Resonance in AC Circuits.pdf.....well explained notes

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1. ELECTRICAL ELECTRONICSCOMMUNICATION INSTRUMENTATION
Electrical Science: 2021-22
Lecture 16
Resonance in AC Circuits
By Dr. Sanjay Vidhyadharan

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Resonance in RLC Series AC Circuits
Z
min= R at Resonant Frequency where X
L= X
C
I
max= V/R

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QUALITY FACTOR (Q)
The“sharpness”oftheresonanceinaresonantcircuitismeasured
quantitativelybythequalityfactorQ.
•Thequalityfactorrelatesthemaximumorpeakenergystoredtothe
energydissipatedinthecircuitpercycleofoscillation:
• It is also regarded as a measure of the energy storage property of a
circuit in relation to its energy dissipation property.

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Tunned Circuits

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QUALITY FACTOR (Q)

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QUALITY FACTOR (Q)

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Resonance in RLC Series AC Circuits

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Resonance in RLC Series AC Circuits
➢QistermedasQfactororvoltage
magnification,becauseV
CorV
LequalsQ
multipliedbythesourcevoltageV.
➢InaseriesRLCcircuit,valuesofVLand
VCcanactuallybeverylargeatresonance
andcanleadtocomponentdamageifnot
recognizedandsubjecttocarefuldesign.

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BANDWIDTH AND HALF POWER FREQUENCIES

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BANDWIDTH AND HALF POWER FREQUENCIES

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BANDWIDTH AND HALF POWER FREQUENCIES

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BANDWIDTH AND HALF POWER FREQUENCIES

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BANDWIDTH AND HALF POWER FREQUENCIES

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BANDWIDTH AND HALF POWER FREQUENCIES

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BANDWIDTH AND HALF POWER FREQUENCIES

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Calculating the Power
Example 1For a RLCseries circuit having a 40.0 Ω resistor, a 3.00 mHinductor, a
5.00 μFcapacitor, and a voltage source with a V
rmsof 120 V. Find the average power
at the circuit’s resonant frequency.

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Resonance in Parallel RLC Circuit
Asthetotalsusceptanceiszeroattheresonantfrequency,theadmittanceisatitsminimum
andisequaltotheconductance,G.Thereforeatresonancethecurrentflowingthroughthe
circuitmustalsobeatitsminimumastheinductiveandcapacitivebranchcurrentsareequal
(I
L=I
C)andare180
o
outofphase.

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Resonance in Parallel RLC Circuit
BW = ƒ
r/QorBW = ƒ
upper-ƒ
lower

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Example 2: A parallel resonance network consisting of a resistor of 60Ω, a capacitor
of 120uF and an inductor of 200mH is connected across a sinusoidal supply voltage
which has a constant output of 100 volts at all frequencies. Calculate, the resonant
frequency, the quality factor and the bandwidth of the circuit, the circuit current at
resonance and current magnification.
Resonance in Parallel RLC Circuit

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Resonance in Parallel RLC Circuit
Example 2:

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Resonance in Parallel RLC Circuit
Example 2:

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Thank you