# The Time Constant of an RC Circuit

Save this PDF as:

Size: px
Start display at page:

Download "The Time Constant of an RC Circuit"

## Transcription

1 The Time Constant of an RC Circuit 1 Objectives 1. To determine the time constant of an RC Circuit, and 2. To determine the capacitance of an unknown capacitor. 2 Introduction What the heck is a capacitor? It s one of the three passive circuit elements: the resistor (which we ve already met), the capacitor (which stores energy in electric fields), and the inductor (which stores energy in magnetic fields, and is the main subject a few weeks from now). Also known as condensers, capacitors store energy an electric field by separating positive and negative charges on opposing terminals known as plates - which may or may not actually be plate-like. Capacitors trace their lineage to the middle of the Eighteenth century and the invention of the Leyden jar. For forty years, the biggest names in natural philosophy spent time in the study of charge storage and improving capacitors, including Volta (for whom we name the volt) and Franklin (of American Founding Father fame). In this lab, we will study the behavior of capacitors while we add or remove charge from the plates. Although we won t touch on it in this lab, RC circuits form the foundation of the modern electronics that underlie a whole host of technologies, including radio, computers, environmental and medical sensors, and - not least of all - the touch screens in cell phones and the touch pads of laptops. 3 Theory We normally write Ohm s Law for the resistor as V (t) = I(t)R. But what is that current I(t)? In the circuits here (see Figure 1), it s just the rate at which charge passes through the resistor. Since all the charge that runs through the resistor ends up going from or to the capacitor, q(t), it must also be the case that I(t) = ± dq(t), where q(t) is the time dependent charge on the capacitor, with the sign depending on whether the charge on the capacitor is increasing or decreasing. For this circuit, we could instead 1

2 Figure 1: The switching circuit used to discuss charging and discharging a capacitor. write Ohm s Law in the form dq(t) = ± V (t) R. In words, a resistor is a passive device where the applied voltage causes charge to flow through the device, while a capacitor is a passive device where the applied voltage causes charge storage in the device; in equation form q(t) = CV (t). The constant C is called the capacitance, and is measured in Farads (named for Michael Faraday, whose research output we will learn about later this semester) where F = C /V. Since capacitors are used to store charge, we must find a way to change the charge state on the capacitor. Let s discuss the circuit in Figure 1. This circuit has three states: 1. The steady state, where the switch is open, no current flows in the resistor, and the charge state on the capacitor is constant, 2. the charging state, where the battery or power supply is connected to the capacitor and adds charge to the capacitor, and 3. the discharging state, where the battery is disconnected, the two plates of the capacitor are connected to each other through the resistor, which removes charge from the capacitor. We can analyze the dynamic states of the circuit using Kirchoff s Rules 1 : 1. The Loop rule (energy conservation) requires the sum of all voltages drops around a closed loop to vanish, and 2. The Junction rule (charge conservation) requires the sum of all currents into a junction to vanish. Let s apply these rules, first to the discharging and then to the charging state: 1. Discharging: In the discharging case, the current will flow off the capacitor in a counter clockwise direction (why?). When we close that switch, Kirchoff s rules become dq(t) V c V R = 0 q(t) RC = 0. 1 As long as the frequencies aren t so high that we can t use the lumped element approximation; talk to your instructor if you want to know more. 2

3 Again, the rate is negative, because the capacitor is discharging, not charging. The method of solution for this equation is given in Appendix A: V c (t) = V R (t) = V s e t/rc, assuming that the initial voltage across the capacitor is V s. This discharge curve is plotted in Figure Charging: In the charging case, the current flows clockwise from the battery (at voltage V s ), through the resistor (at V R ), and across the capacitor V c ; we want to solve for V c as a function of time. Kirchoff s Rules tell us V s V R V c = 0 V s IR q C But here, the current through the resistor depends on the rate at which charge is changing on the capacitor; they have the same sign here since the charge on the capacitor is increasing V s dq(t) dq(t) R q(t) C = 0 + q(t) RC = V s R. We can solve this differential equation too for the time dependent voltage profile across the capacitor; see Appendix A. If we start with a completely discharged capacitor, the voltages across the resistors and capacitors vary as V c (t) = V s ( 1 e t/rc ) V R (t) = V s e t/rc. As the capacitor charges, the voltage across - and hence the charge on - the capacitor rises exponentially, while the voltage across - and hence the current through - the resistor will fall exponentially; see Figure 2. The quantity RC - which appears in the argument of the exponential - is known as the time constant of the system; it has units of time (hence the name), and determines the time interval over which voltages, charges, and currents change in the circuit. The time constant can be tuned by modifying either R or C. In practice, more resistor than capacitor values are commercially available, so it s usually easier to tune the resistor values. Given a known resistance we can measure the time constant of the RC circuit, and algebraically determine the capacitance C. When discharging the capacitor, V c (t) = V s e t/rc. 3

