EE201 – Circuit Theory I2017-2018, Fall

1. Basic Concepts (Chapter 1 of Nilsson - 3 Hrs.)

Introduction, Current and Voltage, Power and Energy

2. Basic Laws (Chapter 2&3 of Nilsson - 6 Hrs.)

Voltage and Current Sources, Ohm’s Law,

Kirchhoff’s Laws, Resistors in parallel and in series, Voltage and Current Division

3. Techniques of Circuit Analysis (Chapter 4 of Nilsson - 9 Hrs.)

Node Analysis, Node-Voltage Method and Dependent Sources, Mesh Analysis, Mesh-CurrentMethod and Dependent Sources, Source Transformations, Thevenin and Norton Equivalents,Maximum Power Transfer, Superposition Theorem

4. Operational Amplifier (Chapter 5 of Nilsson - 6 Hrs.)

Op-Amp Terminals & Ideal Op-Amp, Basic Op-Amp Circuits, Buffer circuit, Inverting andNon-inverting Amplifiers, Summing Inverter, Difference Amplifier, Cascade OpAmp Circuits

5. First Order Circuits (Chapters 6&7 of Nilsson - 9 Hrs.)

Inductors, Capacitors, Series and Parallel Combinations of them, Differentiator & IntegratorCircuits with Op-amp, the Natural Response of an RL & RC Circuits, The Step Response of RLand RC Circuits, A General Solution for Step and Natural Responses, Integrating AmplifierCircuit

6. Second Order Circuits (Chapter 8 of Nilsson - 9 Hrs.)

The Natural Response of a Parallel RLC Circuit, The Forms of Natural Response of a Parallel RLC Circuit, The Step Response of a Parallel RLC Circuit, Natural and Step Responses of a Series RLC Circuit

Review (3 Hrs)

1.12.2017EE201 - Circuit Theory I

EE201 - Circuit Theory I

Michael Faraday (1791–1867), an Englishchemist and physicist, was probably thegreatest experimentalist who ever lived.

He made several contributions in all areas ofphysical science and coined such words aselectrolysis, anode, and cathode. His discoveryof electromagnetic induction in 1831 was amajor breakthrough in engineering because itprovided a way of generating electricity. Theelectric motor and generator operate on thisprinciple. The unit of capacitance, the farad,was named in his honor.

Joseph Henry (1797–1878), an Americanphysicist, discovered inductance andconstructed an electric motor.

He conducted several experiments onelectromagnetism and developed powerfulelectromagnets that could lift objects weighingthousands of pounds. Interestingly, JosephHenry discovered electromagnetic inductionbefore Faraday but failed to publish hisfindings. The unit of inductance, the henry,was named after him.

EE201 - Circuit Theory I

So far we have limited our study to resistive circuits.

In this chapter, we shall introduce two new and important passive linear circuitelements: the capacitor and the inductor.

Unlike resistors, which dissipate energy, capacitors and inductors do not dissipatebut store energy

For this reason, capacitors and inductors are called storage elements.

The application of resistive circuits is quite limited. With the introduction ofcapacitors and inductors in this chapter, we will be able to analyze more importantand practical circuits.

The circuit analysis techniques covered in Chapter 3 are equally applicable tocircuits with capacitors and inductors.

EE201 - Circuit Theory I

An inductor is a passive element designed to store energy in its magnetic field.Inductors find numerous applications in electronic and power systems. They areused in power supplies, transformers, radios, TVs, radars, and electric motors.

Any conductor of electric current has inductive properties and may be regardedas an inductor. But in order to enhance the inductive effect, a practical inductor isusually formed into a cylindrical coil with many turns of conducting wire, as shownin Figure below.

Inductors (L)

EE201 - Circuit Theory I

An inductor is an electrical component that opposesany change in electrical current.

Inductance is the circuit parameter used to describean inductor and it relates the induced voltage to thecurrent.

Inductance is symbolized by the letter L, is measuredin henrys (H), and is represented graphically as a coiledwire—a reminder that inductance is a consequence of aconductor linking a magnetic field.

Inductors (L)

EE201 - Circuit Theory I

Assigning the reference direction of the current in thedirection of the voltage drop across the terminals of theinductor yields;

Inductors (L)

dt

diLv

where ,“v” is measured in volts,“L” in henrys,“i” in amperes,and “t” in seconds.

