information

Goals. Introduction. To understand the use of root mean square (rms) voltages and currents.

Goals. Introduction. To understand the use of root mean square (rms) voltages and currents. Lab 10. AC Circuits Goals To show that AC voltages cannot generally be added without accounting for their phase relationships. That is, one must account for how they vary in time with respect to one another.

More information

CHAPTER 9. Sinusoidal Steady-State Analysis

CHAPTER 9. Sinusoidal Steady-State Analysis CHAPTER 9 Sinusoidal Steady-State Analysis 9.1 The Sinusoidal Source A sinusoidal voltage source (independent or dependent) produces a voltage that varies sinusoidally with time. A sinusoidal current source

More information

Electronics and Instrumentation Name ENGR-4220 Fall 1999 Section Modeling the Cantilever Beam Supplemental Info for Project 1.

Electronics and Instrumentation Name ENGR-4220 Fall 1999 Section Modeling the Cantilever Beam Supplemental Info for Project 1. Name ENGR-40 Fall 1999 Section Modeling the Cantilever Beam Supplemental Info for Project 1 The cantilever beam has a simple equation of motion. If we assume that the mass is located at the end of the

More information

Series and Parallel Resonance

Series and Parallel Resonance School of Engineering Department of Electrical and Computer Engineering 33:4 Principles of Electrical Engineering II aboratory Experiment 1 Series and Parallel esonance 1 Introduction Objectives To introduce

More information

Experiment 9 AC Circuits

Experiment 9 AC Circuits Experiment 9 AC Circuits "Look for knowledge not in books but in things themselves." W. Gilbert (1540-1603) OBJECTIVES To study some circuit elements and a simple AC circuit. THEORY All useful circuits

More information

The Series RLC Circuit and Resonance

The Series RLC Circuit and Resonance Purpose Theory The Series RLC Circuit and Resonance a. To study the behavior of a series RLC circuit in an AC current. b. To measure the values of the L and C using the impedance method. c. To study the

More information

Lab 7 - Inductors and LR Circuits

Lab 7 - Inductors and LR Circuits Lab 7 Inductors and LR Circuits L7-1 Name Date Partners Lab 7 - Inductors and LR Circuits The power which electricity of tension possesses of causing an opposite electrical state in its vicinity has been

More information

I. Introduction to Simple Circuits of Resistors

I. Introduction to Simple Circuits of Resistors 2 Problem Set for Dr. Todd Huffman Michaelmas Term I. Introduction to Simple ircuits of esistors 1. For the following circuit calculate the currents through and voltage drops across all resistors. The

More information

Goals. Introduction. To understand the use of root mean square (rms) voltages and currents.

Goals. Introduction. To understand the use of root mean square (rms) voltages and currents. Lab 10. AC Circuits Goals To show that AC voltages cannot generally be added without accounting for their phase relationships. That is, one must account for how they vary in time with respect to one another.

More information

Chapter 33. Alternating Current Circuits

Chapter 33. Alternating Current Circuits Chapter 33 Alternating Current Circuits C HAP T E O UTLI N E 33 1 AC Sources 33 2 esistors in an AC Circuit 33 3 Inductors in an AC Circuit 33 4 Capacitors in an AC Circuit 33 5 The L Series Circuit 33

More information

Chapter 6: Alternating Current. An alternating current is an current that reverses its direction at regular intervals.

Chapter 6: Alternating Current. An alternating current is an current that reverses its direction at regular intervals. Chapter 6: Alternating Current An alternating current is an current that reverses its direction at regular intervals. Overview Alternating Current Phasor Diagram Sinusoidal Waveform A.C. Through a Resistor

More information

Electromagnetic Oscillations and Currents. March 23, 2014 Chapter 30 1

Electromagnetic Oscillations and Currents. March 23, 2014 Chapter 30 1 Electromagnetic Oscillations and Currents March 23, 2014 Chapter 30 1 Driven LC Circuit! The voltage V can be thought of as the projection of the vertical axis of the phasor V m representing the time-varying

More information

Exercise 2: Parallel RLC Circuits

Exercise 2: Parallel RLC Circuits RLC Circuits AC 2 Fundamentals Exercise 2: Parallel RLC Circuits EXERCSE OBJECTVE When you have completed this exercise, you will be able to analyze parallel RLC circuits by using calculations and measurements.

