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Series and ParallelSeries and ParallelCircuitsCircuits

Kirchoffs Voltage andKirchoffs Voltage andCurrent LawsCurrent Laws

Circuits 1Circuits 1Fall 2005Fall 2005

Harding UniversityHarding University

Jonathan WhiteJonathan White

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OutlineOutline

Node definitionNode definition

KCLKCL The current entering a node is equal to the current leaving a node.The current entering a node is equal to the current leaving a node.

KVLKVL The sum of voltages around a closed loop is 0.The sum of voltages around a closed loop is 0.

Series circuitsSeries circuits Resistors in series addResistors in series add

RReqeqis always greater than R1 and R2is always greater than R1 and R2

Voltage DividersVoltage Dividers Parallel circuitsParallel circuits

Resistors in parallel follow the equation RResistors in parallel follow the equation Reqeq= (R= (R11*R*R22)/(R)/(R1+1+RR2).2). RReqeqis always less thanis always less thanRR11 and Rand R22

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NodesNodes

A node is where 2 or more elements meet.A node is where 2 or more elements meet.

For now, and element can be a resistor, a voltageFor now, and element can be a resistor, a voltagesource, or a current source.source, or a current source.

Each point in the node must be electrically theEach point in the node must be electrically the

same.same.

Exp:Exp:

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Kirchoffs Current LawKirchoffs Current Law

A fundamental law of nature, like the Law ofA fundamental law of nature, like the Law ofConservation of Mass.Conservation of Mass. KCL is the conservation of chargeKCL is the conservation of charge charge cancharge can

neither be created or destroyed.neither be created or destroyed.

KCL definition: The sum of all currentsKCL definition: The sum of all currentsentering a node is equal to the sum of allentering a node is equal to the sum of all

currents leaving the node.currents leaving the node. KCL holds for every node in a network and itKCL holds for every node in a network and it

works at every point in time.works at every point in time.

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KCLKCL

Write equations for the current in each of theWrite equations for the current in each of the

nodes in the circuit below:nodes in the circuit below:

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Kirchoffs Voltage LawKirchoffs Voltage Law

A fundamental law of nature, like the Law ofA fundamental law of nature, like the Law of

Conservation of Energy.Conservation of Energy.

KVL is the conservation of electrical energyKVL is the conservation of electrical energy electrical energy can neither be created or destroyed,electrical energy can neither be created or destroyed,only transferred.only transferred.

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KVLKVL 221.1. As the charge moves from the top of the battery toAs the charge moves from the top of the battery to

the top of Element #1 (along the wire shown inthe top of Element #1 (along the wire shown inpurple), how much energy does the charge lose?purple), how much energy does the charge lose?

2.2. As the charge moves from the top of Element #1As the charge moves from the top of Element #1through Element #1 to the bottom of element #1,through Element #1 to the bottom of element #1,how much energy does the charge lose?how much energy does the charge lose?

3.3. As the charge moves from the bottom of ElementAs the charge moves from the bottom of Element#1 to the top of Element #2, how much energy#1 to the top of Element #2, how much energydoes the charge lose?does the charge lose?

4.4. As the charge moves from the top of Element #2As the charge moves from the top of Element #2through Element #2 to the bottom of element #2,through Element #2 to the bottom of element #2,how much energy does the charge lose?how much energy does the charge lose?

5.5. As the charge moves from the bottom of ElementAs the charge moves from the bottom of Element#2 to the bottom of the battery, how much energy#2 to the bottom of the battery, how much energydoes the charge lose?does the charge lose?

6.6. As the charge moves from the bottom of theAs the charge moves from the bottom of thebattery through the battery to the top of thebattery through the battery to the top of the

battery, how much energy does the charge lose?battery, how much energy does the charge lose?

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KVLKVL -- 33

What is VWhat is Vbb equal to?equal to?

KVL definition: the sum ofKVL definition: the sum of

voltages around a closed loop isvoltages around a closed loop is

0.0.

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KVLKVL -- 44

Write all the KVL equations for the circuitWrite all the KVL equations for the circuit

below:below:

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Series ResistanceSeries Resistance

2 devices are said to be in series when the same current2 devices are said to be in series when the same current

physically flows through both.physically flows through both.

Current flows into one element, through the element, out ofCurrent flows into one element, through the element, out of

the element into the other element, through the secondthe element into the other element, through the secondelement and out of the second element.element and out of the second element. No part of theNo part of the

current that flows through one resistor "escapes" and none iscurrent that flows through one resistor "escapes" and none is

added.added.

You see series resistance everydayYou see series resistance everyday

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Series ResistanceSeries Resistance -- 22

Consider the simplest series resistance:Consider the simplest series resistance:

What is VsWhat is Vs ??

The equivalent resistance for resistors in series isThe equivalent resistance for resistors in series isalways the sum of the individual resistors.always the sum of the individual resistors.

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Voltage DividersVoltage Dividers

Used as volume controls in electronic devicesUsed as volume controls in electronic devices

Provides a continuous sound spectrum, i.e., not digital.Provides a continuous sound spectrum, i.e., not digital.

Used in RC combinations to filter out input noise in devicesUsed in RC combinations to filter out input noise in devices

such as tachometers and such as tachometers and A voltage divider looks like this:A voltage divider looks like this:

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Voltage DividersVoltage Dividers -- 22

How much current flows through RHow much current flows through Raaand Rand Rbb ? Use Ohms Law.? Use Ohms Law.

What is VWhat is Voutout ??

As RAs Rbb goes to 0, whats the value ofgoes to 0, whats the value ofVVoutout ? R? Rbb is then physically like what?is then physically like what?

As RAs Rbb goes to , whats the value ofgoes to , whats the value of

VVoutout ? R? Rbb is then physically like what?is then physically like what?

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Parallel ResistorsParallel Resistors

2 resistors are in parallel if the same physical2 resistors are in parallel if the same physical

voltage appears across each resistor.voltage appears across each resistor.

Each resistor provides its own path for the flow ofEach resistor provides its own path for the flow ofcurrent. If the resistors have different resistancecurrent. If the resistors have different resistancevalues, they will carry different amounts of current,values, they will carry different amounts of current,each in accordance with Ohm's Law.each in accordance with Ohm's Law.

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Parallel ResistorsParallel Resistors -- 22

Consider the simplestConsider the simplest

parallel resistance to theparallel resistance to the

right. What is Iright. What is Ipp??

In parallel resistors, theIn parallel resistors, the

equivalent resistance isequivalent resistance is

always lower than either ofalways lower than either of

the resistors.the resistors.