Series and Parallel Series and Parallel CircuitsCircuits

Kirchoff’s Voltage Kirchoff’s Voltage and Current Lawsand Current Laws

Circuits 1Circuits 1Fall 2005Fall 2005

Harding UniversityHarding University

Jonathan WhiteJonathan White

OutlineOutline Node definitionNode definition KCLKCL

The current entering a node is equal to the current leaving a The current entering a node is equal to the current leaving a node.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 RReqeq is always greater than R1 and R2 is 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).

RReq eq is always less thanis always less than RR1 1 and Rand R22

NodesNodes

A node is where 2 or more elements A node is where 2 or more elements meet.meet. For now, and element can be a resistor, For now, and element can be a resistor,

a voltage source, or a current source.a voltage source, or a current source. Each point in the node must be Each point in the node must be

electrically the same.electrically the same. Exp:Exp:

Kirchoff’s Current LawKirchoff’s Current Law A fundamental law of nature, like the A fundamental law of nature, like the

Law of Conservation of Mass.Law of Conservation of Mass. KCL is the conservation of charge – charge KCL is the conservation of charge – charge

can neither be created or destroyed.can neither be created or destroyed. KCL definition: The sum of all currents KCL definition: The sum of all currents

entering a node is equal to the sum of all entering 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 KCL holds for every node in a network and it works at every point in time.and it works at every point in time.

KCLKCL

Write equations for the current in each Write equations for the current in each of the nodes in the circuit below:of the nodes in the circuit below:

Kirchoff’s Voltage LawKirchoff’s Voltage Law

A fundamental law of nature, like the A fundamental law of nature, like the Law of Conservation of Energy.Law of Conservation of Energy. KVL is the conservation of electrical KVL is the conservation of electrical

energy – electrical energy can neither energy – electrical energy can neither be created or destroyed, only be created or destroyed, only transferred.transferred.

KVL – 2KVL – 21.1. As the charge moves from the top of the As the charge moves from the top of the

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

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

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

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

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

6.6. As the charge moves from the bottom of the As the charge moves from the bottom of the battery through the battery to the top of the battery through the battery to the top of the battery, how much energy does the charge battery, how much energy does the charge lose? lose?

KVL - 3KVL - 3

What is VWhat is Vbb equal to? equal to?

KVL definition: the sum KVL definition: the sum of voltages around a of voltages around a closed loop is 0.closed loop is 0.

KVL - 4KVL - 4

Write all the KVL equations for the Write all the KVL equations for the circuit below:circuit below:

Series ResistanceSeries Resistance 2 devices are said to be in series when the same 2 devices are said to be in series when the same

current physically flows through both.current physically flows through both. Current flows into one element, through the Current flows into one element, through the

element, out of the element into the other element, out of the element into the other element, through the second element and out element, through the second element and out of the second element.  No part of the current of the second element.  No part of the current that flows through one resistor "escapes" and that flows through one resistor "escapes" and none is added.  none is added. 

You see series resistance everydayYou see series resistance everyday

Series Resistance - 2Series Resistance - 2

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

What is VsWhat is Vs ?? The equivalent resistance for resistors The equivalent resistance for resistors

in series is always the sum of the in series is always the sum of the individual resistors.individual resistors.

Voltage DividersVoltage Dividers Used as volume controls in electronic devicesUsed as volume controls in electronic devices

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

Used in RC combinations to filter out input noise Used in RC combinations to filter out input noise in devices such as tachometers and …in devices such as tachometers and …

A voltage divider looks like this:A voltage divider looks like this:

Voltage Dividers - 2Voltage Dividers - 2

How much current flows How much current flows through Rthrough Ra a and Rand Rb b ? Use ? Use Ohm’s Law.Ohm’s Law.

What is VWhat is Voutout ? ?

As RAs Rbb goes to 0, what’s the goes to 0, what’s the value of Vvalue of Voutout ? R ? Rbb is then is then physically like what?physically like what?

As RAs Rbb goes to ∞, what’s the goes to ∞, what’s the value of Vvalue of Voutout ? R ? Rbb is then is then physically like what?physically like what?

Parallel ResistorsParallel Resistors

2 resistors are in parallel if the same 2 resistors are in parallel if the same physical voltage appears across each physical voltage appears across each resistor.resistor. Each resistor provides its own path for Each resistor provides its own path for

the flow of current. If the resistors the flow of current. If the resistors have different resistance values, they have different resistance values, they will carry different amounts of current, will carry different amounts of current, each in accordance with Ohm's Law. each in accordance with Ohm's Law.

Parallel Resistors - 2Parallel Resistors - 2

Consider the simplest Consider the simplest parallel resistance to parallel resistance to the right. What is Ithe right. What is Ipp??

In parallel resistors, In parallel resistors, the equivalent the equivalent resistance is always resistance is always lower than either of lower than either of the resistors.the resistors.