01 Intro

E1.1 Analysis of Circuits (2011) Introduction: 1 1 / 16

E1.1 Analysis of Circuits

Mike Brookes

1: Introduction

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect

Resistor Power Dissipation

Voltage and CurrentSources

Power Conservation

Units and Multipliers

Summary


Organization

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


18 lectures: feel free to ask questions Buy the textbook: Irwin & Nelms Engineering Circuit Analysis

ISBN:9780470873779 33

Previous textbook is also fine but now out of print:DeCarlo & Lin Linear Circuit Analysis ISBN: 0195136667

Weekly study group: Problem sheets - KEEP UP TO DATE Fortnightly tutorial: tutorial problems Online Wiki at http://learn.imperial.ac.uk Lecture slides (including animations) and problem sheets + answers

available from my website:http://www.ee.ic.ac.uk/hp/staff/dmb/courses/ccts1/ccts1.htm

Christmas Test Exam

What are circuits?

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


A circuit consists of electrical or electronic components interconnectedwith metal wires

Every electrical or electronic device is a circuit

What are circuits?

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




Breadboard Printed Integrated

What are circuits?

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





The function of the circuit is determined by which components are usedand how they are interconnected

What are circuits?

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





The function of the circuit is determined by which components are usedand how they are interconnected: the physical positioning of thecomponents usually has hardly any effect.

Circuit Diagrams

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


A circuit diagram shows the way in which the components are connected

Circuit Diagrams

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



Each component has a specialsymbol

Circuit Diagrams

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



Each component has a specialsymbol The interconnecting wires areshown as lines

Circuit Diagrams

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




A node in a circuit is all the points that are connected together via theinterconnecting wires. One of the four nodes in the diagram is coloured red.

Circuit Diagrams

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




A node in a circuit is all the points that are connected together via theinterconnecting wires. One of the four nodes in the diagram is coloured red.Assumption: Interconnecting wires have zero resistance so everywherealong a node has the same voltage.

Circuit Diagrams

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





Junction Crossover Bad Better

Indicate three meeting wireswith a and crossoverswithout one.

Circuit Diagrams

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





Junction Crossover Bad Better

Indicate three meeting wireswith a and crossoverswithout one.

Avoid having four meeting wires in case the disappears; stagger the wiresinstead.

Charge

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Charge is an electrical property possessed by some atomic particles

Charge

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Charge is an electrical property possessed by some atomic particlesCharge is measured in Colombs (abbreviated C)An electron has a charge 1.6 1019C, a proton +1.6 1019C

Charge

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Charge is an electrical property possessed by some atomic particlesCharge is measured in Colombs (abbreviated C)An electron has a charge 1.6 1019C, a proton +1.6 1019CUnlike charges attract, like charges repel

Charge

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Charge is an electrical property possessed by some atomic particlesCharge is measured in Colombs (abbreviated C)An electron has a charge 1.6 1019C, a proton +1.6 1019CUnlike charges attract, like charges repel: the force is fantastically huge

Charge

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



Two people 384,000 km apartEach with 1% extra electrons

Charge

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




Force = 2 108N= 360, 000 their weight

Charge

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




Force = 2 108N= 360, 000 their weight

Consequence: Charge never accumulates in a conductor: everywhere in aconducting path stays electrically neutral at all times.

Current

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Current is the flow of charged particles past a measurement boundary

Current

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Current is the flow of charged particles past a measurement boundaryUsing an ammeter, we measure current in Ampres (usually abbreviated toAmps or A): 1 A = 1 C/sAnalogy: the flow of water in a pipe or river is measured in litres per second

Current

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



The arrow in a circuit diagramindicates the direction we chooseto measure the current.I = +1 A 1 C of +ve chargepasses each point every second inthe direction of the arrow (or else1 C of ve charge in the oppositedirection)

Current

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




I = 1 A 1 C of +ve charge in the direction opposite to the arrow

Current

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





In metals the charge carriers are actually ve: in this course you shouldignore this always.

