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

------(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.

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.

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: ______

  1. 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

  1. Calculate the RMS voltage and measure in DMM. Write down the calculation and record measurement.
  1. 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
Potential across R1 / Current / Potential across R2 / Current

Table 3 - Potential and Current measured with DMM

  1. 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

  1. Find the voltage potential on each node

Node / Voltage Potential (V)
Node 1
Node 2
  1. Measure the Phase angle of the circuit: Remove Rm. Use the input voltageas reference voltage.

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)

  1. Write theequation forthe voltage output ofthesignalgenerator andthe voltageacross R2 as node voltage. Putthese equations in the form of (1).Givethenumericalvaluesforeach parameter. Values from Tables II and V can be usedtofindthe parameters neededto write theseequations.Note,thevaluesgiveninthetablesmaynotbeof thecorrectformtouseinthe equations.

V1(t) = ______

V2(t)=______