AC 1 Fundamentals
Capacitive Reactance
Exercise 3: Parallel RC Circuits
EXERCISE OBJECTIVE
When you have completed this exercise, you will be able to determine characteristics of parallel RC
circuits by using calculated and measured values. You will verify your results with an oscilloscope.
DISCUSSION
XCT =
1
1
1
1
+
+
XC1 XC2 XC3
When just two capacitors are in parallel, you use the product-over-sum method to determine total
capacitive reactance.
XCT =
XC1 × XC2
XC1 + XC2
Capacitive reactance decreases as the number of capacitors in parallel increases, resulting in a higher
circuit current and a lower circuit impedance.
What is the total capacitive reactance (XCT) in the circuit shown below?
XCT =
XC1 × XC2
XC1 + XC2
XCT =
(Recall Value 1)
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When resistors are in parallel, total resistance (RT) is determined from the reciprocal formula. Since there
is only one resistor in the circuit shown above, RT equals R1 (500 :).
consisting of two distinct branches: one resistive branch and one reactive branch.
The voltage across each component in a parallel RC circuit is the same. To determine individual branch
currents, divide the applied voltage (Vac) by the branch impedances.
ICapacitor = VAC
IResistor = VAC
CT
T
In RC parallel circuits, total circuit current (IT) does not equal the individual branch currents but the square
root of the sum of the squares of the individual branch currents.
IT = IR 2 + IC2
Calculate total circuit current (IT).
IR = VAC
T
IC = VAC
CT
pk-pk
pk-pk
IT = IR 2 + IC2
IT =
mApk-pk (Recall Value 2)
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AC 1 Fundamentals
Capacitive Reactance
In a parallel RC circuit, the circuit impedance is determined by the following formula.
Z=
R × XC
R 2 + XC 2
C
and R in parallel is to divide the total current
into the applied voltage.
Z=
VAC
IT
When capacitance is increased in a parallel RC circuit, the capacitive reactance decreases, and more
voltage and circuit current increases.
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PROCEDURE
฀
If necessary, clear the AC 1 FUNDAMENTALS circuit board of all two-post connectors and
any other connections.
฀
shown (be sure to short out R1 and R2 with two-post connectors).
฀
Adjust VGEN for a 10 Vpk-pk, 1 kHz sine wave.
In the next few steps, you will measure the total circuit current (IT
through reactive branch C4 (IC4) and resistive branch R3 (IR3).
฀
฀
Since the voltage across each component in a parallel RC circuit is the same, you can
determine the individual branch currents by dividing the applied voltage (VGEN) by the branch
impedance.
IC4 =
VGEN
10
=
= 6.3 mA pk-pk
XC4
1590
IR3 =
VGEN
10
=
= 6.7 mA pk-pk
R3
1500
Determine total circuit current (IT).
NOTE: To determine the ac circuit current, remove the two-post connector and use the oscilloscope to
measure the peak-to-peak voltage drop across sensing resistor R2. Take the measurement and divide the
value by the resistance of R2 (10 :). Replace the two-post connector before moving on to the next step.
IT = VR2
IT =
mApk-pk (Recall Value 1)
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฀
Capacitive Reactance
Compare your value of measured total circuit current (IT =
mA [Step 5, Recall
Value 1]) to the reactive branch current (IC4
resistive branch current (IR3 = 6.7 mA [second value calculated in Step 4])
Does IT equal the sum of the individual branch currents in a parallel RC circuit?
a. yes
b. no
In the circuit shown, IT is calculated from the following equation.
IC4 = 6.3 mApk-pk
IR3 = 6.7 mApk-pk (second value calculated in Step 4)
IT = IR32 + IC42
IT = (6.7 × 10−3 )2 + (6.3 × 10 −3 )2 = 9.2 mA pk-pk
This calculated value is approximately equal to your measured value of IT
(
mApk-pk [Step 5, Recall Value 1]).
Practically, the total impedance of a parallel RC circuit can be found by dividing the total circuit
current (IT) into the applied voltage (VGEN). Using the previously measured circuit current, the
circuit impedance is equal to:
Z=
*Z
VGEN
10 V
=
IT
_________ mA ([Step 5, Recall Value 1]/1000)
=
:
* Certain calculated answers based on measured Recall Values are not included in the Instructor Guide. The instructor may
use Recall Value nominal answers from the Instructor Guide to determine if the calculated answer by the student is within the
nominal value range.
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Use a two-post connector to add capacitor C3 to the circuit. Readjust VGEN for a 10 Vpk-pk
sine wave at 1 kHz.
Does the added parallel capacitor cause total capacitive reactance (XCT) to increase or to
decrease?
a. increase
b. decrease
฀
Determine the new total circuit current (IT) by using sensing resistor R2.
NOTE: To determine the ac circuit current, remove the two-post connector and use the oscilloscope to
measure the peak-to-peak voltage drop across sensing resistor R2. Take the measurement and divide the
value by the resistance of R2 (10 :). Replace the two-post connector before moving on to the next step.
IT = VR2
IT =
mApk-pk (Recall Value 2)
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Capacitive Reactance
฀
you measured:
Z=
*Z
฀
฀
VGEN
10 V
=
IT
_________ mA ([Step 8, Recall Value 2]/1000)
=
:
Compare your value of circuit impedance with one capacitor (
: [value calculated
in Step 6]) to the value of circuit impedance with two capacitors (
: [value
calculated in Step 9]). Did the added parallel capacitor cause the circuit impedance to
increase or decrease?
a. increase
b. decrease
Do not turn off the equipment. The FACET setup is needed to answer a review question.
CONCLUSION
•
You determine total capacitive reactance of capacitors in parallel from the reciprocal formula.
•
As capacitors are added in parallel, circuit current increases, circuit impedance decreases, and
capacitive reactance decreases.
•
Total circuit current equals the square root of the sum of the squares of the resistive and capacitive
branch currents.
* Certain calculated answers based on measured Recall Values are not included in the Instructor Guide. The instructor may
use Recall Value nominal answers from the Instructor Guide to determine if the calculated answer by the student is within the
nominal value range.
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REVIEW QUESTIONS
1.
circuit board, and connect the circuit shown. Adjust VGEN for a 10 Vpk-pk, 1 kHz sine wave.
With an oscilloscope, monitor the circuit current by observing the voltages across current-sensing
resistor R2.
Place CM switch 10 in the ON postion to add an unseen 0.1 PF capacitor in parallel with C3. While
observing the oscilloscope, turn CM switch 10 off and on.
Based on your observation of the circuit current, you conclude that adding a parallel capacitor to the
RC circuit
a. decreased circuit current.
b. increased circuit impedance.
c. decreased circuit impedance.
d. had no effect on the circuit.
2. An RC circuit consisting of two parallel-connected capacitors with reactances of 750 : and 75 k: has
a total capacitive reactance of
a. 75.75 k:.
b. 743 :.
c. 770 :.
d. 75 k:.
3. The circuit current of a parallel RC circuit equals the square root of the sum of the
a. squares of the resistive and capacitive branch voltages.
b. resistive and capacitive branch voltages.
c. squares of the resistive and capacitive branch currents.
d. resistive and capacitive branch currents.
4. The total capacitive reactance of capacitors in parallel is
a. the sum of the individual capacitances.
b. the sum of the individual reactances.
c. determined from the reciprocal formula.
d. the reciprocal of the individual capacitances.
5. As capacitors are added in parallel,
a. phase angle increases.
b. circuit current decreases.
c. circuit impedance increases.
d. capacitive reactance increases.
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