DE4401 ELECTRICAL AND ELECTRONICS PRINCIPLES 1
APTE 5601 ELECTRICAL AND ELECTRONICS
PRINCIPLES
LAB 5: AC CAPACITANCE
Name:
Student ID:
Date:
Supervisor Signature:
OBJECTIVES
You will connect several circuits illustrating the characteristics of capacitance in ac circuits. In
completing these tasks, you will connect circuits, make measurements, perform calculations, draw
conclusions, and be able to answer questions about the following items related to capacitance:

Characteristics of capacitance in ac circuits
o The XC Formula

Relationship of XC to capacitance value

Relationship of XC to frequency
REQUIREMENTS
For the following Lab you will need:
 Breadboard
 Multimeter
 Oscilloscope
 Signal Generator
 Calculator
NOTE MEASUREMENTS AND OBSERVATIONS CAN BE PERFORMED IN A GROUP,
BUT CONCLUSIONS MUST BE INDIVIDUAL.
DE4401 Lab 5 AC capacitance
Page 1
CAPACITANCE IN AC CIRCUIT: THE XC FORMULA
XC of a capacitor is capacitive reactance in ohms, described by the following formula:
𝑋𝐶 =
1
1
=
𝜔𝐶 2𝜋𝑓𝐶
The formula shows that XC is inversely proportional to the frequency and to the capacitance value.
The rationale we might use in understanding this formula is as follows:
A larger C requires more charge to arrive at a given voltage (difference of potential) between its
plates. This means that more charging (and discharging) current must flow in the circuit in order
for the capacitor to “follow” the ac voltage applied to it at a given frequency than a smaller C
would require under the same conditions. More current flowing for a given applied voltage
indicates a lower opposition. A higher frequency also causes more charge and discharge current to
flow per unit time in order for the voltage across the capacitor to follow the applied voltage.
We aim to verify the XC formula by changing C and f values in a simple RC circuit and
making measurements and appropriate Ohm’s Law calculations to see if the formula is
valid. CALCULATE 𝑿𝑪 now:
YOU WILL NEED:



Resistor 10 kΩ
Capacitors: 0. 1 μF and 1.0 μF
Audio Generator
DE4401 Lab 5 AC capacitance
Page 2
PROCEDURE
1. Connect the initial circuit as in Figure 2.
Figure 2
2. Set the function generator at a frequency of 150 Hz and VA at 3 volts.
a. Measure VR and then calculate I.
VA = ___________________________ V.
VR = ___________________________ V.
I = _____________________ mA.
b. Measure VC and use the calculated I to determine XC by Ohm’s Law (XC = VC /I)
VC = ___________________ V.
XC by Ohm’s Law approximate = ________________ Ω.
c. Calculate XC by the XC formula.
XC by XC formula = __________________________ Ω.
OBSERVATION
Was the XC calculated by the capacitive reactance formula close to the value determined by
Ohm’s Law? ____________________.
Two reasons for the XC values calculated by Ohm’s Law method and XC formula not being the
same might be the resistor and capacitor _____________________________ and meter
________________ effects.
DE4401 Lab 5 AC capacitance
Page 3
PROCEDURE (CONT)
3. Change the frequency to 75 Hz and keep VA at 3 volts. Make the measurements and
calculations described above:
Figure 3
a. Measure VR and then calculate I.
VA = ___________________________ V.
VR = ___________________________ V.
I = _____________________ mA.
b. Measure VC and use the calculated I to determine XC by Ohm’s Law (XC = VC /I)
VC = ___________________ V.
XC by Ohm’s Law approximate = ________________ Ω.
c. Calculate XC by the XC formula.
XC by XC formula = __________________________ Ω.
OBSERVATION
Lowering the frequency to one-half its previous value caused the XC to (increase, decrease)
____________________ to a value nearly (double, half ) ________________ the original.
DE4401 Lab 5 AC capacitance
Page 4
PROCEDURE (CONT)
4. Keep the frequency at 75 Hz, but change C to 1 μF. Measure and calculate as before.
Figure 4
a. Measure VR and then calculate I.
VA = ___________________________ V.
VR = ___________________________ V.
I = _____________________ mA.
b. Measure VC and use the calculated I to determine XC by Ohm’s Law (XC = VC /I)
VC = ___________________ V.
XC by Ohm’s Law approximate = ________________ Ω.
c. Calculate XC by the XC formula.
XC by XC formula = __________________________ Ω.
OBSERVATION
Increasing C by a factor of 10 caused the XC to (increase, decrease)__________.
Did the XC approximately change by a factor of 10? ________.
From the observations we have made, does it appear that the XC formula is functional for
predicting parameters in practical circuits? __________________________.
DE4401 Lab 5 AC capacitance
Page 5
Plot Variation of XC against Frequency and Capacitance value
DE4401 Lab 5 AC capacitance
Page 6
Summary
Capacitive Reactance in AC
Name: ____________________________________________________ Date: __________________
Complete the following review questions, indicating the appropriate response by placing a check
next to the correct answer.
1. XC is measured in ohms because it limits ac current to a value of
a. 0.159 × f × C
b. 0.159/f C
c. V/XC
d. none of these
2. The formula for XC is
a. XC = 2π/fC
b. XC = fC/0.159
c. XC = 1/2πfC
d. none of these
3. For a given value of C, if f is increased, then XC will
a. increase
b. remain the same
c. decrease
4. For a given value of f, if C is decreased, then XC will
a. increase
b. remain the same
c. decrease
5. A capacitor appears to oppose a change in voltage because current must flow before a
difference of potential can be established across a capacitor.
a. True
b. False
6. Since capacitors in series add like resistors in parallel, the XC of two series capacitors will
be
a. greater than either one alone
b. less than either one alone
DE4401 Lab 5 AC capacitance
Page 7
7. Capacitive reactances in parallel add like resistances in
a. series
b. parallel
c. neither of these
8. If C and f are both doubled in a given circuit, the XC will
a. increase two times
b. increase four times
c. decrease two times
d. decrease four times
9. If C is doubled and f is halved in a given circuit, the XC will
a. increase
b. remain the same
c. decrease
10. What is the total capacitive reactance of two series 1-μF capacitors at a frequency of 200
Hz?
a. 3180 Ω
b. 1.59 kΩ
c. 15.9 Ω
d. 31.8 kΩ
e. 318 Ω
f. none of these
DE4401 Lab 5 AC capacitance
Page 8