More information

LAB 8: Activity P52: LRC Circuit

LAB 8: Activity P52: LRC Circuit LAB 8: Activity P52: LRC Circuit Equipment: Voltage Sensor 1 Multimeter 1 Patch Cords 2 AC/DC Electronics Lab (100 μf capacitor; 10 Ω resistor; Inductor Coil; Iron core; 5 inch wire lead) The purpose of

More information

Chapter 31 Alternating Current

Chapter 31 Alternating Current Chapter 31 Alternating Current In this chapter we will learn how resistors, inductors, and capacitors behave in circuits with sinusoidally vary voltages and currents. We will define the relationship between

More information

EXPERIMENT 4: RC, RL and RD CIRCUITs

EXPERIMENT 4: RC, RL and RD CIRCUITs EXPERIMENT 4: RC, RL and RD CIRCUITs Equipment List An assortment of resistor, one each of (330, 1k,1.5k, 10k,100k,1000k) Function Generator Oscilloscope 0.F Ceramic Capacitor 100H Inductor LED and 1N4001

More information

BAKISS HIYANA BT ABU BAKAR JKE,POLISAS

BAKISS HIYANA BT ABU BAKAR JKE,POLISAS BAKISS HIYANA BT ABU BAKAR JKE,POLISAS 1 1. Explain AC circuit concept and their analysis using AC circuit law. 2. Apply the knowledge of AC circuit in solving problem related to AC electrical circuit.

More information

CHAPTER 6: ALTERNATING CURRENT

CHAPTER 6: ALTERNATING CURRENT CHAPTER 6: ALTERNATING CURRENT PSPM II 2005/2006 NO. 12(C) 12. (c) An ac generator with rms voltage 240 V is connected to a RC circuit. The rms current in the circuit is 1.5 A and leads the voltage by

More information

Exercise 1: Series RLC Circuits

Exercise 1: Series RLC Circuits RLC Circuits AC 2 Fundamentals Exercise 1: Series RLC Circuits EXERCISE OBJECTIVE When you have completed this exercise, you will be able to analyze series RLC circuits by using calculations and measurements.

More information

2.0 AC CIRCUITS 2.1 AC VOLTAGE AND CURRENT CALCULATIONS. ECE 4501 Power Systems Laboratory Manual Rev OBJECTIVE

2.0 AC CIRCUITS 2.1 AC VOLTAGE AND CURRENT CALCULATIONS. ECE 4501 Power Systems Laboratory Manual Rev OBJECTIVE 2.0 AC CIRCUITS 2.1 AC VOLTAGE AND CURRENT CALCULATIONS 2.1.1 OBJECTIVE To study sinusoidal voltages and currents in order to understand frequency, period, effective value, instantaneous power and average

More information

EXPERIMENT 4: RC, RL and RD CIRCUITs

EXPERIMENT 4: RC, RL and RD CIRCUITs EXPERIMENT 4: RC, RL and RD CIRCUITs Equipment List Resistor, one each of o 330 o 1k o 1.5k o 10k o 100k o 1000k 0.F Ceramic Capacitor 4700H Inductor LED and 1N4004 Diode. Introduction We have studied

More information

PHY 132 Summer 2000 LAB 9: LRC Circuit (Phases) 1

PHY 132 Summer 2000 LAB 9: LRC Circuit (Phases) 1 PHY 132 Summer 2000 LAB 9: LRC Circuit (Phases) 1 Introduction In this lab we will measure the phases (voltage vs current) for each component in a series LRC circuit. Theory L C V_in R Fig. 1 Generic series

More information

Sirindhorn International Institute of Technology Thammasat University

Sirindhorn International Institute of Technology Thammasat University Sirindhorn International Institute of Technology Thammasat University School of Information, Computer and Communication Technology COURSE : ECS 34 Basic Electrical Engineering Lab INSTRUCTOR : Dr. Prapun

More information

Series and Parallel Resonant Circuits

Series and Parallel Resonant Circuits Series and Parallel Resonant Circuits Aim: To obtain the characteristics of series and parallel resonant circuits. Apparatus required: Decade resistance box, Decade inductance box, Decade capacitance box

More information

Chapter 33. Alternating Current Circuits

Chapter 33. Alternating Current Circuits Chapter 33 Alternating Current Circuits Alternating Current Circuits Electrical appliances in the house use alternating current (AC) circuits. If an AC source applies an alternating voltage to a series

More information

University of Jordan School of Engineering Electrical Engineering Department. EE 219 Electrical Circuits Lab

University of Jordan School of Engineering Electrical Engineering Department. EE 219 Electrical Circuits Lab University of Jordan School of Engineering Electrical Engineering Department EE 219 Electrical Circuits Lab EXPERIMENT 7 RESONANCE Prepared by: Dr. Mohammed Hawa EXPERIMENT 7 RESONANCE OBJECTIVE This experiment

More information

Worksheet for Exploration 31.1: Amplitude, Frequency and Phase Shift

Worksheet for Exploration 31.1: Amplitude, Frequency and Phase Shift Worksheet for Exploration 31.1: Amplitude, Frequency and Phase Shift We characterize the voltage (or current) in AC circuits in terms of the amplitude, frequency (period) and phase. The sinusoidal voltage

More information

PHYSICS - CLUTCH CH 29: ALTERNATING CURRENT.

