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Lab 2: Instrument Familiarization and Electrical Relations, Study notes of Mechatronics

A laboratory exercise designed to help students become familiar with various laboratory instruments and electrical relations. It covers topics such as series and parallel resistance, Kirchhoff's Current Law and Voltage Law, and Ohm's Law. Students are expected to learn how to apply these concepts to circuits and use them to measure current and voltage.

What you will learn

  • How do you use the voltage divider rule to calculate voltages in a circuit?
  • What is Kirchhoff's Voltage Law and how is it applied?
  • What is Kirchhoff's Current Law and how is it applied?
  • How do you calculate the equivalent resistance of resistors connected in series and parallel?
  • How does Ohm's Law relate to resistance, voltage, and current?

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Lab 2
19
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
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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.