4 1 Capacitor charging and discharging curves Discharging Charging V c (t)/v s Figure 2: The capacitor charging and discharging curves. The vertical blue line is the half life point of the charging and discharging timeline. t/rc We can easily measure and use the half-life T1/2 of the discharge: T1/2 is the time it takes for the voltage to fall by half. Substituting into the above equations and solving for T1/2: V s 2 = V se T 1/2 /RC ln 1 2 = T1 /2 RC T1/2 = (C ln 2) R. If we allow R to vary, then this equation defines a line with abscissa R, ordinate T1/2, and slope C ln 2. If we measure multiple (R, T1/2) pairs, we can plot those data points, fit them to a line, and extract the slope - and hence the capacitance. 4 Procedures You should receive an oscilloscope, a function generator, a multimeter, one unknown capacitor, a decade capacitance box, and a decade resistance box. 4.1 Time Constant of an RC Circuit In this part of the experiment, instead of a DC voltage and a mechanical switch, we apply a square wave signal to the capacitor as shown in Figure 3. An ideal square wave has two values: high and low (here V s and 0), and it switches between them instantaneously. The capacitor will charge when the voltage of the square wave is V s ; the capacitor will discharge when the voltage of the square wave is zero. The oscilloscope traces of the charging and discharging of the capacitor are also shown in Figure 3. 4

5 Prototypical Oscilloscope Trace 1 Trace A Trace B V c (t)/v s (a) Measurement Circuit t/rc (b) Oscilloscope Display Figure 3: The left-hand figure is the circuit used to measure the time constant of an RC circuit, while the right-hand figure shows the Oscilloscope traces. If the period of the square wave T s is much less than the time constant τ = RC (T s τ), then the capacitor will start discharging before it has sufficient time to acquire the maximum charge q 0, making measurement of the time constant difficult. What will this look like on the oscilloscope? If T s is much more than τ (T s τ), you will not be able to fit both the charging and discharging portions of the capacitor voltage on the oscilloscope trace at the same time. Why? 1. Construct the circuit shown in Figure 3a. 2. Perform the initial turn-on procedure for the oscilloscope (from the Oscilloscope Lab). To start, set both channels to 0.2 V/div. Make sure that the ground of both traces is at the same position on the screen. 3. Start by setting the frequency of the square wave to about 100 Hz and the output voltage to 0.5 V. 4. Now we have to set R and C. Adjust R to about 8 kω, and C to about 0.1 µf. What is the time constant of this combination? 5. Adjust the frequency of the square wave, and the time and voltage settings of the oscilloscope until you obtain traces similar to Figure 3b. Measure and record R, C, f, V, T1/2, and the oscilloscope settings. 6. Measure the voltage of the decay curve above ground at a number of points using the oscilloscope cursors; similarly, measure the height of the charging curve at a number of points. You will use these to map out the charging/discharging curves, and fit for the time constant. 7. Repeat for a second set of R and C. 4.2 Determine the Capacitance Here, we ll use the same techniques we just did to determine the value of an unknown capacitor. 5

6 1. Replace the known capacitor with the unknown capacitor in the circuit. 2. Set the resistance to about 4 kω, and make the necessary adjustments to the oscilloscope settings to again obtain the appropriate display on the oscilloscope. 3. Measure and record R, f, V, the oscilloscope settings, and T1/2. 4. Repeat for four or five values of R; you need enough points to fit a line through your (R, T1/2) pairs. 5. Use your multimeter to directly measure the capacitance, for comparison to your extracted value. 2 A Derivation of Solutions The differential equations in Section 3 are the simplest of all differential equations to solve: first order, linear equations with constant coefficients. Here, we ll solve a slightly more complicated equation (a first order linear equation with non-constant coefficients) in complete generality, and use this solution to find the solutions we re interested in. Consider the following differential equation: dy(x) + P (x)y(x) = Q(x). This equation looks very much like the equations we found in Section 3 using Kirchoff s Rules. We can solve this in the following way. First, we ll multiply both sides of this equation by a new function, M(x), and we ll first solve for M(x). M(x) dy(x) + M(x)P (x)y(x) = M(x)Q(x). Let s now assume that the left hand side is the expansion of the product rule of M(x)y(x): What must be true for this to hold? Well, d (M(x)y(x)) = M(x)dy(x) This is true if and only if d (M(x)y(x)) = M(x)Q(x). + dm(x) y(x) = M(x)dy(x) + M(x)P (x)y(x). dm(x) = M(x)P (x). 2 The multimeter uses an automated version of exactly this procedure to calculate C, based on a time constant measurement across a precision internal resistor. 6