Current

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





In metals the charge carriers are actually ve: in this course you shouldignore this always.Average electron velocity is surprisingly slow (e.g. 1 mm/s) but (like a waterpipe) the signal travels much faster.

Potential Energy

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


When a ball falls from ashelf, it loses potentialenergy of mgh or,equivalently, gh per kg. h

Potential Energy

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



The potential energy per kg of any point on a mountain range is equal to ghwhere h is measured relative to an equipotential reference surface (e.g. thesurface of a lake).

Potential Energy

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




The potential energy difference between any two points is the energyneeded to move 1 kg from one point to the other.

Potential Energy

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




The potential energy difference between any two points is the energyneeded to move 1 kg from one point to the other.The potential energy difference does not depend on the route takenbetween the points.

Potential Energy

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




The potential energy difference between any two points is the energyneeded to move 1 kg from one point to the other.The potential energy difference does not depend on the route takenbetween the points.The potential enegy difference does not depend on your choice ofreference surface (e.g. lake surface or sea level).

Voltage

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


The electrical potential difference (or voltage difference) between any twonodes in a circuit is the energy per coulomb needed to move a small +vecharge from one node to the the other.We usually pick one of the nodes as a reference and define the voltage at anode to be the voltage difference between that node and the reference.

Voltage

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



The four nodes are labelledA, B, C, G.

We have chosen G as thereference node; indicated by theground symbol.

Voltage

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





The potential difference between A and the ground reference, G, is writtenVA and is also called the voltage at A.

Voltage

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





The potential difference between A and the ground reference, G, is writtenVA and is also called the voltage at A.The potential difference between A and B is written as VAB and shown asan arrow pointing towards A. This is the energy per coulomb in going fromB to A and satisfies VAB = VA VB . (Different from vectors)

Voltage

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





The potential difference between A and the ground reference, G, is writtenVA and is also called the voltage at A.The potential difference between A and B is written as VAB and shown asan arrow pointing towards A. This is the energy per coulomb in going fromB to A and satisfies VAB = VA VB . (Different from vectors)

Easy algebra shows that VAB = VBA and that VAC = VAB + VBC .

Resistors

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


A resistor is made from athin strip of metal filmdeposited onto aninsulating ceramic base.

Resistors

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



The characteristic of acomponent is a graphshowing how the voltageand current are related. Wealways choose the currentand voltage arrows inopposite directions: this isthe passive signconvention.

Resistors

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



The characteristic of acomponent is a graphshowing how the voltageand current are related. Wealways choose the currentand voltage arrows inopposite directions: this isthe passive signconvention.For a resistor, I V and V/I = R, its resistance which is measured inOhms (). This is Ohms Law.

Resistors

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



The characteristic of acomponent is a graphshowing how the voltageand current are related. Wealways choose the currentand voltage arrows inopposite directions: this isthe passive signconvention.For a resistor, I V and V/I = R, its resistance which is measured inOhms (). This is Ohms Law. Sometimes it is more convenient to work interms of the conductance, G = 1/R = I/V measured in Siemens (S).

Resistors

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




The graph shows the characteristic of a 12.5 resistor. The gradient of thegraph equals the conductance G = 80 mS.

Resistors

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




The graph shows the characteristic of a 12.5 resistor. The gradient of thegraph equals the conductance G = 80 mS. Alternative zigzag symbol.

Cause and Effect

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Ohms law relates thevoltage drop across aresistor to the currentflowing in it.

Cause and Effect

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



If the voltage, V , is fixed elsewhere in the circuit, it is convenient to thinkthat V causes the current I to flow.

Cause and Effect

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




If the current, I , is fixed elsewhere in the circuit, it is more convenient tothink that V is caused by the current I flowing through the resistor.

Cause and Effect

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




If the current, I , is fixed elsewhere in the circuit, it is more convenient tothink that V is caused by the current I flowing through the resistor.

Neither statement is more true than the other. It is perhaps truer to saythat I and V are constrained to satisfy V = I R.


1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Gravitational potential energy, mgh, lost by a falling object is transformedinto kinetic energy or heat.


