Download ECE 211 Electrical Circuits Lab I

ECE 213 Electrical Circuits II Lab
LAB #3
Spring 2017
Name ___________________
Section ______________
An Introduction to Circuit Excited with an AC Potential
OBJECTIVE:
The objective of this lab is to measure alternating currents and voltages with a digital multimeter
and an oscilloscope in order to form the mathematical model of sinusoidal function.
COMPONENTS AND EQUIPMENT:
1. Oscilloscope
2. Function Generator
3. Digital Multimeter
BACKGROUND:
A sinusoidal alternating signal can be expressed mathematically in the form
F (t )  A  cos(t   )
--------------(1)
Where ω=2πf
A: the amplitude, is the peak deviation of the function from its center position. "A" is always the
zero-to- peak value of the sinusoid when the wave is expressed in the form of (1).
ω: the angular frequency, specifies how many oscillations occur in a unit time interval, in
radians per second
ϴ: the phase, specifies where in its cycle the oscillation begins at t = 0. Note, although ϴ should
be expressed in radians, in practice it is often given in degrees. When the units of t and ϴ are
not the same, care should be taken to avoid errors that might be caused by mixed units.
Since both sine and cosine functions are sinusoids which can be related by sin x = cos (x - 90°),
the sinusoidal alternating signal in (1) can be expressed either with a sine function as in (1) or a
cosine function. Note: The Oscilloscope generate sine function instead of cosine function.
ECE 213 Electrical Circuits II Lab
LAB #3
Spring 2017
In the laboratory, steady state sinusoidal signals are continuous. Time zero is normally not
specified by the wave itself or by the physics of the experiment. The experimenter can select any
instant as time zero. Given a signal the experimenter can express it either as;
F(ωt) = A sin(ωt)
(2)
or
F(ωt) = A cos(ωt)
(3)
The only difference between (2) and (3) is a shift in the selected time zero of one quarter of the
period of the wave. For these reasons, a steady state signal can be described mathematically with
either a sine function or a cosine function. Once the selection is made it is necessary that related
signals be treated consistently. That is, they must all be properly related to the reference.
Using the rms value
Unless otherwise indicated all values of alternating voltages and currents measured and
used by electricians and electrical engineers are given in RMS values. For a sinusoidal wave
such as (1) the RMS value would be the zero-to-peak value, A, divided by 1.414 (or square root
of 2). The value of 1.414 is only true for a sinusoidal wave. Modern potential and current meters,
almost without exception, display RMS values. This value may depend on measurements of
RMS values, peak values or average values. When the measurement depends on peak or average
measurements it is multiplied by a constant to give the RMS reading. The reading is only correct
for sinusoidal voltages and currents.
Oscilloscope Observation
When making measurements with an oscilloscope a picture is presented rather than a rms value.
An analog measurement can be made from the picture. The scale should be selected to give the
largest picture possible and the peak-to-peak value should be measured to give the best accuracy.
Then the zero-to-peak amplitude can be found by dividing by 2. The rms. value can then be
found by dividing the zero-to-peak value by 1.414. Or the peak-to-peak value as measured on an
oscilloscope can be changed to an RMS value by dividing by 2.*1.414 or 2.828.
ECE 213 Electrical Circuits II Lab
LAB #3
Spring 2017
Figure 1 - AC signal
PROCEDURE:
This experiment will require a number of calculation and will be recorded in your laboratory
notebook.
1. Create the circuit shown in Figure 1. Measure the actual values of the component using
digital multimeter and record these values in Table I.
Figure 2 - Resistive-Capacitive Test circuit
R1
R2
C1
Table 1 - Measured value of the actual component
Name of the instrument for measurement: ________________________________
ECE 213 Electrical Circuits II Lab
LAB #3
Spring 2017
2. Set the function generator to produce a sinusoid with a frequency of 1000 Hz with a 4
volt peak-to-peak. Measure the frequency of the sinusoidal wave using digital multimeter
and oscilloscope.
Frequency measured by DMM
Period of sinusoidal signal from O-Scope
Calculated frequency from O-Scope (1/T)
Percent Error: 100%*(DMM – O-Scope)/O-Scope
Table 2 - Frequency Measurement
3. Calculate the RMS voltage and measure in DMM. Write down the calculation and record
measurement.
4. Measure all of the potentials and determine all the currents in Figure 1. R1 and R2 can be
used directly to find the currents in them by measuring the potential across them and
using ohms law. Explain below the method to measure the potential across a component.
Current in R1
Current in R2
ECE 213 Electrical Circuits II Lab
LAB #3
Spring 2017
Potential across
R1
Current
Potential across
R2
Current
Table 3 - Potential and Current measured with DMM
5. On measuring the capacitor, there is no resistance in series with the Capacitor. So it will
be necessary to either insert an ammeter or a resistance in order to measure the current. If
the resistance of the ammeter is high enough to cause a significant change in the circuit a
measurement resistance should be added in series with the capacitor. This added
resistance, call it Rm, should be small (use 1-10ohm resistor). Place the result in the
following table.
Parameter
Value
Rm measured in DMM
Potential across Rm
Current of Capacitor
Table 4 - Potential and Current of Capacitor
6. Find the voltage potential on each node
Node
Voltage Potential (V)
Node 1
Node 2
7. Measure the Phase angle of the circuit: Remove Rm. Use the input voltage as reference
voltage.
ECE 213 Electrical Circuits II Lab
LAB #3
Spring 2017
Parameter
Time Shift from
reference, t
Direction of shift
from the reference
(left / right/no phase
shift)
Phase angle
calculated from eq
(2)
Potential at Node 1
Potential at Node 2
Table 5 - Phase shift measurement for circuit
Phase angle formula:
-------- (2)
8. Write the equation for the voltage output of the signal generator and the voltage across
R2 as node voltage. Put these equations in the form of (1). Give the numerical values for
each parameter. Values from Tables II and V can be used to find the parameters needed
to write these equations. Note, the values given in the tables may not be of the correct
form to use in the equations.
V1(t) = _________________________________________________________
V2(t)=___________________________________________________________