7 This is a trivial problem to solve: just separate and integrate: M(x) = e P (x)+c = e c e P (x) = c e P (x), where c is the constant of integration for this indefinite integral. Now, go a few lines back up the page: d (M(x)y(x)) = M(x)Q(x). We can solve this one trivially, too, just by integrating; let s make this a definite integral between x 0 and x. We get the left hand side from the Fundamental Theorem of Calculus M(x)y(x) M(x 0 )y(x 0 ) = x x 0 M(x)Q(x), where, since this is an indefinite integral, requires an integration constant c. Finally, then, we can solve the general problem: x ) y(x) = M(x) (M(x 1 0 )y(x 0 ) + M(x)Q(x). x 0 Note that the integration constant in the definition of M(x) cancels here, so it doesn t really matter what it was; let s just choose c = 1. In the case of the charging RC circuit with zero initial charge, x = t, y(x) = q(t), x 0 = 0, y(x 0 ) = 0, P (t) = 1/RC, and Q(t) = V s /R. Integrating gives us M(t) = e t/rc, giving us the solution: q(t) = e t/rc t 0 e t/rc V s R = V s R RCe t/rc ( e t/rc 1 ) = V s C ( 1 e t/rc), where we ve used the integration constant to get the t = 0 value right (here, no charge on the capacitor). Dividing both sides by C gives us the voltage across the capacitor at time t V c (t) = V s ( 1 e t/rc ). In the case of the discharging circuit, we have q(t) = V s Ce t/rc, where we assume the voltage across the capacitor at t = 0 is V s. Again, divide by C to get the voltage profile V c (t) = V s e t/rc. 7

8 Pre-Lab Exercises Answer these questions as instructed on Blackboard; make sure to submit them before your lab session! 1. What is the time constant for an RC circuit with R = 45 kω and C = 1.2 µf? 2. If it takes 5 µs for a capacitor to charge to half the battery voltage, through a 10 kω resistor, what is the capacitance C? 3. A given RC circuit charges through a particular resistor R, and capacitor, C. If I double the capacitance, what happens to the time constant? What if I double the resistance? 8

9 Post-Lab Exercises 1. Determine the time constant of the RC circuit with known capacitance. Do this by plotting your data of time versus the amplitude of the signal. You should fit this data to an exponential, and extract τ. There are a number of ways to do this: (a) use a mathematics package capable of sophisticated statistical analysis, such as R, Octave, Matlab, Mathematica, Root, etc., or (b) using a spreadsheet, fit the data using an exponential trendline analysis. Alternatively, you can transform your spreadsheet data into a linear data set, and do a linear trendline analysis. Estimate the uncertainty of this measured time constant. You should also estimate the time constant from the measured T1/2. Do these multiple experimental extractions agree within your estimated uncertainty? Do they agree with the theoretical expectation given your measured R and C? 2. Determine the unknown capacitance. Plot your (R, T1/2) data pairs, and fit the data to a line. Extract the capacitance from the fitted line parameters. Estimate the uncertainty of this extracted capacitance. You can also estimate the capacitance from the individual (R, T1/2) pairs; estimate your uncertainties. Do these estimates agree with the line fit estimate? 3. Discuss briefly whether you have met the objectives of the lab exercises. 9

### E X P E R I M E N T 7

E X P E R I M E N T 7 The RC Circuit Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics II, Exp 7: The RC Circuit Page

### Charge and Discharge of a Capacitor

Charge and Discharge of a Capacitor INTRODUCTION Capacitors 1 are devices that can store electric charge and energy. Capacitors have several uses, such as filters in DC power supplies and as energy storage

### " = R # C. Create your sketch so that Q(t=τ) is sketched above the delineated tic mark. Your sketch. 1" e " t & (t) = Q max

Physics 241 Lab: Circuits DC Source http://bohr.physics.arizona.edu/~leone/ua/ua_spring_2010/phys241lab.html Name: Section 1: 1.1. Today you will investigate two similar circuits. The first circuit is

### Alternating Current RL Circuits

Alternating Current RL Circuits Objectives. To understand the voltage/current phase behavior of RL circuits under applied alternating current voltages, and. To understand the current amplitude behavior

### Capacitors. We charge a capacitor by connecting the two plates to a potential difference, such as a battery:

RC Circuits PHYS 1112L Capacitors A capacitor is an electrical component that stores charge. The simplest capacitor is just two charged metal plates separated by a non-conducting material: In the diagram

### Experiment #9: RC and LR Circuits Time Constants

Experiment #9: RC and LR Circuits Time Constants Purpose: To study the charging and discharging of capacitors in RC circuits and the growth and decay of current in LR circuits. Part 1 Charging RC Circuits

### Class #12: Experiment The Exponential Function in Circuits, Pt 1

Class #12: Experiment The Exponential Function in Circuits, Pt 1 Purpose: The objective of this experiment is to begin to become familiar with the properties and uses of the exponential function in circuits

### Kirchhoff s Voltage Law and RC Circuits

Kirchhoff s oltage Law and RC Circuits Apparatus 2 1.5 batteries 2 battery holders DC Power Supply 1 multimeter 1 capacitance meter 2 voltage probes 1 long bulb and 1 round bulb 2 sockets 1 set of alligator

