Experiment 5 APPLIED PHYSICS SERIES RESONANT CIRCUIT 5.1 OBJECTIVES: 1. Take observations for series RLC circuit for different values of Resistances and plot resonance curve. 2. Determine its resonance frequency and Q factor. 5.2 SAFETY NOTES: 1. Do not touch buttons and knobs of function generator and oscilloscope unnecessarily. 2. Make connections carefully and call teacher to check the connections before turning on the input signal. 5.3 EQUIPMENTS/ REQUIREMENTS: 1. 1 Function Generator 2. 1 Oscilloscope 3. 1 Digital Multimeter 4. Capacitor 0.1μF, Inductor, Resistances 10Ωand 100Ω (1 each) 6.4 THEORY: When inductor and capacitor are used in an ac circuit, inductive reactance X L increases as the frequency of applied voltage is increased, but capacitive reactance X C decreases with higher frequencies. At a certain frequency, called the resonance frequency f r , the X L becomes equal to X C . This case of equal and opposite reactance is called resonance, and the circuit is called resonant circuit. Since, and At resonant frequency (f = f r ) X L = X C (1) Series Resonant circuit: In series RLC circuit, at low frequencies, there is large capacitive reactance X C so very small current will flow through the circuit and minimum voltage drop across R and L. Since voltage across capacitor V C and voltage across inductor V L opposes each other diametrically, so, the total reactive voltage is V L -V C . At Lab Instructor Arshia Aijaz Page| 5 – 1
Transcript
Experiment 5 APPLIED PHYSICS
SERIES RESONANT CIRCUIT
5.1 OBJECTIVES:1. Take observations for series RLC circuit for different values of Resistances and plot
resonance curve.2. Determine its resonance frequency and Q factor.
5.2 SAFETY NOTES:1. Do not touch buttons and knobs of function generator and oscilloscope unnecessarily.2. Make connections carefully and call teacher to check the connections before turning
on the input signal.
5.3 EQUIPMENTS/ REQUIREMENTS:1. 1 Function Generator2. 1 Oscilloscope3. 1 Digital Multimeter4. Capacitor 0.1μF, Inductor, Resistances 10Ωand 100Ω (1 each)
6.4 THEORY:
When inductor and capacitor are used in an ac circuit, inductive reactance XL increases as the frequency of applied voltage is increased, but capacitive reactance XC decreases with higher frequencies. At a certain frequency, called the resonance frequency fr, the XL becomes equal to XC. This case of equal and opposite reactance is called resonance, and the circuit is called resonant circuit. Since,
and
At resonant frequency (f = fr)XL = XC
(1)
Series Resonant circuit:In series RLC circuit, at low frequencies, there is large capacitive reactance XC so very small current will flow through the circuit and minimum voltage drop across R and L. Since voltage across capacitor VC and voltage across inductor VL opposes each other diametrically, so, the total reactive voltage is VL - VC. At very high frequencies, inductor L will be an open circuit, and again very small current will flow. However, at intermediate frequencies, both XC and XL will be moderate, and the difference between them will be small. At resonance, that difference will be zero, and only R will limit the current flowing in the circuit. At resonance maximum current will flow through the circuit so this circuit is also called acceptor circuit.
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Experiment 5 APPLIED PHYSICS
Q Magnification factor of Resonant Circuit:The sharpness of resonance curve describe the quality, or figure of merit, is indicated by the factor Q. higher the sharpness higher the Q magnification factor. In series RLC circuit,
(2)
Since the series resistance limits the amount of current at resonance so lower the resistance R sharper the increase to maximum current at resonant frequency and higher the Q factor.Q factor can also be calculated by using bandwidth.
Q = fr/Δf (3)
Where, Δf is the bandwidth of resonance curve.
Band Width of Resonance Curve:The width of group of frequencies centered around resonant frequency that gives a response of 70.7% of the maximum or more is called bandwidth of the tuned circuit.
Δf = f2- f1 (4)
5.5 REFERENCES:1. ‘Basic Electronics’, GROB2. ‘Physics’ by Halliday Resnick and Krane.3. www.play-hookey.com/ac_theory/ac_rlc_series.html4. www.wikipedia.com
5.6 EXPERIMENTAL SETUP:
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Experiment 5 APPLIED PHYSICS
5.7 PROCEDURE:6Make connections as shown in figure.1. Use R = 100Ω.
2. Increase the frequency from 2 kHz to 20 kHz of input signal and read output peak-to-peak signal (Vp-p) on oscilloscope as shown in figure 5.4
3. Use appropriate frequency intervals, say 3kHz before and after resonance, and smaller intervals say 0.4 Hz, near the resonance.
4. Repeat observations for R = 10Ω.5. Use back of the sheet for calculations
5.8 OBSERVATIONS:
Frequency kHz
Output Voltage (Volts)
10Ω 100Ω
5.9 GRAPH:Plot graphs of amplitude versus frequency using your observations for each resistance (10Ω, 100Ω). Determine resonance frequency and bandwidth.
5.10 CALCULATIONS: From graph, resonance frequency, fr = _________kHz.
For R=10Ω: From graph f1 = __________ kHz and f2 =__________ kHz. Band width Δf = f2 - f1=__________ kHz. Value of Q factor using graph (Q = fr / Δf) is __________
For R=100Ω:
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Experiment 5 APPLIED PHYSICS
From graph f1 = __________ kHz and f2 =__________ kHz. Band width Δf = f2 - f1=__________ kHz. Value of Q factor using graph (Q = fr / Δf) is __________
