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Laboratory 2
Instrument Familiarization and Basic Electrical Relations
Required Components:
- 2 1k: resistors
- 2 1M: resistors
- 1 2k: resistor
2.1 Objectives
This exercise is designed to acquaint you with the following laboratory instruments which will be used throughout the semester:
- The Oscilloscope
- The Digital Multimeter (DMM)
- The Triple Output DC power Supply
- The AC Function Generator
During the course of this laboratory exercise you should also obtain a thorough working knowledge of the following electrical relations:
- Series and Parallel Equivalent Resistance
- Kirchoff's Current Law (KCL)
- Kirchoff's Voltage Law (KVL)
- Ohm's Law
- The Voltage Divider Rule
- The Current Divider Rule
The experiments to be performed during this laboratory are also designed to introduce you to two very important instrument characteristics:
- The output impedance of a real source
- The input impedance of a real instrument
2.2 Introduction
A thorough explanation of the proper use of each of the instruments above will be presented when you come to the laboratory. You should already be familiar with the basic electrical relations listed above; however, a quick review will follow.
2.2.1 Series and Parallel Equivalent Resistance
It can be shown that when resistors are connected in series the equivalent resistance is the sum of the individual resistances:
Figure 2.1 Series Resistors
For resistors connected in parallel,
Figure 2.2 Parallel Resistors
For two resistors in parallel, Equation 2.2 can be written as:
R (^) eq = R 1 + R 2 + } +R (^) N
R 1 R 2 R (^) N
R (^) eq
R 1
R 2
R N
R (^1)
R (^2)
R (^) N
…
R (^) eq
R 1 R 2
R 1 +R 2
or
Figure 2.4 Kirchoff’s Current Law
2.2.4 Ohm's Law
Ohm’s Law states that the voltage across an element is equal to the resistance of the element times the current through it:
Figure 2.5 Ohm’s Law
2.2.5 The Voltage Divider Rule
The voltage divider rule is an extension of Ohm's Law and can be applied to a series resistor circuit shown in Figure 2.6.
I = I 1 +I 2
I (^1)
I (^2)
I
V = IR
V
I
Figure 2.6 Voltage Division
The current flowing in the circuit is
Applying, Ohm's Law, the voltage across R 2 is
Thus the voltage divider relation is
2.2.6 The Current Divider Rule
The current divider rule is can be derived by applying Ohm's Law to the parallel resistor circuit shown in Figure 2.7.
Figure 2.7 Current Division
R (^1)
R (^2)
V I
V (^) o
I
V
R (^) eq
-------- V
R 1 +R 2
V (^) o = IR (^2)
V (^) o V
R 2
R 1 +R 2
= §^ ·
R (^1) R (^2)
V
I I (^2)
characteristics that are somewhat different from the ideal cases. The terminal characteristics of the real sources and meters you will be using in the laboratory may be modeled using ideal sources and meters as illustrated in Figures 2.8 through 2.
Figure 2.8 Real Voltage Source with Output Impedance
Figure 2.9 Real Ammeter with Input Impedance
Figure 2.10 Real Voltmeter with Input Impedance
V
R (^) o Output Impedance
Ideal Voltage Source
Real Voltage Source
Input Impedance
Ideal Ammeter
Real Ammeter
I R (^) i
Input Impedance
Ideal Voltmeter
Real Voltmeter
R (^) i V
In some instances as you will see, the input impedance of a meter or the output impedance of a source can be neglected and very little error will result. However, in many applications where the impedances of the instruments are of a similar magnitude to those of the circuit serious errors will occur.
As an example of the effect of input impedance, if you use an oscilloscope or multimeter to measure the voltage across R 2 in Figure 2.6, the equivalent circuit is:
Figure 2.11 Effect of Input Impedance
The equivalent resistance of the parallel combination of R 2 and Ri is:
Therefore, the actual measured voltage would be:
If Ri is large compared to R 2 (usually the case), and the measured voltage (Vo ) would be
close to the expected ideal voltage division result of. However, if R 2 is not small
compared to Ri , the measured voltage will differ from the ideal result based on Equations 2.20 and
2.21.