### The RC Circuit. Pre-lab questions. Introduction. The RC Circuit

The RC Circuit Pre-lab questions 1. What is the meaning of the time constant, RC? 2. Show that RC has units of time. 3. Why isn t the time constant defined to be the time it takes the capacitor to become

### RC Circuits and The Oscilloscope Physics Lab X

Objective RC Circuits and The Oscilloscope Physics Lab X In this series of experiments, the time constant of an RC circuit will be measured experimentally and compared with the theoretical expression for

### RC Circuits. 1 Introduction. 2 Capacitors

1 RC Circuits Equipment DataStudio with 750 interface, RLC circuit board, 2 voltage sensors (no alligator clips), 2x35 in. leads, 12 in. lead Reading Review operation of DataStudio oscilloscope. Review

### EE 1202 Experiment #4 Capacitors, Inductors, and Transient Circuits

EE 1202 Experiment #4 Capacitors, Inductors, and Transient Circuits 1. Introduction and Goal: Exploring transient behavior due to inductors and capacitors in DC circuits; gaining experience with lab instruments.

### Experiment 9 ~ RC Circuits

Experiment 9 ~ RC Circuits Objective: This experiment will introduce you to the properties of circuits that contain both resistors AND capacitors. Equipment: 18 volt power supply, two capacitors (8 µf

### W03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören

W03 Analysis of DC Circuits Yrd. Doç. Dr. Aytaç Gören ELK 2018 - Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits (self and condenser) W04 Transistors and

### LRC Circuits. Purpose. Principles PHYS 2211L LAB 7

Purpose This experiment is an introduction to alternating current (AC) circuits. Using the oscilloscope, we will examine the voltage response of inductors, resistors and capacitors in series circuits driven

### The current that flows is determined by the potential difference across the conductor and the resistance of the conductor (Ohm s law): V = IR P = VI

PHYS1000 DC electric circuits 1 Electric circuits Electric current Charge can move freely in a conductor if an electric field is present; the moving charge is an electric current (SI unit is the ampere

### EMF and Terminal Voltage Resistors in Series and Parallel Kirchhoff s Rules EMFs in Series and Parallel; Charging a Battery Circuits with Capacitors

Chapter 19 DC Electrical Circuits Topics in Chapter 19 EMF and Terminal Voltage Resistors in Series and Parallel Kirchhoff s Rules EMFs in Series and Parallel; Charging a Battery Circuits with Capacitors

### College Physics II Lab 8: RC Circuits

INTODUTION ollege Physics II Lab 8: ircuits Peter olnick with Taner Edis Spring 2015 Introduction onsider the circuit shown. (onsult section 23.7 in your textbook.) If left for long enough, the charge

### Chapter 5: Analysis of Time-Domain Circuits

Chapter 5: Analysis of Time-Domain Circuits This chapter begins the analysis of circuits containing elements with the ability to store energy: capacitors and inductors. We have already defined each of

### Name: Lab Partner: Section:

Chapter 6 Capacitors and RC Circuits Name: Lab Partner: Section: 6.1 Purpose The purpose of this experiment is to investigate the physics of capacitors in circuits. The charging and discharging of a capacitor

### EXPERIMENT NUMBER 8 CAPACITOR CURRENT-VOLTAGE RELATIONSHIP

1 EXPERIMENT NUMBER 8 CAPACITOR CURRENT-VOLTAGE RELATIONSHIP Purpose: To demonstrate the relationship between the voltage and current of a capacitor. Theory: A capacitor is a linear circuit element whose

### FREQUENTLY ASKED QUESTIONS October 2, 2012

FREQUENTLY ASKED QUESTIONS October 2, 2012 Content Questions Why do batteries require resistors? Well, I don t know if they require resistors, but if you connect a battery to any circuit, there will always

### Discharging and Charging a Capacitor

Name: Partner(s): Desk #: Date: Discharging and Charging a Capacitor Figure 1. Various types of capacitors. "Capacitors (7189597135)" by Eric Schrader from San Francisco, CA, United States - 12739s. Licensed

### NEON BULB OSCILLATOR EXPERIMENT

NEON BULB OSCILLATOR EXPERIMENT When we combine a neon bulb with the circuit for charging up a capacitor through a resistor, we obtain the worlds simplest active electronic circuit that does something

### A MODEL OF VOLTAGE IN A RESISTOR CIRCUIT AND AN RC CIRCUIT

A MODEL OF VOLTAGE IN A RESISTOR CIRCUIT AND AN RC CIRCUIT ARJUN MOORJANI, DANIEL STRAUS, JENNIFER ZELENTY Abstract. We describe and model the workings of two simple electrical circuits. The circuits modeled

### Storing And Releasing Charge In A Circuit

Storing And Releasing Charge In A Circuit Topic The characteristics of capacitors Introduction A capacitor is a device that can retain and release an electric charge, and is used in many circuits. There

