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Transcript of AC Principles Series RLC
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 1/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 2/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 3/89
The same applies to AC circuits
Current is the same in all components V supply will be the sum of VR and VXL
The total opposition to current flow, impedance in a.c.circuits, is the sum of R and XL
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 4/89
If I = 2A, R = 40, XL = 30 Then:
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 5/89
The supply voltage would be?
100V
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 6/89
WHY?????
How can 80 + 60 = 100
It must be remembered that the voltage
drop across the resistor is in phase withcurrent and the voltage drop across the
inductor leads the current by 90°
The problem must be solved as a vector or
phasor
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 7/89
As this is a series circuit current is
common to all components and is
used as reference.
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 8/89
The voltage drop across the
resistor is in phase with the current
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 9/89
The voltage on the inductor leads
by 90°
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 10/89
Using the end to end method VXL
can be drawn at the end of VR
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 11/89
The supply voltage can now be
found
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 12/89
The angle between the voltage and
the current is also useful
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 13/89
For our circuit
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 14/89
Therefore
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 15/89
Total opposition to current flow
Rather thanresistance, this isreferred to as
impedance on a.c.circuits
It is still measured inohms, but has thesymbol Z
For our circuitcalculate theimpedance
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 16/89
Using Ohm¶s law
Z =V SUPPLY
I SUPPLY
Z =100
2
Z = 50
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 17/89
It is possible to make another
triangle, known as an impedance
triangle
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 18/89
Our impedance triangle is shown
as:
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 19/89
The power consumed by the circuit
can now be determined
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 20/89
The inductor consumes no power
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 21/89
The inductor appears to consume 120W, but
watts cannot be used. So VA, Volts x Amps,
is used. VAR for reactive
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 22/89
The circuit consumes 160W but
appears to consume 200.
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 23/89
Power triangle
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 24/89
This can be shown as:
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 25/89
Power factor
Power factor is the ratio between true Power and
Apparent Power.
This is also the cosine of the angle between the
True and Apparent power
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 26/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 27/89
Using the triangles
Using Ohm¶s law (V = IR) and the power formula
(P = VI) you can move from one triangle to the
other.
Multiple by current to move to the right
Divide by current to move to the left
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 28/89
Multiply or divide a side by current
to move between triangles
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 29/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 30/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 31/89
Resistors and Capacitors on AC
Current is the same in all components V supply will be the sum of VR and VXC
The total opposition to current flow, impedance in a.c.circuits, is the sum of R and XC
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 32/89
If I = 2A, R = 40, XC = 30 Then:
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 33/89
The supply voltage would be?
100V
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 34/89
WHY?????
How can 80 + 60 = 100
It must be remembered that the voltage
drop across the resistor is in phase withcurrent and the voltage drop across the
Capacitor lags the current by 90°
The problem must be solved as a vector or
phasor
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 35/89
As this is a series circuit current is
common to all components and is
used as reference.
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 36/89
The voltage drop across the
resistor is in phase with the current
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 37/89
The voltage on the capacitor lags
by 90°
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 38/89
Using the end to end method VXC
can be drawn at the end of VR
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 39/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 40/89
The supply voltage can now be
found
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 41/89
The angle between the voltage and
the current is also useful
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 42/89
For our circuit
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 43/89
Therefore
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 44/89
Total opposition to current flow
Rather thanresistance, this isreferred to asimpedance on a.c.circuits
It is still measured inohms, but has thesymbol Z
For our circuitcalculate theimpedance
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 45/89
Using Ohm¶s law
Z =V SUPPLY
I SUPPLY
Z =100
2
Z = 50
It i ibl t k th
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 46/89
It is possible to make another
triangle, known as an impedance
triangle
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 47/89
Our impedance triangle is shown
as:
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 48/89
The power consumed by the circuit
can now be determined
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 49/89
The inductor consumes no power
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 50/89
The inductor appears to consume 120W, but
watts cannot be used. So VA, Volts x Amps,
is used. VAR for reactive
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 51/89
The circuit consumes 160W but
appears to consume 200.
