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Hart, Hutchens, Prf. Strandquist, AC Circuits, Wednesday 2:00 pm
AC Circuits
Kalli Hart, Patrick Hutchens
Date due: April 10, 2023, Date submitted: April 10, 2023
Lab section: Wednesday 2:00 – 4:00pm, Lab instructor: Prf. Strandquist
Abstract:
The experiment sought to verify that Ohm’s laws, the equations, and the phasor
diagrams associated with AC circuits holds true in reality. This is important since the ability to
reliably work with and use AC current is a cornerstone to modern day technology and society.
The experiment found that the equations reliably predicted the self-inductance of the inductor
(0.172 H), the capacitance of the capacitor (11.69 𝜇𝐹), and the total voltage of the system (25.78
V). These were all within the acceptable ranges of the theoretical values.
Data and Analysis:
Figure 1:
Capacitor (12e-3 F)
Voltage:
(V)
Figure 2:
Resistor (101.6
O)
22.2
9.92
Both
24.3
Inductor
Voltage:
(V)
Resistance:
VRL:
Theta:
Figure 3:
11.72
98.4
9.84
32.9
VR
10.08
VC
22.7
VL
VR+C+L
(measured)
11.79
VLL
6.405
L
0.17
VTotal (calculated)
25.78
25.679
The following phasor diagrams were used to calculate the voltage across the resistor and the
capacitor (VR+C). The Inventor software was used to calculate the value to be 24.3 V.
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Hart, Hutchens, Prf. Strandquist, AC Circuits, Wednesday 2:00 pm
The following phasor diagram was used to calculate the measured voltage across the resistor,
inductor, and capacitor and was also calculated using Inventor software. The voltage across the
resistor, inductor, and capacitor and the phase angle was used as the input to find the value of
25.782 V.
The following equation used the current measurement from the galvanometer and the measured
resistance of the inductor to get the voltage across the resistance of the inductor. This value
was later used as shown below.
𝑣𝑅𝐿 = 𝐼 ∗ 𝑅𝐿
𝑣𝑅𝐿 = 0.1 ∗ 98.4
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Hart, Hutchens, Prf. Strandquist, AC Circuits, Wednesday 2:00 pm
𝑣𝑅𝐿 = 9.84
The phase angle (𝜃) was calculated using the voltage across the resistance of the inductor and
the voltage across the inductor. Was later used to calculate VR+L+C.
cos(𝜃) =
𝑣𝑅𝐿
𝑣𝐿
𝜃 = cos−1
𝑣𝑅𝐿
𝑣𝐿
𝜃 = cos −1
9.84
11.79
𝜃 = 32.9°
The following equation was used to find the capacitance of the capacitor used from the angular
frequency of the AC power provided by the outlets and the measured voltage across the
capacitor.
𝑉𝐶 =
𝐶=
𝐼
𝜔𝐶
𝐼
𝜔𝑉𝐶
(0.1)
(120𝜋)(22.7)
𝐶=
𝐶 = 11.69 𝜇𝐹
The following equation derived from Ohm’s Law was used to find the self-inductance of the
inductor using the measured current, angular frequency of the AC current from the wall outlets,
and the voltage across the inductance of the inductor. The expected value of the self-inductance
was 0.1-0.2 H, making this value a reasonable answer.
𝑉𝐿𝐿 = 𝐼𝜔𝐿
𝐿=
𝐿=
𝑉𝐿𝐿
𝐼𝜔
(6.49)
(0.1)(120𝜋)
𝐿 = 0.172 𝐻
Error Analysis:
The sources of error in the experiment could include some small amount of voltage
being dissipated by the wires and various imperfections of the circuit. However, it is unlikely that
that effect would be sufficiently large to cause any meaningful impact. Another source of error
that would be far more likely is the human error of miscalculations and from misreading the
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Hart, Hutchens, Prf. Strandquist, AC Circuits, Wednesday 2:00 pm
galvanometer. While none were noticed, it is always possible that some of the measurement
devices were in the wrong setting or some other slight but impactful error.