PHYSICS - CLUTCH CH 29: ALTERNATING CURRENT. !! www.clutchprep.com CONCEPT: ALTERNATING VOLTAGES AND CURRENTS BEFORE, we only considered DIRECT CURRENTS, currents that only move in - NOW we consider ALTERNATING CURRENTS, currents that move in Alternating

More information

15. the power factor of an a.c circuit is.5 what will be the phase difference between voltage and current in this

15. the power factor of an a.c circuit is.5 what will be the phase difference between voltage and current in this 1 1. In a series LCR circuit the voltage across inductor, a capacitor and a resistor are 30 V, 30 V and 60 V respectively. What is the phase difference between applied voltage and current in the circuit?

More information

The period is the time required for one complete oscillation of the function.

The period is the time required for one complete oscillation of the function. Trigonometric Curves with Sines & Cosines + Envelopes Terminology: AMPLITUDE the maximum height of the curve For any periodic function, the amplitude is defined as M m /2 where M is the maximum value and

More information

PHYSICS WORKSHEET CLASS : XII. Topic: Alternating current

PHYSICS WORKSHEET CLASS : XII. Topic: Alternating current PHYSICS WORKSHEET CLASS : XII Topic: Alternating current 1. What is mean by root mean square value of alternating current? 2. Distinguish between the terms effective value and peak value of an alternating

More information

3. Apparatus/ Materials 1) Computer 2) Vernier board circuit

3. Apparatus/ Materials 1) Computer 2) Vernier board circuit Experiment 3 RLC Circuits 1. Introduction You have studied the behavior of capacitors and inductors in simple direct-current (DC) circuits. In alternating current (AC) circuits, these elements act somewhat

More information

RLC-circuits TEP. f res. = 1 2 π L C.

RLC-circuits TEP. f res. = 1 2 π L C. RLC-circuits TEP Keywords Damped and forced oscillations, Kirchhoff s laws, series and parallel tuned circuit, resistance, capacitance, inductance, reactance, impedance, phase displacement, Q-factor, band-width

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2005 Experiment 10: LR and Undriven LRC Circuits

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2005 Experiment 10: LR and Undriven LRC Circuits MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.0 Spring 005 Experiment 10: LR and Undriven LRC Circuits OBJECTIVES 1. To determine the inductance L and internal resistance R L of a coil,

More information

Communication Circuit Lab Manual

Communication Circuit Lab Manual German Jordanian University School of Electrical Engineering and IT Department of Electrical and Communication Engineering Communication Circuit Lab Manual Experiment 3 Crystal Oscillator Eng. Anas Alashqar

More information

LECTURE 19. Alternating Current Generators (DEMO)

LECTURE 19. Alternating Current Generators (DEMO) ETURE 9 A Generators A ircuits Start by considering simple circuits with one element (R,, or ) in addition to the driving emf. It will lead to Oscillations and Driven R circuits Alternating urrent Generators

More information

Resonant Frequency of the LRC Circuit (Power Output, Voltage Sensor)

Resonant Frequency of the LRC Circuit (Power Output, Voltage Sensor) 72 Resonant Frequency of the LRC Circuit (Power Output, Voltage Sensor) Equipment List Qty Items Part Numbers 1 PASCO 750 Interface 1 Voltage Sensor CI-6503 1 AC/DC Electronics Laboratory EM-8656 2 Banana

More information

ALTERNATING CURRENT. Lesson-1. Alternating Current and Voltage

ALTERNATING CURRENT. Lesson-1. Alternating Current and Voltage esson- ATENATING UENT Alternating urrent and oltage An alternating current or voltage is that variation of current or voltage respectively whose magnitude and direction vary periodically and continuously

More information

PHYSICS 221 LAB #6: CAPACITORS AND AC CIRCUITS

PHYSICS 221 LAB #6: CAPACITORS AND AC CIRCUITS Name: Partners: PHYSICS 221 LAB #6: CAPACITORS AND AC CIRCUITS The electricity produced for use in homes and industry is made by rotating coils of wire in a magnetic field, which results in alternating

