Lab 9 - AC Circuitsx

piquantdistractedElectronics - Devices

Oct 5, 2013 (4 years and 1 month ago)

151 views

R the
AC Circuits: Oscillospes


Vanessa Breguez

Thomas Kincheloe

Group 1

PHY 114 7:30am Mondays

Section 81464

TA: Hank Lamm

11/8
/2011











Abstract

The goal of these experiments was to determine the relationship between the RMA value and the
amplitude of the voltage, the relationship of the period and the frequency of the signal and to
determine the resonance frequency of a driven RLC circuit through
the exploration of the power
dissipated on the load resistor.

In Part I, the period was determined to be






, and the calculated frequency was 1000Hz.
The DC offset from the oscilloscope was




, and through the DMM was





; the percent
difference was 5.87. The two values agreed. The



as measured from the oscilloscope was
0.85V, and from the DMM it was 0.573V. The percent difference was determined to be 4.8%.
The unknown frequency was found to be 2000Hz. The actual v
alue was 1987Hz, with a 1%
discrepancy.

The theoretical angular frequency


was calculated to




. The angular frequency
from the oscilloscope was




, form the graphical method it was 10




.
The percent discrepancies were 1% a
nd 0%, respectively. Both values were found to agree.

The
biggest sources of error in these experiments came from the resistor, capacitor and the inductor
which all had a 10% tolerance.

Objectives


The goal of this lab was to investigate the sine wave AZ signal from signal generator,
thus determining the relationship between both the RMA value and the amplitude of the voltage,
as well as the period of frequency of the signal. The resonant frequency w
as also determined for
a driven RLD circuit from the exploration of the dissipated power on the load resistor. Some of
the measurements taken included frequency (Hz) and voltage (V).


Procedures

Materials

Oscilloscope, AC power supply, DMM, decade resista
nce box, a capacitor, an inductor.


Part I: AC Signals

The circuit was connected as shown in Figure 1. The signal generator was set to a 1000Hz sine
wave of magnitude about 1V measured on the DMM (AC). DMM on AC position read the RMS
value. The cal knob on the signal generator was set to the calibrated positio
n.
The SEC/DIV was
adjusted on the scope to display one complete period of the measured waveform. The CAL knob
was clicked into the calibrated position. The period
T

of the wave was measured. The frequency
was given by
f
(Hz) = 1/T(sec). The frequency was
computed and compared with the signal
generator setting.


The scope was set to DC offset of zero, while the DMM (DC) was observed. The DMM was
changed to AC, and then the amplitude of the sine wave was determined from the scope trace
and this was compare
d to the reading from the DMM.

The signal generator was then positioned in such a way that the frequency from the generator
was not displayed (the displayed was covered). The frequency was changed by randomly rotating
the frequency adjustment knob and the

unknown frequency was determined.


Part II

The circuit was connected as shown in Figure 2 using a load resistance





, a
capacitor






, and inductance




. The AC power supply was turned on (signal
generator) and it was set to a

sine wave mode about 1



and frequency 1000Hz. The RMS
value was adjusted of a voltage value of 1



on the signal generator using the reading from
the scope. Both waves were obtain
ed on the scope simultaneously.


The resonant frequency



was found and recorded where the current through



was at a
maximum (by measuring the voltage across it). Three independent readings were taken.

The voltage drop on the resistor versus frequency
f

were measured as the resonance was tuned
though
range 800
-
3000 Hz. For each frequency
f

the average power dissipated was calculated in
the resistance
R
. Resistance versus power was plotted in Graphical Analysis (GA). The data was
fit with the expression:

































Where
A represents
RMS voltage


, B represents resistance
R
,




represents the
capacitance
C

of such value, angular frequency


is variable in the equation, represented by
x
.



Experimental Data

Part I

Period of oscilloscope:






.

Frequency: 10000Hz


DMM voltage: 0.0943 V

Oscilloscope voltage:











Amplitude of sine wave:


From scope: 0.85 V


From DMM: 0.573 V

Unknown frequency:


Using scope: 2000Hz


Generator display: 1987 Hz

Part II

Resonant frequency


: 170
4Hz, 1699Hz, 1704Hz.

See attached Graph 1 and Graph 2.

Results

Part I

Source

Voltage (V)

% Difference

DMM

0.943

5.87

Oscilloscope

1.00

Table 1.
Shows the
DC offset
as gathered from the DMM and the oscilloscope, and compares
the two values.

Source

Voltage (V)

% Difference

DMM

0.
60

4.8

Oscilloscope

0.573

Table 2.
Shows the



as gathered from the DMM and the oscilloscope, and compares the two
values.

Unknown

Frequency (Hz)

% Discrepancy

Gathered from scope

1987

1

Generator display

2000

Table 3.
Shows the unknown frequency as determined by the scope, and the actual value as
generated in the display, as well as the percent discrepancy.

