Measurement of Resistance, Capacitance, Inductance and Resonant Frequencies of RLC using Oscilloscope

x
x (17) 
The trace may be either a line or oval depending on the value of the oscillation phase: 
• If ϕ = 0 and ϕ = π, a diagonal line (figure 5a) is displayed. It is corresponding to 
resistance circuit. 
• If ϕ = ± π/2, a vertical oval trace is displayed (figure 5b). It is corresponding to 
either RC or LR circuit. If a suitable resistor is used so that U0x = U0y a circular 
trace will be displayed. 
• If ϕ gets an arbitrary value then the trace will be an oblique oval (figure 5c). It is 
corresponding to RLC circuit. In case of resonance that is the case of ZL = ZC as 
mentioned above in part 1, a diagonal line is displayed as shown in figure 5a. 
(a) (b) (c) 
Figure 5. Signal form on oscilloscope screen produced by two perpendicular oscillations 
3. Introduction to function generator 
A function generator (FG) is a device containing an electronic oscillator, a circuit that is 
capable of creating a repetitive waveform. The most common waveform is a sine wave, 
but saw-tooth, step (pulse), square, and triangular waveform. Function generators are 
typically used in simple electronics repair and design; where they are used to stimulate a 
circuit under test. The oscilloscope is then used to measure the circuit's output. Function 
generators vary in the number of outputs they feature, frequency range, frequency 
accuracy and stability, and several other parameters. 
The function generator GF8020F used in this experiment is shown in figure 6a. A typical 
FG can provide frequencies up to 20 MHz and uses a BNC connector, usually requiring a 
50 or 75 ohm termination as shown in figure 6b. This connector is also used for OS in 
measurement. 
1 
2 
3 
4 
7 
5 
6 8 9 
10 
(a) 
(b) 
Figure 6. Front panel of function generator GF8020F (a) and BNC connector (b) 
(1. On/off power switch; 2. LED indicating power on; 3. Scale switching buttons of 
generated frequency range, e.g 1K, 10K, and 100K (Hz); 4. switching button for output 
option of sine waveform; 5. Adjustor for output voltage amplitude; 6. Voltage output for 
BNC connection; 7. Voltage output of square pulse; 8. Adjustor for rough frequency; 
9. Adjustor for fine frequency; 10. LEDs display of output frequency) 
II. EXPERMENTAL PROCEDURE 
A. Preparation 
1.1 Learn to know the way of using oscilloscope. 
1.2 Learn to know the way of using function generator. 
1.3. Learn to know the way of using BNC connection and measurement probs. 
B. Measurement of resistance, capacitance, and inductance 
1. Resistance measurement of unknown resistor 
1.1. Connect all the terminals using the banana plug cords and install resistance box 
(denoted as R0) and unknown resistor RX based on the circuit layout shown in figure 7. 
1.2. Switch to power on FG. Choose the frequency range of 1K (using button group 3) 
and sine waveform (using button 4). Adjust knobs 8 and 9 to set an initial measurement 
frequency of about 500 Hz (or 1000 Hz). 
1.3. Switch to power on OS. Observe to see a trace in the form of a illuminated vertical 
line displayed on the screen. 
FG 
8020H 
OS
5020C 
Y 
X 
A 
R0 
RX A 
B B C C 
Figure 7. Circuit layout for measurement of resistance, capacity, and inductivity 
1.4. Regulating the resistance box R0 so that the trace displayed on screen of OS becomes 
a diagonal line. Then, UX = UY = URo that is, 
RX = R0 (18) 
Make a data table (denoted table 1) then record the value of frequency f and the 
respective value of R0 in it. 
Note: the resistance box R0 are regulated by turning up its knobs with the order from 
greater range (∼thousands ohm) to smaller one (∼ohm or ∼one tenths ohm), respectively. 
1.5. Repeat the experimental procedure with other frequencies (may be either 1000, and 
1500 Hz or 1500, and 2000 Hz). 
1.6. Turn off OS and FG; turn down the knobs of the changeable resistor R0 to zero 
positions and uninstall the resistor RX from the measurement circuit in order to prepare 
for next measurement. 
2. Capacitance measurement of unknown capacitor 
2.1. Install the unknown capacitor CX at the position of the measured resistor RX as 
shown in figure 7. 
2.2. Switch to power on FG. Choose the frequency range of 10K (using button group 3) 
and sine waveform (using button 4). Adjust knobs 8 and 9 to set an initial measurement 
frequency of about 1000 Hz. 
2.3. Switch to power on OS. Observe to see a trace in the form of illuminated upright 
oval displayed on the screen. For convenient and exact observing, adjust knobs 7 and 10 
to move the oval trace so that its center is coincided with the center of the coordinate axes 
of the screen. 
2.4. Regulating the resistance box R0 so that the oval trace becomes a circle. 
Make a data table (denoted table 2) then record the value of frequency f and the 
respective value of R0 in it. 
Note: Regulating the resistance box R0 by turning up its knobs with the order from 
greater range (∼thousands ohm) to smaller one (∼ohm or ∼one tenths ohm), respectively. 