1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



Current in a resistoralways flows from ahigh voltage (morepositive) to a lowvoltage (morenegative).

When current flows through a resistor, the electrical potential energy that islost is transformed into heat.


1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





The power dissipated as heat in a resistor is equal to V I Watts (W). 1 Wattequals one Joule of energy per second. Since V and I always have thesame sign (see graph) the power dissipation is always positive.


1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary





The power dissipated as heat in a resistor is equal to V I Watts (W). 1 Wattequals one Joule of energy per second. Since V and I always have thesame sign (see graph) the power dissipation is always positive.

P = V I gives the power absorbed by any component.For a resistor only: V/I = R which gives the equivalent expressionsP = V I = V

2

/R = I2R.

Voltage and Current Sources

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Energy in an electrical circuit is supplied by voltage and current sources

An ideal voltage sourcemaintains the same valueof V for all currents. Itscharacteristic is a verticalline with infinite gradient.There are two commonsymbols.

V

I

11 2

0.1

0.2

0.1

0.2

I

V 1.5V


1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




V

I

11 2

0.1

0.2

0.1

0.2

I

V 1.5V

An ideal current sourcemaintains the same valueof I for all voltages. Itscharacteristic is a horizontalline with zero gradient.Notice that I is negative.

V

I

11 2

0.1

0.2

0.1

0.2

I

V180mA


1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




V

I

11 2

0.1

0.2

0.1

0.2

I

V 1.5V

An ideal current sourcemaintains the same valueof I for all voltages. Itscharacteristic is a horizontalline with zero gradient.Notice that I is negative.

V

I

11 2

0.1

0.2

0.1

0.2

I

V180mA

If the source is supplying electrical energy to a circuit, then V I < 0.However, when a recharcheable battery is charging, V I > 0.

Power Conservation

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


In any circuit some circuit elements will be supplying energy and othersabsorbing it. At all times, the power absorbed by all the elements will sumto zero.

Power Conservation

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary



The circuit has two nodeswhose potential difference is10 V.

Ohms Law:I = V

R= 0.01 A

Power Conservation

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




Ohms Law:I = V

R= 0.01 A

Power absorbed by resistor:PR = V1 I1 = (+10) (+0.01) = +0.1W

Power Conservation

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




Ohms Law:I = V

R= 0.01 A


For Ohms law or power dissipation, V and I can be measured eitherway round but must be in opposite directions (passive sign convention).

Power Conservation

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




Ohms Law:I = V

R= 0.01 A



PR = V2 I2 = (10) (0.01) = +0.1W

Power Conservation

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




Ohms Law:I = V

R= 0.01 A



PR = V2 I2 = (10) (0.01) = +0.1W

Power absorbed by voltage source:PS = VS IS = (+10) (0.01) = 0.1W

Power Conservation

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary




Ohms Law:I = V

R= 0.01 A



PR = V2 I2 = (10) (0.01) = +0.1W

Power absorbed by voltage source:PS = VS IS = (+10) (0.01) = 0.1W

Total power absorbed by circuit elements: PS + PR = 0


1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Quantity Letter Unit Symbol

Charge Q Coulomb CConductance G Siemens S

Current I Amp AEnergy W Joule J

Potential V Volt VPower P Watt W

Resistance R Ohm

Value Prefix Symbol

103 milli m106 micro 109 nano n1012 pico p1015 femto f

Value Prefix Symbol

103 kilo k106 mega M109 giga G1012 tera T1015 peta P

Summary

1: Introduction

Organization

What are circuits?

Circuit Diagrams

Charge

Current

Potential Energy

Voltage

Resistors

Cause and Effect



Power Conservation


Summary


Circuits and Nodes Charge, Current and Voltage Resistors, Voltage Source and Current Sources Power Dissipation and Power Conservation

For further details see Irwin & Nelms Chapter 1.

1: IntroductionOrganizationWhat are circuits?Circuit DiagramsChargeCurrentPotential EnergyVoltageResistorsCause and EffectResistor Power DissipationVoltage and Current SourcesPower ConservationUnits and MultipliersSummary

01 Intro

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