Note that the voltage across the terminals of an inductor is proportional tothe time rate of change of the current in the inductor.

EE201 - Circuit Theory I

Inductors (L)

dt

diLv

We can make two important observations here.

First, if the current is constant, the voltage across the ideal inductor is zero. Thus theinductor behaves as a short circuit in the presence of a constant, or dc, current.

When “i” is constant

Second, current cannot change instantaneously in an inductor; that is, the currentcannot change by a finite amount in zero time.

0v

EE201 - Circuit Theory I

Inductors (L)

dt

diLv

We can also express the current of an inductor with respect to the voltage drop on itby using the equation above.

t

dvL

ivdtL

diLdivdt )(11

or

t

t

tidvL

i0

)()(1

0

EE201 - Circuit Theory I

Inductors (L) – Power and Energy

Power:

t

t

tidvL

vpidt

diLivp

0

)()(1

. 0

Energy:

2

2

1.. LiwdiiLdwi

dt

diL

dt

dwp

EE201 - Circuit Theory I

Example:

EE201 - Circuit Theory I

Example:

EE201 - Circuit Theory I

Example:

For an inductor L=1H, thecurrent through it is given infigure. Find and draw thevoltage across it?

Answer:

EE201 - Circuit Theory I

A capacitor is a passive element designed to store energy in its electric field.Besides resistors, capacitors are the most common electrical components.

Capacitors are used extensively in electronics, communications, computers, andpower systems. For example, they are used in the tuning circuits of radio receiversand as dynamic memory elements in computer systems.

A capacitor is an electrical component that consists of two conductors separatedby an insulator or dielectric material.

The capacitor is the only device other than a battery that can store electricalcharge.

Capacitors (C)

EE201 - Circuit Theory I

The circuit parameter of capacitance is represented by the letterC is measured in farads (F), and is symbolized graphically by twoshort parallel conductive plates.

Because the farad is an extremely large quantity of capacitance,practical capacitor values usually lie in the picofarad (pF) tomicrofarad (F) range.

Capacitors (C)

When a voltage source v is connected to the capacitor, thesource deposits a positive charge (q) on one plate and a negativecharge (−q) on the other. The capacitor is said to store the electriccharge. The amount of charge stored, represented by q, is directlyproportional to the applied voltage v so that;

Cvq

EE201 - Circuit Theory I

Capacitance is the ratio of the charge on one plate of a capacitorto the voltage difference between the two plates, measured infarads (F).

Capacitors (C)

v

qC

EE201 - Circuit Theory I

The current is proportional to the rate at which the voltageacross the capacitor varies with time, or, mathematically,

Capacitors (C)

dt

dvCi

where ,“v” is measured in volts,“C” in farads,“i” in amperes,and “t” in seconds.

First, if the voltageis constant, the current through the ideal capacitor is zero. Thus thecapacitor behaves as a open circuit in the presence of a constant, or dc, voltage.

When “v” is constant

Second, voltage cannot change instantaneously in an capacitor; that is, the voltagecannot change by a finite amount in zero time.

0i

EE201 - Circuit Theory I

We can also express the voltage of an inductor with respect to the current through onit by using the equation above.

t

diC

vidtC

dvCdvidt )(11

or

t

t

tvdiC

v0

)()(1

0

Capacitors (C)

dt

dvCi

EE201 - Circuit Theory I

Capacitors (C) – Power and Energy

Power:

t

t

tvdiC

ipdt

dvCvivp

0

)()(1

. 0

Energy:

2

2

1.. CvwdvvCdw

dt

dvCv

dt

dwp

EE201 - Circuit Theory I

Example:

EE201 - Circuit Theory I

Example:

EE201 - Circuit Theory I

Example:

EE201 - Circuit Theory I

Example:

EE201 - Circuit Theory I

Series & Parallel Combinations of Inductors

Neq LLLL 21

Neq LLLL

1111

21

EE201 - Circuit Theory I

Series & Parallel Combinations of Capacitors

Neq CCCC 21

Neq CCCC

1111

21

EE201 - Circuit Theory I

EE201 - Circuit Theory I

Applications : Integrator and Differentiator

EE201 - Circuit Theory I

Example:

Answer:

EE201 - Circuit Theory I

END OF CHAPTER 5 – Part I