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Lab 1 RLC Series Circuit Resonance, Complex Impedance 01-11-2024
Complements: Complex Numbers
Solution of the forced harmonic mechanical oscillator usingphasors
Representation of harmonic waves using phasors
Writeup required
The write up report for Lab-1 due date is Thursday Feb 1st
Send electronic copy to kacharat@pdx.edu (with copy to andres@pdx.du)
Complementary information
LC Parallel Circuit Resonance, complex impedance
PURPOSE
To observe the frequency-dependence of impedance in an alternating current (AC) circuit. We will measure the resonance frequency and use its value to determine the inductance of a coil, assuming the values of the capacitance and the resistor. The oscilloscope will be used to measure the phase lags between voltage and the current across a resistor, a capacitor and an inductor. The analysis is undertaken using complex variable.
THEORETICAL CONSIDERATIONS
I. Impedance
IA. The RLC Circuit in series
IB Relationship between the voltage and current across each element
Resistance
Capacitor complex impedance
Inductor complex impedance
II. Kirchhoff law for the RLC circuit
III. How to calculate and measure current amplitude Io(w) and phase lag j (w) ?
Complex impedance of the RLC-series circuit
Calculation of Io and j
IV. Resonance
Resonance condition
Relative orientation of the phasors input voltage vA and current response i at different values of w
Example: Analysis at resonance and out of resonance conditions
EXPERIMENTAL CONSIDERATIONS
Experimental setup
Measurements
a) Find the resonance frequency. Use the result to figure out the value of L
b) Plot as a function of w (make sure the input voltage remains constant as you select the different values of w.)
c) Plot the experimental values of | z | = Zo = as a function of w
d) Plot the experimental values of the phase vs frequency, j = j (w)
e) Influence of the resistance (Repeat the experiments using at least two different values)
f) Measurement of the complex voltages across R, C and L.
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