electric sunum
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RLC CIRCUITS
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What is Rlc Circuit ?
An RLC circuit is an electrical
circuit consisting of a
resistor, an inductor, and a
capacitor, connected in seriesor in parallel.
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There are many applications
for this circuit
For instance,
Tuning, Radio receivers,
Television sets, Band-Pass
filter, Band-Stop filter, Low orHigh pass filter
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How to calculate Element Impedence ?
Curcuit element Resistance (R) Reactance (X) Impededance (Z)
Resistor R 0 ZR = R
=R < 00
Inductor 0 L ZL = jL
= L < +900
Capacitor 0 1/C ZC = 1/jC
= 1/C < -900
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Series Rlc Circuits
In this circuit , the three components are all in
series with the voltage source
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i(t) = Imax sin(t)
The instantaneous voltage across a pureresistor, VR is "in-phase" with the current.
The instantaneous voltage across a pure
inductor, VL "leads" the current by 90oThe instantaneous voltage across a pure
capacitor, VC "lags" the current by 90o
Therefore, VL and VC are 180o "out-of-
phase" and in opposition to each other.
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Individual Voltage Vectors
we can not simply add together
VR, VL and VC to find the supply
voltage, VS across all threecomponents as all three voltage
vectors point in different
directions with regards to the
current vector
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Therefore we have to find the
supply voltage, VS as thePhasor Sum of the three
component voltages combinedtogether vectorially
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The governing differential equation can be
found by substituting into Kirchhoff's voltage
law (KVL) the constitutive equation for each ofthe three elements
http://en.wikipedia.org/wiki/Kirchhoff's_voltage_lawhttp://en.wikipedia.org/wiki/Kirchhoff's_voltage_lawhttp://en.wikipedia.org/wiki/Constitutive_equationhttp://en.wikipedia.org/wiki/Constitutive_equationhttp://en.wikipedia.org/wiki/Constitutive_equationhttp://en.wikipedia.org/wiki/Kirchhoff's_voltage_lawhttp://en.wikipedia.org/wiki/Kirchhoff's_voltage_law -
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Phasor Diagram for a Series RLCCircuit
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Voltage Triangle
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Current has the same amplitude
and phase in all the componentsof a series RLC circuit. Then the
voltage across each component
can also be described
mathematically according to the
current flowing through, and thevoltage across each element as
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By substituting these values into Pythagoras's equation above
for the voltage triangle will give us:
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The impedance of a Series RLC Circuit
As the three vector voltages are out-of-phase
with each other, XL, XC and R must also be
"out-of-phase" with each other with the
relationship between R, XL and XC being thevector sum of these three components
thereby giving us the circuits overall
impedance, Z. These circuit impedances canbe drawn and represented by an Impedance
Triangle as in next slide
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Th i d Z f i RLC i i
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The impedance Z of a series RLC circuitdepends upon the angular frequency, as doXL and XC If the capacitive reactance is greater
than the inductive reactance, XC > XL then theoverall circuit reactance is capacitive giving aleading phase angle. Likewise, if the inductivereactance is greater than the capacitive
reactance, XL > XC then the overall circuitreactance is inductive giving the series circuita lagging phase angle. If the two reactance'sare the same and X
L= X
Cthen the angular
frequency at which this occurs is called theresonant frequency and produces the effect ofresonance.
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Then the magnitude of the current
depends upon the frequency applied
to the series RLC circuit. When
impedance, Z is at its maximum, the
current is a minimum and likewise,when Z is at its minimum, the
current is at maximum. So the above
equation for impedance can be re-
written as
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Example
A series RLC circuit containing a
resistance of 12, an inductance of
0.15H and a capacitor of 100uF areconnected across a 100V, 50Hz
supply. Calculate the total circuit
impedance, the circuits current,power factor and draw the voltage
phasor diagram.
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Inductive Reactance, XL.
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Capacitive Reactance, XC
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Circuit Impedance, Z.
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Circuits Current, I.
Voltages across the Series RLC Circuit, VR, V
L,
VC.
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Circuits Power factor and Phase Angle,
Phasor diagram