W. Sautter 2007

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AMPS

volts

Ammeters measurecurrent in amperes

and are alwayswired in series in

the circuit.

Voltmeters measurepotential in voltsand are always

wired in parallel in the circuit.

wiring

battery

voltmeter

ammeter

resistance

capacitor

+ -

A

V

junction

terminal

AC generator

Variableresistance

Variablecapacitor

ELECTRON PUMP

(SOURCE VOLTAGE)[ENERGY IN]

LOAD(RESISTANCE)[ENERGY OUT]

CONDUCTOR

ELECTRONSOUT OF SOURCE

ELECTRONSOUT OF LOAD

ELECTRONSBACK TOSOURCE

ELECTRONSINTOLOAD

HIGHER ENERGY ELECTRONS LOWER ENERGY ELECTRONS

CONDUCTOR

PotentialIn volts

(joules / coul)

CurrentIn amperes

(coul / second)

ResistanceIn ohms

(volts / amp)

Drop across a resistance

Current passingThrough the

resistor

volts

Battery current

Electrons haveLess Energy

Electrons haveMore Energy Electrons get

An energy boost

current

volts

Resistor current

Electrons haveMore Energy

Electrons haveLess Energy Energy is lost

In the resistor

There are three generally types of electrical circuits:

(1) Series circuits in which the current created by the voltagesource passes through each circuit component in succession.

R2 A2

R 1

R 3

A1

Arrows showCurrent pathThrough each

component

(2) Parallel circuits in which the current created by the voltagesource branches with some passing through one component andwhile the rest of the current passes through other components.

Arrows showCurrent pathThrough each

component

Junction or Branching points

A1R1

R2

R3

A2

A3

A4

R 4

(3) Series Parallel circuits or combination circuits

which contain series segments and parallel

segments.

R1

R2

R3

A1

A2

A3

A4

R 4

SERIES

PARALLEL

Arrows showCurrent pathThrough each

component

All electrical circuit analysis requires the useof two fundamental laws called

Kirchhoff’s Laws

FIRST LAWAll current entering a junction point must equal all current leaving that junction point

Junctionpoint

Current Entering ( I1 )

Current Leaving ( I2 )

Current Leaving ( I3 )

I1 = I2 + I3

SECOND LAWAround any complete loop, the sum of the

voltage rises must equal the sum of voltage drops

Battery(voltage rise)

Resistance 1(voltage drop 1)

Resistance 2(voltage drop 2)

Resistance 3(voltage drop 3)

Current flow

Complete loop

V(Battery) = V1 + V2 + V3

+ -

R2

R1

A2

A1

At

V1

EMF

Kirchhoff’s Laws Around a loop

V rises = V dropsA loop is a completedPath for current flow

Battery

V2

Loop #1

Loop #2

Loop #3

+ -

Complete currentPaths in a circuit

When using Kirchhoff’s laws we apply the principlesof conventional current flow.

When current leaves the positive (+) terminal of a voltage source and enters the negative (-) terminal

a voltage rise occurs across the source. If the current enters the positive and exits the negative a of a voltage

source a voltage drop occurs across the source.

When tracing a current loop, if the assumed directionof the current and the loop direction are the same,

a voltage drop occurs across a resistance.If the assumed direction of the current and the

loop direction are opposite, a voltage rise occursacross the the resistance.

Battery( 6 volts)

+ -

CurrentflowV = + 6 v

Currentflow

V = - 6 v

When using Kirchhoff’s laws we apply the principlesof conventional current flow.

When current leaves the positive (+) terminal of a voltage source and enters the negative (-) terminal

a voltage rise occurs across the source.

If the current enters the positive and exits the negative a of a voltage source a voltage drop occurs across

the source.

When tracing a current loop, if the assumed directionof the current and the loop direction are the same,

a voltage drop occurs across a resistance.

resistor

V = + 6 vA voltage

rise

AssumedCurrent flow

V = - 6 vA voltage

drop

Loopdirection

AssumedCurrent flow

Loopdirection

If the assumed direction of the current and theloop direction are opposite, a voltage rise occurs

across the the resistance.

Series ResistanceRt = R1 + R2 + ….

EMF = V1 + V2 + V3 + Vi

In a series circuit:(1) The total resistance of the circuit is the sum of

the resistance values in the circuit.

(2) The sum of all voltage drops across the resistorsin the circuit equals the voltage rise of the source.

The through each resistance is the same.

I TOTAL = I1 = I2 = I3 = Ii

R2 A2

V2

R 1EMF

Ri

R 3

V1

V3

A1

R = ResistanceIn ohms

VoltmetersIn parallel

AmmetersIn series

Series ResistanceRt = R1 + R2 + ….

Ammeters readThe same everywhere

In the circuitA1 = A2

EMF = V1 + V2 + V3 + Vi

In a parallel circuit:(1) The reciprocal of the total resistance of the circuit is the sum

of the reciprocals of the resistance values in the circuit.

Parallel Resistance1/Rt = 1/R1 + 1/R2 ….

(2) The sum of the voltage drops across the resistors in a branch of the circuit equals the voltage rise of the source.

V source= V1 = V2 = V3 = Vi

(3) All current entering a junction = all currentleaving the junction

I TOTAL = I1 + I2 + I3 + Ii

R1

R2

R3

A1

A2

A3

A4

V2

V3

EMF

V1

Parallel Resistance1/Rt = 1/R1 + 1/R2 ….

Kirchhoff’s Laws(1) All current enteringA junction = all current

Leaving the junction(2) Around a loop

V rises = V drops

Junctionpoints

VoltmetersIn parallel

AmmetersIn series

BatteryR = Resistance

In ohms

R1

R2

R3

A1

A2

A3

A4

V1

R 4V4

V2

V3

EMF

Ri

PARALLEL

SERIES

Parallel Resistance1/Rt = 1/R1 + 1/R2 ….

Series ResistanceRt = R1 + R2 + ….

Kirchhoff’s Laws(1) All current enteringA junction = all current

Leaving the junction(2) Around a loop

V rises = V drops

resistors

capacitors

Integratedcircuits