### RC Circuit (Power amplifier, Voltage Sensor)

Object: RC Circuit (Power amplifier, Voltage Sensor) To investigate how the voltage across a capacitor varies as it charges and to find its capacitive time constant. Apparatus: Science Workshop, Power

### Chapter 7 Direct-Current Circuits

Chapter 7 Direct-Current Circuits 7. Introduction...7-7. Electromotive Force...7-3 7.3 Resistors in Series and in Parallel...7-5 7.4 Kirchhoff s Circuit Rules...7-7 7.5 Voltage-Current Measurements...7-9

### Lab #4 Capacitors and Inductors. Capacitor and Inductor Transient Response

Capacitor and Inductor Transient Response Capacitor Theory Like resistors, capacitors are also basic circuit elements. Capacitors come in a seemingly endless variety of shapes and sizes, and they can all

### How many laws are named after Kirchhoff?

Chapter 32. Fundamentals of Circuits Surprising as it may seem, the power of a computer is achieved simply by the controlled flow of charges through tiny wires and circuit elements. Chapter Goal: To understand

### SERIES-PARALLEL DC CIRCUITS

Name: Date: Course and Section: Instructor: EXPERIMENT 1 SERIES-PARALLEL DC CIRCUITS OBJECTIVES 1. Test the theoretical analysis of series-parallel networks through direct measurements. 2. Improve skills

### Lab 5: Basic Direct-Current Circuits Edited 11/20/14 by Joe Skitka, Stephen Albright, WL, JCH & DGH

Lab 5: Basic Direct-Current Circuits Edited 11/20/14 by Joe Skitka, Stephen Albright, WL, JCH & DGH Objective This set of mini-experiments aims to verify rules governing the addition of resistors and capacitors

### Physics 2306 Experiment 7: Time-dependent Circuits, Part 1

Name ID number Date Lab CRN Lab partner Lab instructor Objectives Physics 2306 Experiment 7: Time-dependent Circuits, Part 1 To study the time dependent behavior of the voltage and current in circuits

### Ch 18 Direct Current Circuits. concept #2, 5, 10, 12, 13, 23 Problems #1, 5, 6, 11, 17, 25, 31, 32, 33, 35, 36, 37

Ch 18 Direct Current Circuits concept #2, 5, 10, 12, 13, 23 Problems #1, 5, 6, 11, 17, 25, 31, 32, 33, 35, 36, 37 currents are maintained by a source of emf (battery, generator) Sources of emf act as charge

### Physics 260 Calculus Physics II: E&M. RC Circuits

RC Circuits Object In this experiment you will study the exponential charging and discharging of a capacitor through a resistor. As a by-product you will confirm the formulas for equivalent capacitance

### Resistor-Capacitor (RC) Circuits

Resistor-Capacitor (RC) Circuits Introduction In this second exercise dealing with electrical circuitry, you will work mainly with capacitors, which are devices that are used to store charge for later

### The Nerve as a Capacitor

HPP Activity 72v1 The Nerve as a Capacitor Exploration - How Does a Neuron Transmit a Signal? Electrical processes are essential to the working of the human body. The transmission of information in the

### BASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE-4 SOME USEFUL LAWS IN BASIC ELECTRONICS

BASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE-4 SOME USEFUL LAWS IN BASIC ELECTRONICS Hello everybody! In a series of lecture on basic electronics, learning by doing, we now

### Lab 4 - Capacitors & RC Circuits

Lab 4 Capacitors & RC Circuits L41 Name Date Partners Lab 4 Capacitors & RC Circuits OBJECTIVES To define capacitance and to learn to measure it with a digital multimeter. To explore how the capacitance

### The R-C series circuit

School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 4 The C series circuit 1 Introduction Objectives To study the

### RC transients. EE 201 RC transient 1

RC transients Circuits having capacitors: At DC capacitor is an open circuit, like it s not there. Transient a circuit changes from one DC configuration to another DC configuration (a source value changes

### Step Response of RC Circuits

Step Response of RC Circuits 1. OBJECTIVES...2 2. REFERENCE...2 3. CIRCUITS...2 4. COMPONENTS AND SPECIFICATIONS...3 QUANTITY...3 DESCRIPTION...3 COMMENTS...3 5. DISCUSSION...3 5.1 SOURCE RESISTANCE...3

### MAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START

Laboratory Section: Last Revised on December 15, 2014 Partners Names Grade EXPERIMENT 10 Electronic Circuits 0. Pre-Laboratory Work [2 pts] 1. How are you going to determine the capacitance of the unknown

### A2 PHYSICS CAPACITORS - Test SOLUTION

Q1. A charged capacitor of capacitance 50 F is connected across the terminals of a voltmeter of resistance 200 k. When time t = 0, the reading on the voltmeter is 20.0 V. Calculate (a) the charge on the

