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Measurement of Resistance, Capacitence, Inductance and Resonant Frequencies of RLC Using Oscilloscope

The document reports on an experiment to measure resistance, capacitance, inductance and resonant frequencies of an RLC circuit using an oscilloscope. It details the experimental procedure and results, performs data analysis to calculate averages and uncertainties, and compares the theoretical resonant frequency to the measured values.

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huyhoang01bg
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30 views5 pages

Measurement of Resistance, Capacitence, Inductance and Resonant Frequencies of RLC Using Oscilloscope

The document reports on an experiment to measure resistance, capacitance, inductance and resonant frequencies of an RLC circuit using an oscilloscope. It details the experimental procedure and results, performs data analysis to calculate averages and uncertainties, and compares the theoretical resonant frequency to the measured values.

Uploaded by

huyhoang01bg
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Experiment Report 1

MEASUREMENT OF RESISTANCE, CAPACITENCE,


INDUCTANCE AND RESONANT FREQUENCIES OF RLC
USING OSCILLOSCOPE
Class: 736043 - PH1026 Verification of the instructors
Group: 3
Name: Hong Huy Hoang
Student ID: 20227813
I. EXPERIMENTAL MOTIVATIONS:
- Understand a typical circuit
- Learn how to use electrical equipment including oscilloscope and function
generator
- Improving experimental skills.
II. EXPERIMENTAL RESULTS:
1. Resistance Measurement:

Trial f (Hz) R(Ω)


1 500 2201
2 1000 2200
3 1500 2206
2. Capacitance Measurement:

Trial f (Hz) R (Ω) 1


CX= (F)
2 πf R0
−7
1 1000 239 6.37 ×10
−7
2 2000 119 6.63 ×10
−7
3 3000 79 6.63 ×10
3. Inductance Measurement:

1
Trial f (Hz) R (Ω) R0
L x= (H )
2 πf
−3
1 1000 2504 3.50 ×10
−3
2 1500 4167 3.66 ×10
−3
3 2000 6180 3.50 ×10
4. Determination of Resonant Frequency:

Trial Series RLC (Hz) Parallel RLC (Hz)


1 1017 1012
2 1005 1009
3 1010 1016
III. Data Analysis:
1. Resistance Measurement:

We have: R X =R0
3

∑ Ri
R x = i=1 =2163(Ω)
3

√∑ (
3
2
R xi−R x )
i=1
Δ Rx ≈ S . D ≈ =12(Ω)
√3

Hence:

R x =2163 ±12(Ω)

2. Capacitence Measurement:

We have:
3

∑ C xi
C X = i=1 =6.54 ×10−7 (F )
3

√∑
3
Δ C X ≈ S . D≈ ¿¿¿¿¿
i=1

2
Hence:
−7
C X = ( 6.54 ± 0.12 ) × 10 (F)

3. Inductance Measurement:

We have:
3

∑ L xi
L x = i=1 =3.55 ×10−3 ( H)
3

√∑
3
2
(L xi−L x )
i=1 −3
Δ L x ≈ S . D≈ =0.08 ×10 (H)
√3
Hence:
−3
L X =(3.55 ± 0.08)× 10 (H )

4. Determination of Resonant Frequency:


a. Series RLC Circuit:
3

∑ f xi
f x = i=1 =1040 (Hz)
3

√∑ (
3
2
f Xi−f X )
i=1
Δ f x≈ S.D ≈ =8(Hz)
√3
Hence:

f X− Series=1040 ± 8(Hz)

b. Parallel RLC Circuit:


3

∑ f xi
f X= i=1 =1028(Hz)
3

3
√∑ (
3
2
f Xi−f X )
i=1
Δ f X ≈ S . D≈ =6(Hz)
√3

4
Hence:
f X−¿ =1028 ±6 (Hz)

c. Theoretical Result and Conclusion:


1
f=
2 π √ LC

1
f X= =3303.1(Hz)
2 π √ 3.55 ×10−3 × 6.54 ×10−7

Δ f X ≈ S . D≈ 3303.1 ×
√( )(
3.14
.
2 3.55 ) (
0.01 2 −1 0.08 2 −1 0.12 2
+ + .
2 6.54
=49.1(Hz))
Hence:

f X−Theoretical =3303.1± 49.1 ( Hz )

IV. Conclusion:
- The theoretical result of resonant frequency is approximately equal to the
directly measured results. We can see that the RLC circuit (with properly
small resistance) becomes a good approximation to an ideal LC circuit.

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