R (^1)
R (^2)
V i V (^) o
R (^) i
voltmeter
R (^) eq
R 2 R (^) i R 2 +R (^) i
V (^) o
R (^) eq R 1 +R (^) eq
= ---------------------V (^) i
R (^) eq |R (^2) R (^2) R 1 +R (^2)
-------------------V (^) i
2.4 Laboratory Procedure / Summary Sheet
Group: ____ Names: _________________________ _____________________________
(1) Select five separate resistors whose nominal values are listed below. Record the band colors for each resistor in the table below. Then connect each resistor to the multimeter using alligator clips and record the measured value for each resistor.
Make sure you keep track of each of the five resistors (e.g., by laying them out in order on the table with labels, or in the breadboard).
(2) Now construct the voltage divider circuit shown using resistors R 1 and R 2 listed
above and set Vi to 10 Vdc using the DC power supply. When using a
power supply or function generator, always adjust
the supply voltages before making connections to the
circuit. Also be very careful to check that the power
and ground leads are not touching when power is
applied. This creates a short that can blow a fuse or
damage the device.
Figure 2.12 Voltage Divider Circuit
Resistor Band Colors Measured Value ( : ) R 1 : 1k:
R 2 : 1k:
R 3 : 2k:
R 4 : 1M:
R 5 : 1M:
R (^1)
R (^2)
I
V V^ o i
Data for the circuit and instructions on the previous two pages:
- compute the current using the voltage value measured
(3) Repeat part 2 using the same resistors R 1 and R 2 but using the function generator to
drive the circuit at 1KHz with a 3V amplitude (6V peak-to-peak) sine wave. See the video demonstrations on the Lab Book website to see how everything is connected. If an error message appears on the function generator display during power up, just press any button and wait briefly for the message to clear.
NOTE - If using the Philips PM5193 function
generator, be sure to connect to the lower
“OUTPUT” jack (not the upper “TTL OUT” jack).
Complete the table below by measuring or calculating the appropriate values. In your calculations, use the actual (measured) values for R 1 and R 2. Use rms values for all table entries. Be aware that the Lab multimeters cannot detect or measure small I (^) rms currents accurately.
- compute the current using the voltage value measured
Input Voltage V (^) i (V) Output Voltage V (^) o (V) (^) Current (mA)
Calculated 10 V Multimeter Oscilloscope *
Input Voltage (Vrms )
Output Voltage (V (^) rms)
Current (I (^) rms in mA)
Calculated
Multimeter * Oscilloscope *
3V
(4) Repeat part 2 (Vi = 10 Vdc) using R 4 and R 5 in place of R 1 and R 2. In this case, the
impedances of the instruments are close in value to the load resistances and therefore affect the measured values. Sketch the equivalent circuit for the instruments (voltage supply, and voltmeter or oscilloscope) and the attached circuit. Use this schematic to explain differences between actual (measured) and theoretical values.
Complete the table below by measuring or calculating the appropriate values. In your calculations, use the actual (measured) values for R 4 and R 5.
*: compute the current using the voltage value measured since current cannot be measured directly on an oscilloscope and since the currents are too small to measure on the NI ELVIS.
Input Voltage (V) Output Voltage (V) (^) Current (mA) * Calculated Multimeter Oscilloscope
(6) Repeat part 5 with a 3 V amplitude 500 Hz sine wave ( ).
Complete the table below by measuring or calculating the appropriate values. In your calculations, use the actual (measured) values for R 1 , R 2 , and R 3. Use rms values for all table entries.
*** compute the current using the voltage value measured**
Normally, the input impedance of a meter or the output impedance of a source can be neglected and very little error will result. However, in some applications where the impedances of the instruments are of a similar magnitude to those of the circuit, serious errors will occur.
I (^) 1rms (mA) I^ 2rms (mA)^ I^ 3rms (mA)
Calculated
Multimeter *^ *^ * Oscilloscope * * *
V = 3 sin 1000 St
LAB 2 QUESTIONS
Group: ____ Names: _________________________ _____________________________
(1) Describe how you read resistor values and tolerances.
(2) Derive formulas, using the voltage divider and current divider rules, for the following voltage and current in Figure 2.14, using V, R 1 , R 2 , and R 3 only.
V 1 = _________________________ I 3 = __________________________
(3) From the data collected in Part 4, calculate the input impedance of the oscilloscope and the voltmeter.
Zin (scope) = _________________________
Zin (DMM) = _________________________
Hint: Use Equations 2.22 and 2.23. Also, if using the attenuator probe, be sure to account for the probe’s impedance (see Section 3.3 in Lab 3).
(4) The AC wall outlet provides 110 V (^) rms at 60Hz. Sketch and label one period of this
waveform.