### Problem Solving 8: RC and LR Circuits

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Problem Solving 8: RC and LR Circuits Section Table and Group (e.g. L04 3C ) Names Hand in one copy per group at the end of the Friday Problem

### CAPACITANCE IN A RC CIRCUIT

5/16 Capacitance-1/5 CAPACITANCE IN A RC CIRCUIT PURPOSE: To observe the behavior of resistor-capacitor circuit, to measure the RC time constant and to understand how it is related to the time dependence

### EXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR CIRCUITS

EXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR 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 &

### Physics 9 Fall 2009 Homework 6 - Solutions

. Chapter 32 - Exercise 8. Physics 9 Fall 29 Homework 6 - s How much power is dissipated by each resistor in the figure? First, let s figure out the current in the circuit. Since the two resistors are

### First Order Transient Response

First Order Transient Response When non-linear elements such as inductors and capacitors are introduced into a circuit, the behaviour is not instantaneous as it would be with resistors. A change of state

### = (0.400 A) (4.80 V) = 1.92 W = (0.400 A) (7.20 V) = 2.88 W

Physics 2220 Module 06 Homework 0. What are the magnitude and direction of the current in the 8 Ω resister in the figure? Assume the current is moving clockwise. Then use Kirchhoff's second rule: 3.00

### CHAPTER 28 ELECTRIC CIRCUITS

CHAPTER 8 ELECTRIC CIRCUITS 1. Sketch a circuit diagram for a circuit that includes a resistor R 1 connected to the positive terminal of a battery, a pair of parallel resistors R and R connected to the

### Electricity & Electronics 8: Capacitors in Circuits

Electricity & Electronics 8: Capacitors in Circuits Capacitors in Circuits IM This unit considers, in more detail, the charging and discharging of capacitors. It then investigates how capacitors behave

### Chapter 21 Electric Current and Direct-Current Circuit

Chapter 2 Electric Current and Direct-Current Circuit Outline 2- Electric Current 2-2 Resistance and Ohm s Law 2-3 Energy and Power in Electric Circuit 2-4 Resistance in Series and Parallel 2-5 Kirchhoff

### More Concepts. I = dq. Current is the rate of flow of charge around a circuit.

RC Circuits In this presentation, circuits with multiple batteries, resistors and capacitors will be reduced to an equivalent system with a single battery, a single resistor, and a single capacitor. Kirchoff's

### Discharge of a Capacitor

Discharge of a Capacitor THEORY The charge Q on a capacitor s plate is proportional to the potential difference V across the capacitor. We express this with Q = C V (1) where C is a proportionality constant

### 1: (ta initials) 2: first name (print) last name (print) brock id (ab13cd) (lab date)

1: (ta initials) 2: first name (print) last name (print) brock id (ab13cd) (lab date) Experiment 1 Capacitance In this Experiment you will learn the relationship between the voltage and charge stored on

### EXPERIMENT 6 CLIPPING AND CLAMPING DIODE CIRCUITS

EXPERIMENT 6 CLIPPING AND CLAMPING DIODE CIRCUITS OBJECTIVES To understand the theory of operation of the clipping and clamping diode circuits. To design wave shapes that meet different circuits needs.

### Lab 5 RC Circuits. What You Need To Know: Physics 226 Lab

Lab 5 R ircuits What You Need To Know: The Physics In the previous two labs you ve dealt strictly with resistors. In today s lab you ll be using a new circuit element called a capacitor. A capacitor consists

### Kirchhoff s Laws. Kirchhoff's Law #1 - The sum of the currents entering a node must equal the sum of the currents exiting a node.

Kirchhoff s Laws There are two laws necessary for solving circuit problems. For simple circuits, you have been applying these equations almost instinctively. Kirchhoff's Law #1 - The sum of the currents

### RC Circuits. The purpose of this lab is to understand how capacitors charge and discharge.

Department of Physics and Geology Purpose Circuits Physics 2402 The purpose of this lab is to understand how capacitors charge and discharge. Materials Decade Resistance Box (CENCO), 0.1 µf, 0.5µF, and

### Name Date Day/Time of Lab Partner(s) Lab TA

Name Date Day/Time of Lab Partner(s) Lab TA Objectives LAB 7: AC CIRCUITS To understand the behavior of resistors, capacitors, and inductors in AC Circuits To understand the physical basis of frequency-dependent

### RC CIRCUIT. THEORY: Consider the circuit shown below in Fig. 1: a S. V o FIGURE 1

RC CIRCUIT OBJECTIVE: To study the charging and discharging process for a capacitor in a simple circuit containing an ohmic resistance, R, and a capacitance, C. THEORY: Consider the circuit shown below

### Time dependent circuits - The RC circuit

Time dependent circuits - The circuit Example 1 Charging a Capacitor- Up until now we have assumed that the emfs and resistances are constant in time, so that all potentials, currents and powers are constant

### Filters and Waveform Shaping

Physics 333 Experiment #3 Fall 211 Filters and Waveform Shaping Purpose The aim of this experiment is to study the frequency filtering properties of passive (R, C, and L) circuits for sine waves, and the

### ECE201 Laboratory 1 Basic Electrical Equipment and Ohm s and Kirchhoff s Laws (Created by Prof. Walter Green, Edited by Prof. M. J.

