Partner: Hirbod B.
Partner: Wonyoung J.
TA: Hank Lamm
November 3rd 2011
The main goal of this experiment to Investigate the sine wave AC signal from signal generator using the scope and determine the relationships between the rms value and the amplitude of the voltage as well as the period and the frequency of the signal. The following are the results of the lab: T= 10-3seconds, Vo=1.4V , 2% discrepancy in Vrms, 7.1% discrepancy in V0, ω=1.1*104±2.5*103, ωotheoretical=10846.5 Hz , 0.3% discrepancy in ω0. Objectives:
To learn the relationship between the rms value and the amplitude of the voltage and the period and the frequency of the signal. Determine the resonant frequency of a driven RLC circuit from the exploration of the dissipated power on the load resistor.
Part 1 AC Signals
Connect the circuit, set the signal generator to a 1000 Hz sine wave of magnitude about 1V measured on the DMM. Adjust the SEC/DIV control on the scope to display one complete period of the measured waveform. Measure the period T of the wave, The frequency is given by f (Hz) = 1/T(sec). Compute the frequency. DC offset: Be sure the scope is on DC coupling. Pull out the OFFSET knob on the signal generator and watch the scope as you turn it. Adjust the DC offset so the average (center) of the sine wave is about 1.0 volts. Switch the DMM to DC, and compare its reading with the scope. Switch the scope to AC coupling and explain the result. RMS: Set the signal generator DC offset accurately to zero, watching the DMM (DC). Change the DMM to AC, then determine the amplitude of the sine wave (V0 = VPP /2) from your scope trace and compare with the reading from the DMM. Now position the signal generator in such a way that you will not able to read the frequency from the generator’s display. Change the frequency by randomly rotating the frequency adjustment knob and try to determine the unknown frequency using the scope and compare with the generator’s display value.
Part 2: Resonance in RLC Circuit
Connect the circuit using Rload = 200 Ω, C = 0.1μF and L = 85 mH. Connect Channel 1 of the scope across the signal generator. Attach Channel 2 leads from the scope across the resistor. Turn on the AC power supply and make sure that it is set to a sine wave mode about 1 Vrms and frequency 1000 Hz. Adjust the rms value of the voltage 1 Vrms on the signal generator using the reading from the scope. Find and record the resonant frequency f0 where the current through Rload is maximum. Take 3 independent readings to get the errors. Measure the voltage drop on the resistor vs. frequency f as you tune through resonance in the range 800-3000 Hz. For the frequency range 800-1500 Hz use 100 Hz intervals; for the range 1500-1800 use 50 Hz intervals; and for the range 1800-3000 Hz use 100 Hz intervals. For each frequency f calculate the average power dissipated in the resistance and plot the average power P versus angular frequency in GA. 5. Fit these data with a modified expression
y=A2B(10-7x)2(10-7Bx)2+(xC)2-12= Vrms2R(Cω)2(RωC)2+(ωωo)2-12=P(ω) You should put in Vrms and R as parameter and C as known constant. Compare your values of ω0 from the various methods.
T = 1 millisecond per square on the reader.
DMM = 0.994 V
Vo = 1.5V
1000Hz = 0.979V
1.70 KHz ±0.1 = 4.27 V
1.68 KHz ±0.1 = 4.20 V
1.69 KHz ±0.1 = 4.25 V
Look at graph for complete list of frequencies ranging from 800Hz – 3030Hz and their corresponding voltages.
The equation below displays the fundamental principle of how Ac signals take the form of sin waves:
In above equation Vdc represents the Dc offset, which adds a constant voltage to the entire wave and shifts the sine wave vertically. Vo is the amplitude of the wave and the angular frequency is represented by ω ( Hz)