More information

EXPERIMENT FREQUENCY RESPONSE OF AC CIRCUITS. Structure. 8.1 Introduction Objectives

EXPERIMENT FREQUENCY RESPONSE OF AC CIRCUITS. Structure. 8.1 Introduction Objectives EXPERIMENT 8 FREQUENCY RESPONSE OF AC CIRCUITS Frequency Response of AC Circuits Structure 81 Introduction Objectives 8 Characteristics of a Series-LCR Circuit 83 Frequency Responses of a Resistor, an

More information

Reactance and Impedance

Reactance and Impedance eactance and Impedance Theory esistors, inductors, and capacitors all have the effect of modifying the size of the current in an AC circuit and the time at which the current reaches its maximum value (in

More information

Design of a Regenerative Receiver for the Short-Wave Bands A Tutorial and Design Guide for Experimental Work. Part I

Design of a Regenerative Receiver for the Short-Wave Bands A Tutorial and Design Guide for Experimental Work. Part I Design of a Regenerative Receiver for the Short-Wave Bands A Tutorial and Design Guide for Experimental Work Part I Ramón Vargas Patrón rvargas@inictel-uni.edu.pe INICTEL-UNI Regenerative Receivers remain

More information

PHYS 3322 Modern Laboratory Methods I AC R, RC, and RL Circuits

PHYS 3322 Modern Laboratory Methods I AC R, RC, and RL Circuits Purpose PHYS 3322 Modern Laboratory Methods I AC, C, and L Circuits For a given frequency, doubling of the applied voltage to resistors, capacitors, and inductors doubles the current. Hence, each of these

More information

EE 241 Experiment #7: NETWORK THEOREMS, LINEARITY, AND THE RESPONSE OF 1 ST ORDER RC CIRCUITS 1

EE 241 Experiment #7: NETWORK THEOREMS, LINEARITY, AND THE RESPONSE OF 1 ST ORDER RC CIRCUITS 1 EE 241 Experiment #7: NETWORK THEOREMS, LINEARITY, AND THE RESPONSE OF 1 ST ORDER RC CIRCUITS 1 PURPOSE: To verify the validity of Thevenin and maximum power transfer theorems. To demonstrate the linear

More information

13 th Asian Physics Olympiad India Experimental Competition Wednesday, 2 nd May 2012

13 th Asian Physics Olympiad India Experimental Competition Wednesday, 2 nd May 2012 13 th Asian Physics Olympiad India Experimental Competition Wednesday, nd May 01 Please first read the following instructions carefully: 1. The time available is ½ hours for each of the two experimental

More information

Test Your Understanding

Test Your Understanding 074 Part 2 Analog Electronics EXEISE POBLEM Ex 5.3: For the switched-capacitor circuit in Figure 5.3b), the parameters are: = 30 pf, 2 = 5pF, and F = 2 pf. The clock frequency is 00 khz. Determine the

More information

EE 42/100: Lecture 8. 1 st -Order RC Transient Example, Introduction to 2 nd -Order Transients. EE 42/100 Summer 2012, UC Berkeley T.

EE 42/100: Lecture 8. 1 st -Order RC Transient Example, Introduction to 2 nd -Order Transients. EE 42/100 Summer 2012, UC Berkeley T. EE 42/100: Lecture 8 1 st -Order RC Transient Example, Introduction to 2 nd -Order Transients Circuits with non-dc Sources Recall that the solution to our ODEs is Particular solution is constant for DC

More information

LEP RLC Circuit

LEP RLC Circuit RLC Circuit LEP Related topics Kirchhoff s laws, series and parallel tuned circuit, resistance, capacitance, inductance, phase displacement, Q-factor, band-width, loss resistance, damping Principle The

More information

Exercise 1: Series Resonant Circuits

Exercise 1: Series Resonant Circuits Series Resonance AC 2 Fundamentals Exercise 1: Series Resonant Circuits EXERCISE OBJECTIVE When you have completed this exercise, you will be able to compute the resonant frequency, total current, and

More information

FREQUENCY RESPONSE OF R, L AND C ELEMENTS

FREQUENCY RESPONSE OF R, L AND C ELEMENTS FREQUENCY RESPONSE OF R, L AND C ELEMENTS Marking scheme : Methods & diagrams : 3 Graph plotting : - Tables & analysis : 2 Questions & discussion : 3 Performance : 2 Aim: This experiment will investigate

More information

Experiment Guide: RC/RLC Filters and LabVIEW

Experiment Guide: RC/RLC Filters and LabVIEW Description and ackground Experiment Guide: RC/RLC Filters and LabIEW In this lab you will (a) manipulate instruments manually to determine the input-output characteristics of an RC filter, and then (b)

