Republic of the Philippines
BULACAN STATE UNIVERSITY
COLLEGE OF ENGINEERING
City of Malolos, Bulacan
CIRCUITS 2
LABORATORY MANUAL
Names:
_______________________________________________
_______________________________________________
_______________________________________________
_______________________________________________
Section:
Instructor:
Score:
Date:
Engr. Diane H. Villanueva
Capacitive Reactance
ACTIVITY No. 4
OBJECTIVES
To examine the capacitive reactance and its relationship to capacitance and frequency, including
a plot of capacitive reactance versus frequency.
INTRODUCTION
The current – voltage characteristic of a capacitor is unlike that of typical resistors. While resistors
show a constant resistance value over a wide range of frequencies, the equivalent ohmic value
for a capacitor, known as capacitive reactance, is inversely proportional to frequency. The
capacitive reactance may be computed via the formula:
𝑋𝐶 = −𝑗
1
2𝜋𝑓𝐶
The magnitude of capacitive reactance may be determined experimentally by feeding a capacitor
a known current, measuring the resulting voltage, and dividing the two, following Ohm’s law.
This process may be repeated across a range of frequencies to obtain a plot of capacitive reactance
versus frequency. An AC current source may be approximated by placing a large resistance in
series with an AC voltage, the resistance being considerably larger than the maximum reactance
expected.
EQUIPMENT AND MATERIALS
AC function generator
(1) 1 μF capacitor
Oscilloscope
(1) 2.2 μF capacitor
Digital Multimeter
(1) 10 kΩ resistor
SCHEMATIC DIAGRAM
Figure 4.1 Series RC Circuit
PROCEDURE
1. Using Figure 4.1 with Vin = 10 V p-p and R = 10 kΩ, and assuming that the reactance of
the capacitor is much smaller than 10kΩ and can be ignored, determine the circulating
current using measured component values and record in Table 4.1.
2. Build the circuit of Figure 4.1 using R = 10 kΩ, and C = 1 μF. Place one probe across the
generator and another across the capacitor. Set the generator to a 200 Hz sine wave and
10 V p-p. Make sure that the Bandwidth Limit of the oscilloscope is engaged for both
channels. This will reduce the signal noise and make for more accurate readings.
3. Calculate the theoretical value of Xc and record in Table 4.2.
4. Record the peak-to-peak capacitor voltage and record in Table 4.2.
5. Using the source current from Table 4.1 and the measured capacitor voltage, determine
the experimental reactance and record it in Table 4.2. Also compute and record the
deviation.
6. Repeat steps three through five for the remaining frequencies of Table 4.2.
7. Replace the 1 μF capacitor with the 2.2 μF unit and repeat steps two through six, recording
results in Table 4.3.
8. Using the data of Tables 4.2 and 4.3, create plots of capacitive reactance versus frequency
on a graphing paper. Plot to scale. Create separate graphs for 1 μF and 2.2 μF capacitors
and label properly.
DATA TABLES
Table 4.1 Current Source
𝑖𝑠𝑜𝑢𝑟𝑐𝑒 (𝑝−𝑝)
Table 4.2 Reactance and Voltage of 1 μF Capacitor
Frequency (Hz)
200
400
600
800
1.0 k
1.2 k
1.6 k
2.0 k
XC Theory (Ω)
VC(p-p) Exp (V)
XC Exp (Ω)
% Dev
XC Exp (Ω)
% Dev
Table 4.3 Reactance and Voltage of 2.2 μF Capacitor
Frequency (Hz)
200
400
600
800
1.0 k
1.2 k
1.6 k
2.0 k
XC Theory (Ω)
VC(p-p) Exp (V)
QUESTIONS
1. What is the relationship between capacitive reactance and frequency?
Capacitive reactance (X_C) is inversely proportional to frequency (f), as indicated by the
formula:
XC= 1 /2πfC1
This implies that when the frequency is raised, capacitive reactance lowers, permitting greater
current flow through the capacitor. At lower frequencies, however, the reactance increases,
limiting current flow. This is the reason capacitors are usually applied in high-pass filters,
allowing high-frequency signals while blocking low-frequency signals.
2. How does capacitive reactance depend on capacitance?
The capacitive reactance is also directly proportional to the reciprocal of capacitance (C), and the
equation remains the same:
XC= 1 /2πfC1
A greater capacitance yields smaller reactance, allowing for greater AC current flow at the same
frequency. This is because a capacitor with larger capacitance can supply and accept more charge
per cycle. This is important in such applications as power factor correction, where capacitors are
3. Suppose the experiment were to be repeated using frequencies 10 times those of Table 4.2.
If the frequency is ten times higher, the capacitive reactance will be reduced by the same factor.
Consequently:
- The graphs plotted would shift downwards, showing smaller (X_C) values at every frequency
point.
- The capacitor would carry more current, practically acting as a short circuit at high frequencies.
- The voltage drop across the capacitor would be much smaller.
- On a linear scale, the inverse relationship would still hold but be compressed towards lower
reactance values.
- In a log-log graph, the line would curve in the same downward direction but shift appropriately.
This is exactly what is desired for signal processing where applications include removing
unwanted low-frequency noise using high-pass filters.
4. What if the experiment were done with frequencies 10 times lower than in Table 4.2?
If the frequency were lowered by a factor of 10:
- The capacitive reactance would go up ten times, so that the capacitor would be even closer to
an open circuit for AC.
- The graphs plotted would move higher up, on graphs showing very large (X_C) values for all
frequencies.
- The capacitor would limit the flow of AC current, with greater voltage drop across it.
- The curve of reactance on a linear graph would stretch up, highlighting its resistance to lowfrequency signals.
- Capacitors are less efficient at passing AC at lower frequencies in real-world circuits, and that
is why they are commonly employed to filter out DC signals.
This is the reason why capacitors are an important component of low-pass filters, passing lower
frequencies while suppressing higher frequencies.