ECE201 Laboratory 1 Basic Electrical Equipment and Ohm s and Kirchhoff s Laws (Created by Prof. Walter Green, Edited by Prof. M. J. Roberts) Objectives The objectives of Laboratory 1 are learn to operate

### Measurement of Capacitance

Measurement of Capacitance Pre-Lab Questions Page Name: Class: Roster Number: Instructor:. A capacitor is used to store. 2. What is the SI unit for capacitance? 3. A capacitor basically consists of two

### Vessel holding water. Charged capacitor. Questions. Question 1

ELEN236 Capacitors This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,

### Experiment 8 RC Circuits

Experiment 8 ircuits Nature, to be commanded, must be obeyed. F. Bacon (1561-1626) OBJETIVE To study a simple circuit that has time-dependent voltages and current. THEOY ircuits with steady currents and

### Lab #4 examines inductors and capacitors and their influence on DC circuits.

Transient DC Circuits 1 Lab #4 examines inductors and capacitors and their influence on DC circuits. As R is the symbol for a resistor, C and L are the symbols for capacitors and inductors. Capacitors

### EE 1202 Experiment #2 Resistor Circuits

EE 1202 Experiment #2 Resistor Circuits 1. ntroduction and Goals: Demonstrates the voltage-current relationships in DC and AC resistor circuits. Providing experience in using DC power supply, digital multimeter,

### 9.1 Variable currents 1: Discharging a capacitor

Scott Hughes 8 March 2005 Massachusetts Institute of Technology Department of Physics 8.022 Spring 2005 Lecture 9: Variable currents; Thévenin equivalence 9.1 Variable currents 1: Discharging a capacitor

### Pre-Lab 7 Assignment: Capacitors and RC Circuits

Name: Lab Partners: Date: Pre-Lab 7 Assignment: Capacitors and RC Circuits (Due at the beginning of lab) Directions: Read over the Lab Handout and then answer the following questions about the procedures.

### Resistor Capacitor (RC) Circuits

Resistor Capacitor (RC) Circuits So far, we know how to handle resistors in a circuit: What happens when the switch is closed? A steady current flows in the circuit What happens if we also put a capacitor

### PHYS 2426 Engineering Physics II EXPERIMENT 5 CAPACITOR CHARGING AND DISCHARGING

PHYS 2426 Engineering Physics II EXPERIMENT 5 CAPACITOR CHARGING AND DISCHARGING I. OBJECTIVE: The objective of this experiment is the study of charging and discharging of a capacitor by measuring the

### Study Guide and Review for Electricity and Light Lab Final

Study Guide and Review for Electricity and Light Lab Final This study guide is provided to help you prepare for the lab final. The lab final consists of multiplechoice questions, usually two for each unit,

### INTRODUCTION TO ARBITRARY/FUNCTION GENERATOR

Page 1 of 7 INTRODUCTION TO ARBITRARY/FUNCTION GENERATOR BEFORE YOU BEGIN PREREQUISITE LABS Introduction to MATLAB Introduction to Oscilloscope EXPECTED KNOWLEDGE Ohm s law & Kirchhoff s laws Operation

### Inductors in AC Circuits

Inductors in AC Circuits Name Section Resistors, 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

### ELEC 2020 EXPERIMENT 6 Zener Diodes and LED's

ELEC 2020 EXPERIMENT 6 Zener Diodes and LED's Objectives: The experiments in this laboratory exercise will provide an introduction to diodes. You will use the Bit Bucket breadboarding system to build and

### Episode 129: Discharge of a capacitor: Q = Q o e -t/cr

Episode 129: Discharge of a capacitor: Q = Q o e -t/cr Students will have already seen that the discharge is not a steady process (Episode 125), but it is useful to have graphical evidence before discussing

### Experiment V: The AC Circuit, Impedance, and Applications to High and Low Pass Filters

Experiment : The AC Circuit, Impedance, and Applications to High and Low Pass Filters I. eferences Halliday, esnick and Krane, Physics, ol. 2, 4th Ed., Chapters 33 Purcell, Electricity and Magnetism, Chapter

### Resistance Review Following the potential around a circuit Multiloop Circuits RC Circuits

DC Circuits esistance eview Following the potential around a circuit Multiloop Circuits C Circuits Homework for today: ead Chapters 6, 7 Chapter 6 Questions, 3, 0 Chapter 6 Problems, 7, 35, 77 Homework

### Lab 5 RC Circuits: Charge Changing in Time Observing the way capacitors in RC circuits charge and discharge.

Print Your Name Lab 5 RC Circuits: Charge Changing in Time Observing the way capacitors in RC circuits charge and discharge. Print Your Partners' Names Instructions October 15, 2015October 13, 2015 Read

