Electric Sunum

7/30/2019 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

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