Contents

Introduction ........................................................................................................................................... 3
Objective ................................................................................................................................................ 5
Experimental Work ............................................................................................................................... 5
List of Equipment and Components ................................................................................................. 5
Experimental Procedure.................................................................................................................... 5
• Part I: Sinusoidal Steady-State Power Calculations: ..................................................................... 6
• Part II: Power factor correction: ................................................................................................... 6
Results.................................................................................................................................................... 7
o Steady wave power calculations ................................................................................................... 7
o Power factor correction ................................................................................................................ 8
Discussion .............................................................................................................................................. 9
Post lab questions ................................................................................................................................ 9
Conclusion ........................................................................................................................................... 10
Reference ............................................................................................................................................. 11

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 Introduction
Theory
Power factor
The cosine of the phase angle between the voltage and the current is the power factor:
𝑝𝑓 = cos(𝜃𝑣 − 𝜃𝑖 )
The angle of power factor is 𝜃 = 𝜃𝑣 − 𝜃𝑖

• With a lagging power factor, an inductive load results from the current trailing the
voltage.
• Leading power factor: capacitive load because current precedes voltage.
• A purely resistive load has a unity power factor, which is defined as the current in phase
with the voltage.
The ratio of average power to apparent power is another way to describe power factor:
𝑃
𝑝𝑓 =
𝑆
Power factor correction is the process of raising the power factor as near to unity as possible
without changing the voltage or current applied to the initial load. This is often accomplished by
adding a reactive element in parallel with the load.

The power triangle

A geometric link between the power factor angle is 𝜃 = 𝜃𝑣 − 𝜃𝑖 , apparent power |𝑆|, ractive power
Q, and average power P is provided by complex power.

Figure 1: a power triangle

Figure 2: summary of AC power term

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Steady-state power calculations
The sinusoidal steady-state average, reactive, and power calculations for the voltage
supply and passive circuit parts are displayed in figure 3.

Figure 3: Summary of average and reactive power calculations

Conservation of power
Energy conservation dictates that the total of the complex, average, and reactive
powers connected to each n element in a circuit made up of n elements must equal
zero:
𝑛 𝑛 𝑛

∑ 𝑠𝑖 = 0 ∑ 𝑝𝑖 = 0 ∑ 𝑄𝑖 = 0
𝑖=1 𝑖=1 𝑖=1

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Objective
• To calculate average, reactive, complex powers by measuring the voltage and current.
• To measure the phase shift 𝜃 = 𝜃𝑣 − 𝜃𝑖 and calculate the power factor.
• To verify the conservation of complex power of a circuit.
• To correct the power factor of a load

Experimental Work
List of Equipment and Components
The equipment and materials listed below were used to conduct the experiment:

• Function generator (FG)

• Digital storage oscilloscope (DSO)
• Digital multimeter (DMM)
• Resistance Substitution Box
• Inductance Substitution Box
• Capacitance Substitution Box

Experimental Procedure
There is 2 sections to the experiment. These sections entail monitoring the voltage and current,
computing the phase shift 𝜃 = 𝜃𝑣 − 𝜃𝑖 , and calculating the power factor to determine the
average, reactive, complex powers.
First Connect the circuit shown in Figure 4 on the breadboard after choosing four resistors as per
the prelab instructions.

Figure 4: circuit diagram

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 • Part I: Sinusoidal Steady-State Power Calculations:

1. 1.Adjust the second Resistance Substitution Box to set 𝑅1 = 1𝑘Ω, or use a 1𝑘Ω discrete
resistor.
2. Adjust the second Resistance Substitution Box to set 𝑅3 = 2𝑘Ω, or use a 2𝑘Ω discrete resistor.
3. Adjust the Inductance Substitution Box to set L=100mH.
4. Adjust the Capacitance Substitution Box to set 𝐶 = 0.1𝜇𝐹.
5. Set the Function Generator (FG) to produce a 1 kHz sinusoidal waveform with the required
voltage level. And make sure that the ‘High Output Impedance’ is activated.
6. Connect the circuit as shown in the circuit diagram in Figure 4.
7. Turn on the oscilloscope and load the default oscilloscope setup.
8. Connect channel 1 probe on the oscilloscope to the source node, and channel 2 probe to the
resistor 𝑅1 node. Use auto-scale.
9. Adjust the horizontal scale (time per division), horizontal position vertical scale (voltage per
division) and vertical position as suitable.
10. Measure the period T and the resistor 𝑅1 voltage 𝑉𝑅1 𝑃𝑃.
11. Use the Math function to display 𝑉𝑅𝐿𝐶 , the voltage of the parallel combination (L || C || 𝑅3 ) and
measure it peak-to-peak.
12. Use the cursors to measure the time shift ΔT between 𝑉𝑆 and 𝑉𝑅1
13. Calculate the phase shift 𝜃 and the power factor.
14. Complete the measured values in Table 1-1 in the datasheet.
15.Complete the power calculations in Table 1-2 in the datasheet using the measured values in
Table 1-1.

• Part II: Power factor correction:

16. Adjust the Capacitance Substitution Box to set 𝐶 = 0.25𝜇𝐹.

17. Redo the steps (12) and (13).
18. Complete the measured values in Table 1-3 in the datasheet.

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Results
This section supplies a summary of the experiment's findings from both the simulation and the real
world. The OrCAD simulation and the waveform for every part is seen below.
o Steady wave power calculations

Table 1-1: Voltage and Time Measurements

𝑉𝑆 𝑃𝑃 (V) 𝑉𝑅1 𝑃𝑃 (V) 𝑉𝑅𝐿𝐶 𝑃𝑃 (V) Δ𝑇 (𝜇𝑠) 𝑇 (𝜇𝑠) 𝜃° pf

Simulated 10 6.0880 3.912 96.576 1000 34.76 0.978

Measured 10 5.92 5.44 76 1000 27.36 0.888

Table 1-2: Power calculations

𝑃𝑉𝑆 (mV) 𝑄𝑉𝑆 (mVAR) 𝑃𝑅1 (mV) 𝑃𝑅3 (mV) 𝑄𝐿 (mVAR) 𝑄𝐶 (mVAR)
Simulated -25.2 -17.02 50 25 0.072 34.577
Measured -25.2 -17.02 50 25 0.072 34.577

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o Power factor correction

Table 2:Power Factor Correction

Sinusoidal Δ𝑇 (𝜇𝑠) 𝜃° pf
Simulated 0 0 1
Measured 0 0 1

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Discussion
Post lab questions

Part I: Steady-State Power Calculations

Q1 Verify that the average power generated equals the average power absorbed using the
simulated values in Table 1-2.

∑ 𝑃 = −25.2 ∗ 10−3 + 50 ∗ 10−3 + 25 ∗ 10−3 = 0.0492 𝑊

Q2 Verify that the reactive power generated equals the reactive power absorbed using the
simulated values in Table 1-2.

∑ 𝑄 = −17.02 ∗ 10−3 + 0.072 ∗ 10−3 + 34.577 ∗ 10−3 = 0.0176 𝑉𝐴𝑅

Part II: Power Factor Correction

Q3: Why it is important to correct the power factor of a load?
reduces the amount of current drawn, which lowers power costs, produces less heat, and
lengthens the electrical system's lifespan.
Q4: Find the ideal value of the capacitor theoretically that will result in unity power factor .
𝑄𝐶 = 34.557VAR V = 10V
100
𝑋𝐶 = = 2.89Ω
34.557
1 1
𝐶= = = 0.05𝜇𝐹
2𝜋𝑓𝑋𝐶 2 ∗ 𝜋 ∗ 1 ∗ 2.89

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Conclusion
• The experiment leads us to the conclusion that when the capacitance diminishes, ∆𝑇 and 𝜃
approach zero, altering the pf to unity.
• Each circuit element has a unique complex power, and the total of all the circuit elements'
complex powers equals 0.
• Reactive power and the resistor are equivalent in any electrical circuit as resistance in a
circuit has only one act of power.

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Reference
Riedel, N. &. (n.d.). electric circuits. pearson.
Fundamentels of electrical circuits lab manual

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