Assignment
ELECTROTECHNOLOGY
ELTK1200
ASSIGNMENT #6
SOLUTIONS
1.
One method
XC > XL j capacitive circuit - leading
Impedance triangle
Power triangle
Phasor diagram
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2.
(a)
f = 60Hz.
XC > XL j capacitive circuit - leading
Phasor diagram
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(b)
f = 250Hz.
XL > XC j inductive circuit - lagging
Phasor diagram
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(c)
f = 120Hz.
XL = XC j resistive circuit
In the notes, we have dealt with XL > XC and XC > XL.
At a specific frequency XL = XC, the inductive and capacitive reactances cancel each
other out. This frequency is called resonant frequency and it has a special
importance in the electrical world. For us, at this point in the course, just note what
happens when XL = XC.
Phasor diagram
At resonant frequency, a RLC series circuit has no triangles.
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3.
(a)
(b)
VC > VL j capacitive circuit
- leading
(c)
(d)
(e)
(f)
(g)
When a capacitor and an inductor are connected in an ac circuit, the capacitor acts
as a source for the inductor and reactive power flows between the two devices. This
(usually) decreases the reactive power (QNET) the source has to provide to the circuit.
As can be seen from this example, these voltages and powers can be quite large as
compared to the source. VL and VC can be large compared to VS because they are
opposite in polarity and cancel each other out. The capacitor supplies some or all
of the reactive power the inductor requires.
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(f)
Impedance triangle
Phasor diagram
Power triangle
4.
(a)
>
ELTK1200
j inductive circuit - lagging
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(b)
(c)
(d)
(e)
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Impedance triangle
ELTK1200
Phasor diagram
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Power triangle
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5.
XC > XL j capacitive circuit - leading
Current leads the voltage by 18.2°. We are given
, which
makes voltage the reference at 0°, so the current waveform will be:
time
radians
6.
Lagging, so VL > VC
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7.
To help you with this question, we have a memory mnemonic, where rye is spelt
rhyming with lie or die.
ELI the ICEman drinks RIE.
ELI drinks RIE with ICE.
or
The keywords are ELI, RIE and ICE. E is an abbreviation for voltage (EMF) and I is
current. R, L and C indicate a circuit which is resistive, purely inductive or capacitive.
The relationship of E and I to the circuit letter describes the relationship between
voltage and current in that circuit.
ELI, where E is followed by I, indicates that in a purely inductive circuit L, voltage
leads current by 90° or using current as the reference, current lags voltage by 90°.
RIE, where E and I are on the same side, indicates that in a resistive circuit R,
voltage and current are in phase with each other.
ICE, where I is followed by E, indicates that in a capacitive circuit C, current leads
voltage by 90°.
Now, when we put different combinations of R, L and C in series with each other,
these relationships are maintained.
Take a series RL circuit. As the current flows through the resistor, it produces a
voltage drop VR, which is in phase with the current. When the current flows through
the inductor, it produces a voltage drop VL, which leads the current by 90°. The
source voltage VS is the vector addition of these two components. So I lags VS by
an angle between 0° and 90°.
With RLC series circuits, the relationship depends on the vertical legs,
), then I lags VS by . If
If
(or
or
or
), then I leads VS by . Finally, when
and the triangles disappear (
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
(xi)
ELTK1200
R
C
L
RC
RL
RLC (XL > XC)
RLC (XC > XL)
RLC (VC < VL)
RLC (S = P)
RLC (VL = VC)
RLC (QL < QC)
(c)
(e)
(a)
(d)
(b)
(b)
(d)
(b)
(c)
(c)
(d)
,
and
.
(or
, then I is in phase with VS
,
and
).
I and VS are in phase.
I leads VS by 90°.
I lags VS by 90°.
I leads VS by an angle between 0° and 90°.
I lags VS by an angle between 0° and 90°.
I lags VS by an angle between 0° and 90°.
I leads VS by an angle between 0° and 90°.
I lags VS by an angle between 0° and 90°.
I and VS are in phase.
I and VS are in phase.
I leads VS by an angle between 0° and 90°.
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