**Unformatted text preview: **Physics 2 Lab
Experiment 8.1
Series LCR resonance
Prof. Marjan
10/25/2018 Purpose The purpose of this experiment is to study resonance in a series inductor-capacitor-resistor
(LCR) circuit by examining the voltage across the resistor as a function of frequency of the
applied sine wave. Equipment
L-C-R board with L = 3.3 mH, C = 0.39 μ F, R = 100 Ω , PASCO 850 interface, one voltage sensor (PASCO UI-5100), computer. Theory
In a series RLC circuit there becomes a frequency point were the inductive reactance of the
inductor becomes equal in value to the capacitive reactance of the capacitor. In other words, XL
= XC. The point at which this occurs is called the Resonant Frequency point, ( ƒr ) of the circuit,
and as we are analysing a series RLC circuit this resonance frequency produces a Series
Resonance.
Series Resonance circuits are one of the most important circuits used electrical and electronic
circuits. They can be found in various forms such as in AC mains filters, noise filters and also in
radio and television tuning circuits producing a very selective tuning circuit for the receiving of
the different frequency channels. Conclusion
By observing the characteristics of a series RLC circuit, we were able to determine the
resonance of the circuit. It can be concluded that four values depend on the frequency of the
function generator, which are impedance, capacitive reactance, inductive reactance, and the
phase shift angle between voltage and current. The extreme values (maximum or minimum) are
reached at resonance. We got a percent error of 3%. Human error, estimation, and minor
fluctuations in the power supply were sources of error. Nicole Samuelson
Physics 2 Lab
Experiment 8.2 Phase angle ϕ versus frequency
Prof. Marjan
10/25/2018 Purpose
The purpose of this experiment is to measure the phase angle
circuit at f ❑ < f res (theory) , f ❑ = f res (theory) , f ❑ > ϕ of the series LCR f res (theory) . Equipment
L-C-R board with L = 3.3 mH, C = 0.39 μ F, R = 100 Ω , PASCO 850 interface, one voltage sensor (PASCO UI-5100), computer. Theory
Same as 8.1 . Conclusion
When completing this experiment, we were able to understand that the phase angle can
be determined in a LCR circuit when the time difference between the sine waves are
found. This can be proven by looking at the Lissaious curve (oval shape) as well as the
3 -D curve to find the angle. In order to produce the Lissaious curve, an individual would
have to apply the source voltage and voltage across the resistor to the y-axis and x-axis
inputs to an oscilloscope, which causes the differences between v ❑ and v R to produce an elliptical pattern on the screen. When obtaining the elliptical pattern, one
must then time it perfectly so the pattern forms a straight line. By doing so, this
becomes an intuitive and accurate approach when finding the resonance frequency of
the series LCR circuit. After obtaining our data regarding the Lissaious curve, we were
able to acquire accurate results, due to capturing a decent straight line. Furthermore,
we were able to understand what the fast Fourier transform (FFT) converts, which is
time to frequency. We learned that FFT is the most important numerical algorithm of this
lifetime and it contains a sine which consists of a single frequency only that is known to
exist over infinite time that never changes. Rooms for error within our experiment can
be from not capturing precisely the correct straight line which lead to incorrect data
throughout the experiment. ...

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- Fall '18
- RLC, Prof. Marjan