Abstract:
In this experiment we will study the effect of resonance in circuit with
elements in series. And discussing the value of main factor ( total current & total
voltage drop) in circuit at resonance situation.
Introduction:
In its most simple form, the resonant circuit consists of an inductor and
a capacitor together with a voltage or current source. Although the circuit is
simple, it is one of the most important circuits used in electronics. As an
example, the resonant circuit, in one of its many forms, allows us to select a
desired radio or television signal from the vast number of signals that are
around us at any time.
Whereas there are various configurations of resonant circuits, they all have
several common characteristics. Resonant electronic circuits contain at least one
inductor and one capacitor and have a bell-shaped response curve centered at
some resonant frequency, fr, as illustrated in Figure below.
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A simple series resonant circuit is constructed by combining an ac
source with an inductor, a capacitor, and optionally, a resistor as shown in Figure
a. By combining the generator resistance, RG, with the series resistance, R S, and
the resistance of the inductor coil, Rcoil, the circuit may be simplified as illustrated
in Figure b. (R = RG +RS +Rcoil).
Resonance occurs when the reactance of the circuit is effectively
eliminated, resulting in a total impedance that is purely resistive. We see that by
setting the reactances of the capacitor and inductor equal to one another, the
total impedance, ZT, is purely resistive since the inductive reactance which is on
the positive j axis cancels the capacitive reactance on the negative j axis. The
total impedance of the series circuit at resonance is equal to the total circuit
resistance. By letting the reactances be equal we are able to determine the series
resonance frequency, as follows:
The phasor form of the voltages and current is shown in Figure below.
Notice that since the inductive and capacitive reactances have the same
magnitude, the voltages across the elements must have the same magnitude but
be 180° out of phase.
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Objectives:
• Able to analysis series resonant RLC circuits by using calculations and
measurements.
• Able to compute the resonant frequency, total current, and impedance in a
series RLC circuit by using standard formulas and procedures. We will
verify results with an oscilloscope.
Equipment required:
• F.A.C.E.T. base unit
• AC 2 FUNDAMENTALS circuit board
• Oscilloscope
• Generator
• Multimeter
• Two-Post Connectors
• Terminal Posts
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Procedures:
1. Locate the RLC/RESONANCE/POWER circuit block, and connect the circuit
shown.
2. Adjust the generator output voltage (VGEN) for a 15VpK-pK, 20 kHz sine wave.
3. Connect channel 2 of the oscilloscope across series combination L1 and C1, as
shown.
Increase the frequency of the generator to tune for series resonance as determined
by a voltage null across series combination L1 and C1.
Results:
Using generator and oscilloscope we find frequency resonance between 30k Hz
& 35k Hz
⸫ fr ≈ 33.33k Hz
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Using calculation
1 1
𝑓𝑟 = = = 33.931𝑘 𝐻𝑧
2𝜋√𝐿𝐶 2𝜋√10 × 10−3 × 0.0022 × 10−6
This show the result in measure and calculate is so close.
And ZT = R2 + R3 + j(xL - xC) ⸪ xL - xC = 0
ZT = R2 + R3
= 1000 +10 = 1010 Ω
𝑉𝐺𝑒𝑛 15
And 𝐼𝑇 = = = 14.85 𝑚𝐴
𝑍𝑇 1010
1000
𝑉𝑅2 = 15 × = 14.85 𝑉
1000+10
10
𝑉𝑅3 = 15 × = 0.15 𝑉
1000+10
By applying KVL:
-VGen + VR2 + VR3 =? 0
-15 + 14.85 + 0.15 = 0
Discussion:
• At the resonant frequency, XL equals XC, and they cancel one another,
leaving only the circuit resistance to control current.
• At series resonance, circuit current is maximum and in phase with the
applied voltage.
• Inductance and capacitance values affect the resonant frequency.
• Circuit resistance has no resonant frequency (fr), but it does affect
impedance and current.
• The voltage drops across the reactive components (XL and XC) are
significantly higher than the applied voltage and peak at resonance.
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Conclusion:
At end of the this experiment we have learned how to drive a series circuit
to resonance situation by using oscilloscope and generator. And we study the
current and voltage values in resonance.
References:
1. Introductory Circuit Analysis by Robert L. Boylestad 11th Edition.
2. Circuit Analysis: Theory and Practice by Robbins & Miler 2nd Edition.
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