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT 4 Understand single-phase alternating current (ac) theory Single phase AC

### Transistor Amplifiers

Physics 3330 Experiment #7 Fall 1999 Transistor Amplifiers Purpose The aim of this experiment is to develop a bipolar transistor amplifier with a voltage gain of minus 25. The amplifier must accept input

### = V peak 2 = 0.707V peak

BASIC ELECTRONICS - RECTIFICATION AND FILTERING PURPOSE Suppose that you wanted to build a simple DC electronic power supply, which operated off of an AC input (e.g., something you might plug into a standard

### Department of Electrical Engineering and Computer Sciences University of California, Berkeley. First-Order RC and RL Transient Circuits

Electrical Engineering 42/100 Summer 2012 Department of Electrical Engineering and Computer Sciences University of California, Berkeley First-Order RC and RL Transient Circuits When we studied resistive

### PHYS 2426 Engineering Physics II (Revised July 7, 2011) AC CIRCUITS: RLC SERIES CIRCUIT

PHYS 2426 Engineering Physics II (Revised July 7, 2011) AC CIRCUITS: RLC SERIES CIRCUIT INTRODUCTION The objective of this experiment is to study the behavior of an RLC series circuit subject to an AC

### Chapter 11. Capacitors Charging, Discharging, Simple Waveshaping Circuits

Chapter 11 Capacitors Charging, Discharging, Simple Waveshaping Circuits Source: Circuit Analysis: Theory and Practice Delmar Cengage Learning Introduction When switch is closed at, capacitor charging

### Recitation 6 Chapter 21

Recitation 6 hapter 21 Problem 35. Determine the current in each branch of the circuit shown in Figure P21.35. 3. Ω 5. Ω 1. Ω 8. Ω 1. Ω ɛ 2 4 12 Let be the current on the left branch (going down), be the

### Teacher s Guide - Activity P50: RC Circuit (Power Output, Voltage Sensor)

Teacher s Guide - Activity P50: RC Circuit (Power Output, Voltage Sensor) Concept DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) Circuits P50 RC Circuit.DS (See end of activity) (See end of activity)

### Capacitors. Goal: To study the behavior of capacitors in different types of circuits.

Capacitors Goal: To study the behavior of capacitors in different types of circuits. Lab Preparation A capacitor stores electric charge. A simple configuration for a capacitor is two parallel metal plates.

### Frequency response of a general purpose single-sided OpAmp amplifier

Frequency response of a general purpose single-sided OpAmp amplifier One configuration for a general purpose amplifier using an operational amplifier is the following. The circuit is characterized by:

### Homework 6 Solutions PHYS 212 Dr. Amir

Homework 6 Solutions PHYS Dr. Amir Chapter 5: 9. (II) A 00-W lightbulb has a resistance of about Ω when cold (0 C) and 0 Ω when on (hot). Estimate the temperature of the filament when hot assuming an average

### Physics Lab 202P-8. Understanding RC Circuits NAME: LAB PARTNERS:

Physics Lab 202P-8 Understanding RC Circuits NAME: LAB PARTNERS: LAB SECTION: LAB INSTRUCTOR: DATE: EMAIL ADDRESS: Penn State University Created by nitin samarth Physics Lab 202P-8 Page 1 of 16 Physics

### Dr. Julie J. Nazareth

Name: Dr. Julie J. Nazareth Lab Partner(s): Physics: 133L Date lab performed: Section: Capacitors Parts A & B: Measurement of capacitance single, series, and parallel combinations Table 1: Voltage and

### Chapter 28. Direct Current Circuits

Chapter 28 Direct Current Circuits Direct Current When the current in a circuit has a constant direction, the current is called direct current Most of the circuits analyzed will be assumed to be in steady

### Lab #4 Thevenin s Theorem

In this experiment you will become familiar with one of the most important theorems in circuit analysis, Thevenin s Theorem. Thevenin s Theorem can be used for two purposes: 1. To calculate the current

### à 7.Electrical Circuits and Kirchhoff's Rules

1 à 7.Electrical Circuits and Kirchhoff's Rules Electrical circuits involving batteries and resistors can be treated using a method of analysis developed by Kirchoff. There are just two Kirchhoff's rules:

### Resistors in Series and Parallel

Resistors in Series and Parallel INTRODUCTION Direct current (DC) circuits are characterized by the quantities current, voltage and resistance. Current is the rate of flow of charge. The SI unit is the

### Coupled Electrical Oscillators Physics 3600 Advanced Physics Lab Summer 2010 Don Heiman, Northeastern University, 5/10/10

Coupled Electrical Oscillators Physics 3600 Advanced Physics Lab Summer 00 Don Heiman, Northeastern University, 5/0/0 I. Introduction The objectives of this experiment are: () explore the properties of