ELECTRICAL ENGINEERING DEPARTMENT
Electrical Circuits 2 Manual
ACTIVITY 2B
IMPEDANCE OF RL CIRCUITS: PARALLEL RL CURCUITS
2B.1 Program Outcomes (POs) Addressed by the Activity
b. ability to design and conduct experiments, as well as to analyze and interpret data
d. ability to function on multidisciplinary teams
e. ability to identify, formulate, and solve engineering problems
g. ability to communicate effectively
2B.2 Activity’s Intended Learning Outcomes (AILOs)
At the end of this activity, the student shall be able to:
a. measure properly the voltage and current in a parallel RL circuit.
b. calculate the voltage and current in a parallel RL circuit.
c. evaluate results by comparing measured and calculated values.
2B.3 Objectives of the Activity
The objectives of this activity are to:
1. determine the characteristics of parallel RL circuits by using calculated
and measured values.
2. verify the result with an oscilloscope
2B.4 Principle of the Activity
When inductors are in parallel, the total inductive reactance is determined from reciprocal formula.
1
𝑋𝐿𝑇 = 1 1 1
+ +
𝑋𝐿1 𝑋𝐿2 𝑋𝐿3
When the two inductors are in a parallel, use the product-over-sum method to find the
inductive reactance.
𝑋𝐿1 × 𝑋𝐿2
𝑋𝐿𝑇 = 𝑋𝐿1 +𝑋𝐿2
Inductive reactance decreases as the number of inductors in parallel increases. The result is higher
circuit current and lower circuit impedance
ACTIVITY 2: IMPEDANCE OF RL CIRCUITS
As in circuits with resistors only, the voltage drop across each component in a parallel RL circuit
is the same. Figure 2.2-1 shows a parallel RL circuit. The total inductive is reactance is
determined as follows.
𝑋 ×𝑋
𝑋𝐿𝑇 = 𝑋𝐿1 + 𝑋𝐿2
𝐿1 𝐿2
1000 ×1500
𝑋𝐿𝑇 = 1000 +1500
15 × 105
𝑋𝐿𝑇 = 2,500
𝑋𝐿𝑇 = 600 Ω
Total resistance is that of R1
RT = R1 = 750Ω
Figure 2.2-1
The coil resistance of L1 and L2 were ignored to simplify the calculation. If coil resistance
is so small that they have minimal or no measurable effect on circuit performance, you can ignore
them.
Knowing total resistance and reactance, you can simplify the parallel circuit to two distinct
branches. Figure 2.2-2 shows the simplified (equivalent) parallel circuit.
Figure 2.2-2
The individual branch currents are determined from the applied voltage (Vac), Ohm’s law
and the branch Impedances. The current flowing through the resistive branch is show below.
ACTIVITY 2: IMPEDANCE OF RL CIRCUITS
IR = Vac / RT
IR = 8/750
IR = 0.0107 Apk-pk
The current through the inductive branch is determined as follows.
IL = Vac/ XLT
IL = 8/600
IL = 0.0113 Apk-pk
The total circuit (LT) current in milliamperes is calculated as shown.
IT = √IR 2 + IL 2
IT = √[0.0107)2 + (0.0113)2 ]
IT = 17.070 mApk-pk
Finally, the circuit impedance is determined from Vac, IT and Ohm’s Law
Z = Vac / IT
Z = 8 / 0.01707
Z = 468 Ω
2B.5 Materials/Equipment
1 – F.A.C.E.T. Base Unit
1 – AC1 FUNDAMENTALS Circuit board
2 – 15 Vdc Power Supply
1 – Osilloscope, dual trace
1 – Generator, sine wave
1 – Multimeter
ACTIVITY 2: IMPEDANCE OF RL CIRCUITS
2B.6 Procedure/s
1. Turn off the power sources. Insert the AC1 FUNDAMENTALS circuit board into the
base unit. Install the GENERATOR BUFFER if required. Turn on the power sources.
3. On the INDUCTANCE/ INDUCTIVE REACTANCE circuit bock, connect the
circuit shown Figure 2.2-3(a). Adjust VGEN so that Vac’ the voltage across R3 and L4’
equals as 3 Vpk-pk 20 kHz sine wave. Consider Vac as the input voltage to the circuit so
that the series resistor R1 can be ignored. With R1 ignored, the circuit shown in Figure
2.2-3(b) results.
Figure 2.2-3
3. Calculate XLT an RT (XLT = 2πfL4, RT = R3). Record your result in Table 2.2-1.
What type of circuit is shown in Figure 2.2-3(b)? __________________________.
XLT RT IL4 IR3 IT IT
(CALCULATED) (MEASURED)
Table 2.2-1
4. Calculate the current flowing through L4 (IL4 = Vac / XLT) and R3 (IR3 = Vac / RT).
Record your results in Table 2.2-1.
5. 5. Using the individual branch current (IL4 and IR3), calculate the total circuit [IT
(calculated) =√IR4 2 + IL3 2]. Record your result in Table 2.2-1.
ACTIVITY 2: IMPEDANCE OF RL CIRCUITS
6. Measure IT by using current sensing resistor R2 [IT (measured) = VR2/R2]. Record your
result in Table 2.2-1. Do the calculated and measured values of IT agree?
IT = ___________A
7. Copy the values for XLT and IT (measured) from Table 2.2-1 to Table 2.2-2(under the
column for parallel circuit with a single inductor).
PARALLEL RL CIRCUIT PARALLEL RL CIRCUIT WITH A
WITH A SINGLE INDUCTOR TWO INDUCTORS
XLT
IT
Z
Table 2.2-2
8. Determine the circuit impedance (Z = Vac/IT). Record your result in Table 2.2-2.
9. Use a two-post connector to add inductor L to the circuit as shown in Figure 2.2-4.
Readjust Vac to 3 Vpk-pk. Calculate the new value of XLT [XLT = XL3 XL4) / (XL3 + XL4)].
Record your result in Table 2.2-2. Did the added parallel inductor cause the total inductive
reactance to increase or decrease? ____________________________________________.
Figure 2.2-4
10. Measure the new IT, and record your result in Table 2.2-2 (IT = VR2/R2). Did IT increase
with the added parallel inductor? _____________________________________________
11. Use Vac and the measue value of IT to determine the circuit impedance (X = Vac/ IT).
Record your result in Table 2.2-2. Did the added parallel inductor cause the circuit
impedance to increase or decrease? ___________________________________________
ACTIVITY 2: IMPEDANCE OF RL CIRCUITS
2B.7 Activity Report
Section: Date Performed:
Course Code: Date Submitted:
Course Title:
Instructor:
Group No.: Activity No.:
Group Members: Signature:
1.
2.
3.
4.
5.
2B.7.1 Calculations
ACTIVITY 2: IMPEDANCE OF RL CIRCUITS
2B.7.2 Conclusion/s: Write at least three (3) conclusions.
ACTIVITY 2: IMPEDANCE OF RL CIRCUITS
2B.7.3 Rating (See Attached Rubric)
ACTIVITY 2: IMPEDANCE OF RL CIRCUITS
