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Alternating Current
Electricity
NCEA A.S 3.6
Text Chapters 18-19
Why AC?
It can be produced directly from
generators
It can be controlled by a wide range of
components eg resistors,capacitors and
inductors.
The max voltage can be changed easily
using a transformer
The frequency of the AC can be used for
timing
AC Current
AC Voltage
AC
Power
P=VxI
Multiplying
the graphs
gives us a
graph
where the
power is
always
positive
AC Power
The average voltage in ac is zero since
there is an equal amount of positive and
negative voltage.
Same for current
The average value of the power used in ac
is half that of the peak power
RMS Values
Since voltage and current are always
changing we need some way of averaging
out their effect.
We use r.m.s values (root-mean-square)
The r.m.s values are the DC values which
give the same average power output
RMS Values
AC Voltage
DC Voltage
(with same
power output)
Vmax
Vrms
RMS Values
Vrms
Vmax

2
I rms
I max

2
(See text pg 295-296 for derivations of these formulae)
AC in Capacitors
In a DC circuit, the current flows until the cap is
fully charged and then stops.
In an AC circuit, the current can continue to flow,
as the plates become alternately charged
positively and negatively
~
Reactance
For both AC and DC circuits, the voltage
across the resistor is related to the current
by V=IR
A similar relationship exists for a capacitor:
Vc  IX c
~
Where Xc is the reactance of the capacitor
Reactance
Reactance is a measure of how a
capacitor can limit alternating current
Unit: Ohms
It is similar to resistance but differs in that
it is dependent on the frequency of the ac
supply.
It also depends on the size of the
capacitor.
Reactance
1
Xc 
2

fC
Explanations:
Higher f means cap never gets full before
current direction changes, so never limits
current, so low X
Higher C means that it takes more charge to fill
it, so never fills before current direction changes,
so never limits current, so low X
Phase Relationship
In a DC circuit the voltage across
components connected in series will add
up to the supply voltage
In AC circuits this does not happen
Eg.
VS
VS  12V
VC  6V
VR  8V
VS  VC  VR
~
VC
VR
Phase Relationship
Reasons:


The meters used to measure the voltage will
give rms values, not actual voltages at a
point in time
The voltages across the resistor and capacitor
are out of phase with each other ie they do
not both reach maxs and mins at the same
time.
Phase Relationship
The current in the circuit will always be in
phase with VR (Reason: because R is constant
so bigger V gives bigger I)
This can be shown on a phasor diagram:
VR
ω
VR
I VR
t
I
Phase Relationship
VC will lag 90° behind I (and therefore VR)
because the max current flows when the
voltage across it’s plates is zero, ie
uncharged, and zero current flows when
voltage is max ie cap is fully charged
The phasor diagram will look like:
Phase Relationship
VR
ω
I
VC
VC
VR
t
I
The voltage phasors are not necessarily the
same size, but are always 90°out of phase
RC Circuits
The total voltage in the circuit can be
found by adding the VR and VC phasors
together
2
2
2
VS  VR  VC
Vs
ω
VC
VC
VR
VS
t
VR
Impedance
VR=IR
VC=IXC
VS=IZ
R
Z
XC
The current is the same everywhere in the circuit
so VR and VC are proportional to R and XC
This combination of resistance and reactance
which both act to limit the current is called
impedance Z
Z
R
2
X
2
C

AC in Inductors
In a DC circuit an inductor produces an
opposing voltage whenever the current
changes.
In an AC circuit, the current is always
changing so the inductor is always
producing an opposing voltage so is
always limiting the amount of current that
can flow
~
Reactance
For both AC and DC circuits, the voltage
across the resistor is related to the current
by V=IR
A similar relationship exists for an inductor:
VL  IX L
~
Where XL is the reactance of the inductor
Reactance
It measures how well an inductor can limit
alternating current
It depends on the frequency of the ac
supply.
It depends on the size of the inductor.
Reactance
X L  2fL
Explanations:
Higher f means faster rate of change of current,
so more back e.m.f, so less current, so higher XL
Higher L means more back e.m.f, so less
current, so higher XL
Phase Relationship
VL will lead I (and therefore VR) by 90°
because the greatest back e.m.f occurs
when the current is changing most rapidly,
which is when it is passing through zero.
When the current has reached it’s max, it
is not changing as rapidly so there is no
back e.m.f
The phasor diagram will look like:
Phase Relationship
VR
VL
ω
I
VL
VR
t
I
Again the voltages may be different sizes
but will always be 90° out of phase
LR Circuits
The total voltage in the circuit can be
found by adding the VR and VL phasors
together
2
2
2
VS  VR  VL
VL
ω
VS
VR
VR
VL
Vs
t
Impedance
VL=IXL
XL
VS=IZ
Z
R
VR=IR
The impedance Z is found by adding R and XL
Z
R
2
X
2
L

LCR Circuits
This can be an extremely useful circuit setup, as the current and voltages can
change considerably as the frequency is
changed
~
LCR Circuits
The combined phasor diagram now looks like:
VR
VL
VL
VS
ω
VR
Vs
t
VC
VC
Supply Voltage
The supply
voltage is now
found by adding
all 3 phasors
together
(VL and VC are
combined into one
first)
V  V  (VL  VC )
2
S
2
R
VL=IXL
VS=IZ
VL-VC
VR=IR
2
VC=IXC
Impedance
The impedance of an LCR circuit is a
combination of both the resistance and the
reactance.
It is found by adding phasors:
Z
R
2
 (X L  XC )
2

XL
Z
XL-XC
R
XC
Resonance
At low f, VC>VL
so VR (and
therefore I) is
small.
ie. Capacitors
limit the current
better at low
frequencies
VL
VR
VS
VC
Resonance
At high f, VL>VC
so VR (and
therefore I) is
small.
ie. Inductors limit
the current
better at high
frequencies
VL
VS
VR
VC
Resonance
At resonance,
VL=VC and they
cancel each
other out. So
VS=VR and if VR
is at max then I
is at max.
VL
VS
VR
VC
Resonance
At resonance, a circuit has the maximum
possible current for a given supply voltage
VS .
At resonance:
VL  VC
 IX L  IX C
 X L  XC
Resonant Frequency
A circuit will have
a resonant
frequency f0
which depends
on L and C:
X L  XC
1
2f 0 L 
2f 0C
1
f 
2
4 LC
1
f0 
2 LC
2
0
Rectifying AC
Rectifying – turning AC into DC
Putting a diode into the circuit will do this:
t
Rectifying AC
A bridge rectifier will do this:
t
Rectifying AC
A bridge rectifier circuit looks like this:
240V
AC in
12V
AC
out
(smoothing
cap)
12V
DC
Rectifying AC
A bridge rectifier with a capacitor in
parallel with it will do this: (the bigger the
cap the smoother the DC)
t