Part II


Source

Angular frequency


(Hz)

% Discrepancy (to
theoretical)

% Error

Agree
s?

Calculated
theoretical





-

10

-

Oscilloscope
(averaged)





1

0

Yes

Graph 2





0

0

Yes

Table
4
.
Shows the values for the angular frequencies as gathered by the three different sources,
and compares
the values to the calculated theoretical,
showing the errors, discrepancies, and
whether the values agree or not.




Discussion and Analysis

Part I

In Part I, the frequency was calculated from the period observed through the oscilloscope. The
period was determined to be






, and the
calculated frequency was 1000Hz. The display
also read 1000Hz. This helped conclude that the oscilloscope reading was fairly accurate and that
correctly relates to the displayed frequency (frequency = 1/period).

Through Part I, the
DC

offset was measured

t
hrough the oscilloscope as well as through the
DMM reader. The
DC offset
voltage as gathered through the oscilloscope was




, and
through the DMM was





. The calculated percent difference was 5.87.

The two values were
found to be very close
to eac
h other, as they should, since the DMM and oscilloscope were
measuring the same thing.


The
RMS voltage



was measured through both the oscilloscope and DMM as well. The



as measured from the oscilloscope was measured to be 0.85V, and from the DMM it was
determined to be 0.573V. The percent difference between the two values was determined to be
4.8
%.
This error is probably due to the misreading of the oscilloscope,
or perha
ps simply due to
the fact that the resistor and capacitor had a 10% tolerance.

The frequency generator display was covered for the last portion of Part I. A random frequency
was selected, and through reading the oscilloscope it was determined to be 2000Hz
. Once the
generator display was uncovered, the actual value of the “unknown” frequency was revealed to
be 1987Hz. The percent discrepancy between the observed value and the actual value was
determined to be 1.
These values did agree very well, as they als
o should since they were
measuring the same thing.

For all of these experiments, the biggest sources of error
came from the resistor, capacitor and
the inductor. All three of these had a 10% tolerance to their values. A way a lot of this error
could have b
een eliminated
would be by actually measuring the resistance, capacitance, and
inductance, reducing the error significantly, perhaps to even as low as 1%.

When analyzing the goals of the experiment, it can be seen that the relationship between the
RMS val
ue and the amplitude of the voltage was determined in Part I. The range on the
oscilloscope (the




was measured and determined to be 1.7V. The equation







wa
s used
to determine the height of the wave peak above zero voltage
. Then it was det
ermined that







, thus determining the relationship between



and amplitude.

The relationship
between frequency and period was

also studied in Part I. It was determined that
frequency
f

is the inverse of time
T
, or




.


Part II

The theoretical value of angular frequency


was calculated to be





which
translated to




. This high percent error is due to, once again, that the ca
pacitor
and the inductor values weren’t completely precise (having an error of 10%). The angular
frequency as gathered by directly measuring the resonant frequency off the oscilloscope was





. The


gathered using the graphical method was deter
mined to be





. The percent discrepancies to the theoretical were determined to be 1% and 0%,
respectively. Both values were found to agree with the theoretical since there was such a larger
window of acceptance for values due to the 10% error o
n the theoretical value.

Part II helped determine the resonance frequency of a driven RLC circuit through the exploration
of the power dissipated on the load resistor. Graph 3 shows this relationship as the data perfectly
fit Equation (1) that shows the r
elationship between resonance angular frequency and power.





































Equation (1)

Where



is RMS voltage,
R
is resistance,
C
represents the capacitance, angular frequency


i
s
the variable of the equation
.



Conclusion

The goal of these experiments
was
to determine the relationship between the RMA value and the
amplitude of the voltage, as well as the relationship of the peri
od and the frequency of the signal.
The resonance frequency of a driven RLC circuit was also determined through the exploration of
the power dissipated on the load resistor.

In Part I, the period was determined to be






, and the calculated frequency

was 1000Hz.
The display also read 1000Hz. The DC offset voltage as gathered through the oscilloscope was




, and through the DMM was





. The calculated percent difference was 5.87. The two
values were found to agree. The



as measured from

the oscilloscope was measured to be
0.85V, and from the DMM it was determined to be 0.573V. The percent difference between the
two values was determined to be 4.8%.
The unknown frequency was determined to be 2000Hz.
The actual value was 1987Hz. The percen
t discrepancy between the observed value and the
actual value was determined to be 1.

The theoretical value of angular frequency


was calculated to




. The angular
frequency as gathered from the oscilloscope was




, using the graphical method it
was determined to be




. The percent discrepancies to the theoretical were
determined to be 1% and 0%, respectively. Both values were found to agree with the theoretical.

For all of these experiments, the biggest s
ources of error came from the resistor, capacitor and
the inductor. All three of these had a 10% tolerance to their values.