More information

POLYTECHNIC UNIVERSITY Electrical Engineering Department. EE SOPHOMORE LABORATORY Experiment 5 RC Circuits Frequency Response

POLYTECHNIC UNIVERSITY Electrical Engineering Department. EE SOPHOMORE LABORATORY Experiment 5 RC Circuits Frequency Response POLYTECHNIC UNIVERSITY Electrical Engineering Department EE SOPHOMORE LORTORY Eperiment 5 RC Circuits Frequency Response Modified for Physics 18, rooklyn College I. Overview of Eperiment In this eperiment

More information

AC Theory and Electronics

AC Theory and Electronics AC Theory and Electronics An Alternating Current (AC) or Voltage is one whose amplitude is not constant, but varies with time about some mean position (value). Some examples of AC variation are shown below:

More information

Electronic Circuits Laboratory EE462G Lab #8. BJT Common Emitter Amplifier

Electronic Circuits Laboratory EE462G Lab #8. BJT Common Emitter Amplifier lectronic ircuits Laboratory 46G Lab #8 JT ommon mitter Amplifier npn ipolar Junction Transistor JT in a common-emitter configuration ase ollector V _ n p n V _ mitter For most applications the JT is operated

More information

Lab 3: AC Low pass filters (version 1.3)

Lab 3: AC Low pass filters (version 1.3) Lab 3: AC Low pass filters (version 1.3) WARNING: Use electrical test equipment with care! Always double-check connections before applying power. Look for short circuits, which can quickly destroy expensive

More information

Experiment 8: An AC Circuit

Experiment 8: An AC Circuit Experiment 8: An AC Circuit PART ONE: AC Voltages. Set up this circuit. Use R = 500 Ω, L = 5.0 mh and C =.01 μf. A signal generator built into the interface provides the emf to run the circuit from Output

More information

RLC-circuits with Cobra4 Xpert-Link TEP. 1 2 π L C. f res=

RLC-circuits with Cobra4 Xpert-Link TEP. 1 2 π L C. f res= Related topics Damped and forced oscillations, Kirchhoff s laws, series and parallel tuned circuit, resistance, capacitance, inductance, reactance, impedance, phase displacement, Q-factor, band-width Principle

More information

RC and RL Circuits. Figure 1: Capacitor charging circuit.

RC and RL Circuits. Figure 1: Capacitor charging circuit. RC and RL Circuits Page 1 RC and RL Circuits RC Circuits In this lab we study a simple circuit with a resistor and a capacitor from two points of view, one in time and the other in frequency. The viewpoint

More information

Class: Second Subject: Electrical Circuits 2 Lecturer: Dr. Hamza Mohammed Ridha Al-Khafaji

Class: Second Subject: Electrical Circuits 2 Lecturer: Dr. Hamza Mohammed Ridha Al-Khafaji 10.1 Introduction Class: Second Lecture Ten esonance This lecture will introduce the very important resonant (or tuned) circuit, which is fundamental to the operation of a wide variety of electrical and

More information

TUNED AMPLIFIERS 5.1 Introduction: Coil Losses:

TUNED AMPLIFIERS 5.1 Introduction: Coil Losses: TUNED AMPLIFIERS 5.1 Introduction: To amplify the selective range of frequencies, the resistive load R C is replaced by a tuned circuit. The tuned circuit is capable of amplifying a signal over a narrow

More information

11. AC-resistances of capacitor and inductors: Reactances.

11. AC-resistances of capacitor and inductors: Reactances. 11. AC-resistances of capacitor and inductors: Reactances. Purpose: To study the behavior of the AC voltage signals across elements in a simple series connection of a resistor with an inductor and with

More information

Lab 6 - Inductors and LR Circuits

Lab 6 - Inductors and LR Circuits Lab 6 Inductors and LR Circuits L6-1 Name Date Partners Lab 6 - Inductors and LR Circuits The power which electricity of tension possesses of causing an opposite electrical state in its vicinity has been

More information

DOING PHYSICS WITH MATLAB RESONANCE CIRCUITS RLC PARALLEL VOLTAGE DIVIDER

DOING PHYSICS WITH MATLAB RESONANCE CIRCUITS RLC PARALLEL VOLTAGE DIVIDER DOING PHYSICS WITH MATLAB RESONANCE CIRCUITS RLC PARALLEL VOLTAGE DIVIDER Matlab download directory Matlab scripts CRLCp1.m CRLCp2.m When you change channels on your television set, an RLC circuit is used

More information