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Course: PHYS204
Section: Module 5
Name: Kaitlin Hinds
Instructor Name: Dr. Felix Rizvanov
__________________________________________________________________________
Title
: Current vs. Frequency in an AC Circuit
__________________________________________________________________________
Abstract
: This experiment was set up to prove that the maximum peak current will be found when an AC circuit is set at its resonance frequency. Using a computer program, I was able to study the effect of frequency on peak current within an AC circuit containing a capacitor and inductor. I was able to calculate the resonance frequency and other frequencies to compare the peak currents. Using a constant capacitance and inductance, the highest peak current was overserved when the AC current source was set to its resonance frequency. The peak current rose as the frequency approached the resonance value and tapered off at values greater than the resonance frequency. The lab proved that the AC circuit will produce a higher current for a given voltage when the current source is set to its resonance frequency.
__________________________________________________________________________
Introduction: The purpose of this lab was to study the response of current to varying frequencies within an AC circuit. The experiment seeks to prove the theory that at a certain capacitance and inductance, the maximum current produced within an AC circuit is seen at the resonance frequency. The voltage is held constant throughout, proving the change in current is due to the frequency. As the frequency approaches the resonance frequency, the peak current will
rise. The peak current will then start to decline once past the resonance frequency. The report compares the recorded peak currents at seven different frequencies. Three of these frequencies were lower than the resonance frequency, and three were greater than the resonance frequency. The equation necessary for this experiment:
f
0
=
1
2
π
√
LC
Equation 1
where f
0
represents resonance frequency, L represents inductance, and C represents capacitance. This was used to find the resonance frequency. It was observed that the highest peak current was recorded at the resonance frequency
__________________________________________________________________________
Methods: I used the AC circuit construction kit from PHET Colorado to build an AC circuit containing an inductor, a capacitor, and an AC current source. I set the capacitance at 0.09 Farads and the inductance at 10 Henrys as told in the instructions. For the AC current source, I set the frequency to 0.48 Hz and observed the circuit. Next, I set the frequency to the resonance frequency of 0.16 Hz, and I overserved the circuit. I then compared the two sets of observations.
Afterwards, added a resistor with a resistance of 0.1 Ohms to the circuit. Then, I recorded the peak currents measured at seven different frequencies of 0.10, 0.12, 0.14, 0.16, 0.18, 0.2, and 0.24 Hz. __________________________________________________________________________
Results:
For this experiment, I first observed
an AC circuit at two different frequencies, one
of which being the resonance frequency. First,
I built a circuit that contained an inductor a
capacitor and an AC current source. I then set
the frequency of the current source to 0.48 Hz
and observed a graph of the current and the
graph of the voltage. I noticed that the current
graph was uneven as seen in Figure 1. The
peak current was observed at 0.5 Amps, and
the voltage completed one full cycle every four
seconds. Next, I used Equation 1 to solve for the
resonance frequency using the given inductance of
10 Henrys and capacitance of 0.09 Farads. I found
the resonance frequency to be 0.16, and that is
what I set the frequency of the AC current
source to. I observed the current graph and the
voltage graph and compared my findings with
the findings from figure one. Unlike figure
one, the voltage of this circuit completed a full
cycle in 6 seconds. The current traveled at a
much steadier pace. The peak current was
measured at 15 Amps, as seen in Figure 2.
Then, I added a low resistance-resistor to my
circuit and recorded the peak current at varying
frequencies. The data showed a rise in current
that was its highest at the value for resonance
frequency, and then it tapered off.
The following table illustrates the observed peak current when the AC current source is set to different frequencies.
Frequency (Hz)
0.10
0.12
0.14
0.16
0.18
0.20
0.24
Peak Current (A)
1.5
2.0
3.0
7.5
7.0
5.5
3.0
The data indicates a change in frequency resulted in a change in peak current.
Figure 1 Screen shot of the AC circuit set to a frequency of 0.48 Hz
Figure 2 Screen shot of the AC circuit set to the resonance frequency of 0.16 Hz
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