Alternating Current Alternating Current ElectricityElectricity

NCEA A.S 3.6NCEA A.S 3.6

Text Chapters 18-19Text Chapters 18-19

Why AC?Why AC?

It can be produced directly from It can be produced directly from generatorsgenerators

It can be controlled by a wide range of It can be controlled by a wide range of components eg resistors,capacitors and components eg resistors,capacitors and inductors.inductors.

The max voltage can be changed easily The max voltage can be changed easily using a transformerusing a transformer

The frequency of the AC can be used for The frequency of the AC can be used for timingtiming

AC CurrentAC Current

AC VoltageAC Voltage

AC AC PowerPowerP=VxIP=VxI

Multiplying Multiplying the graphs the graphs gives us a gives us a graph graph where the where the power is power is always always positivepositive

AC PowerAC Power

The average voltage in ac is zero since The average voltage in ac is zero since there is an equal amount of positive and there is an equal amount of positive and negative voltage.negative voltage.

Same for currentSame for current

The average value of the power used in ac The average value of the power used in ac is is halfhalf that of the peak power that of the peak power

RMS ValuesRMS Values

Since voltage and current are always Since voltage and current are always changing we need some way of averaging changing we need some way of averaging out their effect.out their effect.

We use r.m.s values (root-mean-square)We use r.m.s values (root-mean-square)

The r.m.s values are the DC values which The r.m.s values are the DC values which give the same average power outputgive the same average power output

RMS ValuesRMS ValuesAC Voltage DC Voltage

(with same power output)

Vrms

Vmax

RMS ValuesRMS Values

2maxV

Vrms

2maxI

I rms (See text pg 295-296 for derivations of these formulae)

AC in CapacitorsAC in Capacitors

In a DC circuit, the current flows until the cap is In a DC circuit, the current flows until the cap is fully charged and then stops.fully charged and then stops.In an AC circuit, the current can continue to flow, In an AC circuit, the current can continue to flow, as the plates become alternately charged as the plates become alternately charged positively and negatively positively and negatively

~~

ReactanceReactance

For both AC and DC circuits, the voltage For both AC and DC circuits, the voltage across the resistor is related to the current across the resistor is related to the current by V=IRby V=IRA similar relationship exists for a capacitor:A similar relationship exists for a capacitor:

Where XWhere Xcc is the is the reactancereactance of the capacitor of the capacitor

~~

cc IXV

ReactanceReactance

Reactance is a measure of how a Reactance is a measure of how a capacitor can limit alternating currentcapacitor can limit alternating current

Unit: OhmsUnit: Ohms

It is It is similarsimilar to resistance but differs in that to resistance but differs in that it is dependent on the it is dependent on the frequencyfrequency of the ac of the ac supply.supply.

It also depends on the size of the It also depends on the size of the capacitor.capacitor.

ReactanceReactance

Explanations:Explanations:

Higher f means cap never gets full before Higher f means cap never gets full before current direction changes, so never limits current direction changes, so never limits current, so low Xcurrent, so low X

Higher C means that it takes more charge to fill Higher C means that it takes more charge to fill it, so never fills before current direction changes, it, so never fills before current direction changes, so never limits current, so low Xso never limits current, so low X

fCX c 2

1

Phase RelationshipPhase RelationshipIn a DC circuit the voltage across In a DC circuit the voltage across components connected in series will add components connected in series will add up to the supply voltageup to the supply voltage

In AC circuits this does not happenIn AC circuits this does not happen

Eg. Eg.

~~

VS

VCVR

RCS

R

C

S

VVV

VV

VV

VV

8

6

12

Phase RelationshipPhase Relationship

Reasons:Reasons: The meters used to measure the voltage will The meters used to measure the voltage will

give rms values, not actual voltages at a give rms values, not actual voltages at a point in timepoint in time

The voltages across the resistor and capacitor The voltages across the resistor and capacitor are out of phase with each other ie they do are out of phase with each other ie they do not both reach maxs and mins at the same not both reach maxs and mins at the same time.time.

Phase RelationshipPhase RelationshipThe current in the circuit will always be in The current in the circuit will always be in phase with Vphase with VR R (Reason: because R is constant (Reason: because R is constant

so bigger V gives bigger I)so bigger V gives bigger I)

This can be shown on a phasor diagram:This can be shown on a phasor diagram:

VR

VR

It

Iω VR

Phase RelationshipPhase Relationship

VVCC will lag 90 will lag 90° behind I (and therefore V° behind I (and therefore VRR) )

because the max current flows when the because the max current flows when the voltage across it’s plates is zero, ie voltage across it’s plates is zero, ie uncharged, and zero current flows when uncharged, and zero current flows when voltage is max ie cap is fully chargedvoltage is max ie cap is fully charged

The phasor diagram will look like:The phasor diagram will look like:

Phase RelationshipPhase Relationship

The voltage phasors are not necessarily the The voltage phasors are not necessarily the same size, but are always 90same size, but are always 90°out of phase°out of phase

VR

It

Iω

VC

VR

VC

RC CircuitsRC CircuitsThe total voltage in the circuit can be The total voltage in the circuit can be found by adding the Vfound by adding the VRR and V and VCC phasors phasors

together together

VR

tω

VCVR

VC

Vs

VS

222CRS VVV

ImpedanceImpedance

The current is the same everywhere in the circuit The current is the same everywhere in the circuit so Vso VRR and V and VCC are proportional to R and X are proportional to R and XCC

This combination of resistance and reactance This combination of resistance and reactance which both act to limit the current is called which both act to limit the current is called impedance Zimpedance Z