2.5. Complete the table 2 by performing this manipulation for more 2 times according to 
2 different frequencies (may be either 1500, and 2000 Hz or 2000, and 3000 Hz). 
2.6. Turn off OS and FG; turn down the knobs of resistance box R0 to zero positions, and 
uninstall the capacitor CX from the board in order to prepare for next measurement. 
3. Inductance measurement of unknown coil 
3.1. Install the unknown coil LX at the position of the measured resistor RX as shown in 
figure 7. 
3.2. Switch to power on FG. Choose the frequency range of 10K (using button group 3) 
and sine waveform (using button 4). Adjust knobs 8 and 9 to set an initial measurement 
frequency of about 10.000 Hz. 
3.3. Switch to power on OS. Observe to see a trace in the form of illuminated upright 
oval displayed on the screen. For convenient and exact observing, adjust knobs 7 and 10 
to move the oval trace so that its center is coincided with the center of the coordinate axes 
of the screen 
3.4. Regulating the resistance box R0 so that the oval trace becomes a circle. 
Make a data table (denoted table 3) then record the value of frequency f and the 
respective value of R0 in it. 
Note: Regulating the resistance box R0 by turning up its knobs with the order from 
greater range (∼thousands ohm) to smaller one (∼ohm or ∼one tenths ohm), respectively. 
3.5. Complete the table 3 by performing this manipulation for more 2 times according to 
2 different frequencies (may be either 15.000, and 20.000 Hz or 20.000, and 30.000 Hz). 
3.6. Turn off OS and FG; turn down the knobs of the resistance box R0 to zero positions, 
at last, uninstall the coil LX from the board in order to prepare for next measurement. 
C. Determination of resonant frequency of RLC circuit 
1. Series RLC circuit 
1.1. Connect all the terminals using the banana plug cords, and install the resistance box 
R0, the measured capacitor CX, and coil LX based on the circuit layout shown in figure 8. 
Set a value of 1000 Ohm for R0. 
FG 
8020H 
OS
5020C 
Y 
X 
A R0 
CX 
A 
B B 
LX 
Figure 8. Series RLC circuit layout for measurement of resonant frequency 
1.2. Switch to power on FG. Choose the frequency range of 100K (using button group 3) 
and sine waveform (using button 4). 
1.3. Switch to power on OS. Observe to see to see an inclined oval trace displayed on the 
screen of OS. 
1.4. Regulating the knobs 8 and 9 of FG to change the generated frequency so that. The 
oval trace becomes an inclined line. 
 Make a data table (denoted table 4) then record the values of resonant frequency fserries in 
it. 
1.5. Repeat the experimental procedure for more 2 times. 
1.6. Turn off OS and FG and uninstall the capacitor CX from the measurement circuit in 
order to prepare for next measurement. 
2. Parallel RLC circuit 
2.1. 1.1. Connect all the terminals using the banana plug cords, and install the resistance 
box R0, the measured capacitor CX, and coil LX based on the circuit layout shown in 
figure 9. Set a value of 1000 Ohm for R0. 
FG 
8020H 
OS
5020C 
Y 
X 
A R0 
CX 
A 
B B 
LX 
Figure 9. Parallel RLC circuit layout for measurement of resonant frequency 
2.2. Switch to power on FG. Choose the operational regimes similarly part 1. 
2.3. Switch to power on OS. Observe to see if an oblique ellipsoid occurs on the screen. 
1.3. Switch to power on OS. Observe to see to see an inclined oval trace displayed on the 
screen of OS. 
1.4. Regulating the knobs 8 and 9 of FG to change the generated frequency so that. The 
oval trace becomes an inclined line. 
Insert an additional column in table 4 then record the values of resonant frequency fparallel 
in it. 
2.5. Repeat the experimental procedure for more 2 times. 
2.6. Turn off OS and FG and uninstall the resistance box R0, capacitor CX and coil LX 
from the measurement circuit. At last, put all the devices in order. 
3. REQUIREMENTS 
3.1. Before doing the experiment 
Read carefully the instruction to understand: 
- the structure and operational principle of oscilloscope, the way to connect OS with a 
circuit and to manage the signal trace displayed on the oscilloscope’s screen. 
- the way to connect FGs with a circuit and to change the signal forms as well as their 
frequencies. 
3.2. After doing the experiment 
Complete the experimental report with the following requirements: 
- Calculate the unknown resistance. 
- Calculate the unknown capacitance 
 when UC = UX = UY = URo it leads to 
0..2
1 R
Cf
Z
X
X == π (19) 
 Hence: 
0..2
1
Rf
CX π= (20) 
- Calculate the unknown inductance 
 when, UC = UX = UY = URo it results in, 
0..2 RLfZ XL == π (21) 
 Hence: 
f
RLX .2
0
π= (22) 
- Compare the measured value of series and parallel resonant frequency together and. also 
with the predicted value using eq. (2) where L and C are the calculated capacitance and 
inductance as suggested in eq. (20) and (22).