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 52/89
This can be shown as:
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 53/89
Power factor
Power factor is the ratio between true Power and
Apparent Power.
This is also the cosine of the angle between the
True and Apparent power
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 54/89
Summary
All three triangles are the same shape, the difference is the size, each triangle is 2
times larger/smaller than the other. Which is the value of the current
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 55/89
Using the triangles
Using Ohm¶s law (V = IR) and the power formula
(P = VI) you can move from one triangle to the
other.
Multiple by current to move to the right Divide by current to move to the left
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 56/89
Multiply or divide a side by current
to move between triangles
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 57/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 58/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 59/89
Series Resistor, Inductor and
Capacitor
Current is the same in all components
V supply will be the sum of VR,VXL and VXC
The total opposition to current flow, impedance in a.c. circuits, is the sumof R, XL and XC
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 60/89
If I = 2A, R = 40, XL= 45, XC = 15 Then:
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 61/89
The supply voltage would be?
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 62/89
Once again we need to solve via
phasor
It must be remembered that the voltage
drop across the resistor is in phase with
current
The voltage drop across the Inductor leads
the current by 90°
The voltage drop across the Capacitor
lags the current by 90°
As this is a series circuit current is
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 63/89
As this is a series circuit current is
common to all components and is
used as reference.
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 64/89
The voltage drop across the
resistor is in phase with the current
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 65/89
The voltage across the inductor
leads by 90°
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 66/89
The voltage across the Capacitor
lags by 90°
VXL and VXC are 180° out of phase
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 67/89
VXL and VXC are 180 out of phase
with each other, and therefore one
can be subtracted from the other
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 68/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 69/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 70/89
Supply voltage is the phasor sum
of VR and (VXL ± VXC)
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 71/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 72/89
Total opposition to current flow
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 73/89
Using Ohm¶s law
Z =V SUPPLY
I SUPPLY
Z =100
2
Z = 50
It is possible to make another
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 74/89
It is possible to make another
triangle, known as an impedance
triangle
O i d t i l i h
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 75/89
Our impedance triangle is shown
as:
Th d b th i it
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 76/89
The power consumed by the circuit
can now be determined
Th i d t d it
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 77/89
The inductor and capacitor
consumes no power
The inductor and capacitor appear to
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 78/89
The inductor and capacitor appear to
consume power but do not. So VA, Volts x
Amps, is used. VAR for reactive
Th i it 160W b t
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 79/89
The circuit consumes 160W but
appears to consume 200.
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 80/89
Power triangle
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 81/89
This can be shown as:
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 82/89
Power factor
Power factor is the ratio between true Power and
Apparent Power.
This is also the cosine of the angle between the
True and Apparent power
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 83/89
Summary
All three triangles are the same shape, the difference is the size, each triangle is 2times larger/smaller than the other. Which is the value of the current
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 84/89
Using the triangles
Using Ohm¶s law (V = IR) and the power formula
(P = VI) you can move from one triangle to the
other.
Multiple by current to move to the right Divide by current to move to the left
Multiply or divide a side by current
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 85/89
Multiply or divide a side by current
to move between triangles
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 86/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 87/89
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 88/89
What if XC is greater than XL?
If XC is larger than XL
then the triangle will
simply be upside down
If using Pythagoras
theorem, a negativenumber squared equals a
positive number (some
modern calculators do not
do this, so check your calculator now)
8/2/2019 AC Principles Series RLC
http://slidepdf.com/reader/full/ac-principles-series-rlc 89/89
Using the internet
On many sites XL and XC have a j in front
of them to indicate vertical component of
triangle.
XC is also given a negative value ± jXC
This makes Kirchhoff's laws more
accurate, ie VS it the sum of VR, VXL and
VXC.
At trade level however we say VXL - VXC