VR=IR

VC=IXCVS=IZ

R

XCZ

22CXRZ

AC in InductorsAC in InductorsIn a DC circuit an inductor produces an In a DC circuit an inductor produces an opposing voltage whenever the current opposing voltage whenever the current changes.changes.In an AC circuit, the current is always In an AC circuit, the current is always changing so the inductor is always changing so the inductor is always producing an opposing voltage so is producing an opposing voltage so is always limiting the amount of current that always limiting the amount of current that can flowcan flow ~~

ReactanceReactance

For both AC and DC circuits, the voltage For both AC and DC circuits, the voltage across the resistor is related to the current across the resistor is related to the current by V=IRby V=IRA similar relationship exists for an inductor:A similar relationship exists for an inductor:

Where XWhere XLL is the is the reactancereactance of the inductor of the inductor

LL IXV ~~

ReactanceReactance

It measures how well an inductor can limit It measures how well an inductor can limit alternating currentalternating current

It depends on the It depends on the frequencyfrequency of the ac of the ac supply.supply.

It depends on the size of the inductor.It depends on the size of the inductor.

ReactanceReactance

Explanations:Explanations:

Higher f means faster rate of change of current, Higher f means faster rate of change of current, so more back e.m.f, so less current, so higher Xso more back e.m.f, so less current, so higher XLL

Higher L means more back e.m.f, so less Higher L means more back e.m.f, so less current, so higher Xcurrent, so higher XLL

fLX L 2

Phase RelationshipPhase Relationship

VVLL will lead will lead I (and therefore VI (and therefore VRR) by ) by 9090° °

because the greatest back e.m.f occurs because the greatest back e.m.f occurs when the current is changing most rapidly, when the current is changing most rapidly, which is when it is passing through zero. which is when it is passing through zero. When the current has reached it’s max, it When the current has reached it’s max, it is not changing as rapidly so there is no is not changing as rapidly so there is no back e.m.f back e.m.f

The phasor diagram will look like:The phasor diagram will look like:

Phase RelationshipPhase Relationship

Again the voltages may be different sizes Again the voltages may be different sizes but will always be 90but will always be 90° out of phase° out of phase

VR

It

Iω

VL

VR

VL

LR CircuitsLR CircuitsThe total voltage in the circuit can be The total voltage in the circuit can be found by adding the Vfound by adding the VRR and V and VLL phasors phasors

together together

VR

tω

VLVR

VL VsVS

222LRS VVV

ImpedanceImpedance

The The impedance Z impedance Z is found by adding R and Xis found by adding R and XLL

VR=IR

VL=IXLVS=IZ

R

XLZ

22LXRZ

LCR CircuitsLCR Circuits

This can be an extremely useful circuit set-This can be an extremely useful circuit set-up, as the current and voltages can up, as the current and voltages can change considerably as the frequency is change considerably as the frequency is changedchanged

~~

LCR CircuitsLCR Circuits

The combined phasor diagram now looks like:The combined phasor diagram now looks like:

t

VR

ω

VL

VR

VLVs

VS

VC

VC

Supply VoltageSupply VoltageThe supply The supply voltage is now voltage is now found by adding found by adding all 3 phasors all 3 phasors togethertogether

(V(VLL and V and VCC are are

combined into one combined into one first)first)

VR=IR

VL=IXL

VS=IZ

VC=IXC

VL-VC

222 )( CLRS VVVV

ImpedanceImpedanceThe impedance of an LCR circuit is a The impedance of an LCR circuit is a combination of both the resistance and the combination of both the resistance and the reactance.reactance.It is found by adding phasors:It is found by adding phasors:

R

XL

Z

XC

XL-XC

22 )( CL XXRZ

ResonanceResonance

At low f, VAt low f, VCC>V>VLL

so Vso VR R (and (and

therefore I) is therefore I) is small.small.

ie. Capacitors ie. Capacitors limit the current limit the current better at low better at low frequenciesfrequencies

VR

VL

VS

VC

ResonanceResonance

At high f, VAt high f, VLL>V>VCC

so Vso VR R (and (and

therefore I) is therefore I) is small.small.

ie. Inductors limit ie. Inductors limit the current the current better at high better at high frequenciesfrequencies

VR

VL

VS

VC

ResonanceResonance

At resonance, At resonance, VVLL=V=VCC and they and they

cancel each cancel each other out. So other out. So VVSS=V=VR R and if V and if VRR

is at max then I is at max then I is at max.is at max.

VR

VL

VS

VC

ResonanceResonance

At resonance, a circuit has the maximum At resonance, a circuit has the maximum possible current for a given supply voltage possible current for a given supply voltage VVSS..

At resonance:At resonance:

CL

CL

CL

XX

IXIX

VV

Resonant FrequencyResonant Frequency

A circuit will have A circuit will have a resonant a resonant frequency ffrequency f00

which depends which depends on L and C:on L and C:

LCf

LCf

CfLf

XX CL

2

14

1

2

12

0

220

00

Rectifying ACRectifying AC

Rectifying – turning AC into DCRectifying – turning AC into DC

Putting a diode into the circuit will do this:Putting a diode into the circuit will do this:

t

Rectifying ACRectifying AC

A bridge rectifier will do this:A bridge rectifier will do this:

t

Rectifying ACRectifying AC

A bridge rectifier circuit looks like this:A bridge rectifier circuit looks like this:

240V AC in

12V AC out

12V DC(smoothing

cap)

Rectifying ACRectifying AC

A bridge rectifier with a capacitor in A bridge rectifier with a capacitor in parallel with it will do this: (the bigger the parallel with it will do this: (the bigger the cap the smoother the DC)cap the smoother the DC)

t