Download Types of resistors

Experiment #02
 & Y Connected resistors, Light emitting diode
Objectives




To get some hands-on experience with the physical instruments.
To investigate the equivalent resistors,  and Y connected resistors, and KVL/ KCL laws.
To learn about light emitting diodes (LED).
To learn graphical circuit analysis.
1 – Instruments and Circuit Elements Used in This Lab
1.1 - Resistors
Resistors are devices that not only conduct electricity but also dissipate electric energy as heat.
Therefore by adding resistance, supply voltage may be reduced, or current be limited. There are two
general types of resistors: composition resistors and wire-wound resistors. You may get more information
about various types of resistors in Appendix section of this lab note. In order to find out the color code of
the resistors you may consult with the Appendix too (which hopefully you have downloaded and read it
already).
1.2 - Light Emitting Diode - LED
Charge carrier recombination occurs at a pn-junction as electrons cross from the n-side and
recombine with holes on the p-side. When recombination takes place, the charge carriers give up energy in
the form of heat and light. If the semiconductor material is translucent the light is emitted, and the junction
is a light source, that is, a light emitting diode (LED).
1.3 - Breadboard box
A breadboard is used for mounting and interconnecting components of a circuit. Figure 1 shows
the electrical connection scheme of the breadboard box. The most important parts of a breadboard box are
the superstrips which are the white plastic strips with lots of holes for inserting ends of connecting wire.
The narrow superstrips, which have two vertical sets of holes, are connected so that all holes lying on the
same vertical line are connected to each other, i.e., horizontally adjacent holes are not connected to each
other. The two wide superstrips, which have five horizontal sets of holes, are connected such that all holes
lying on the same horizontal line are connected to each other, i.e., vertically adjacent holes are not
connected to each other.
Some breadboards also have the following properties:
 A power switch, which is located on the left-top corner of the breadboard (see figure 1)
 Three knobs for variable 0 to 15 V and a fixed 5 Volt power supplies.
 The ground (GND) post on the top of breadboard is the ground of the power supplies and also
internally connected to the breadboard box case when the power is on, so that the case itself can act as
a ground. Directly below each power supply knob is a hole that wire ends can be inserted into it and
bring the power supply to the terminal strips. It is recommended to wire end a vertical strip to the
GND post in order to provide a safe and common ground for your circuit.
 At the bottom of the breadboard box there are three coaxial connectors. Coaxial cables from signal
generators and oscilloscopes are connected to these connectors. The coaxial cable has a central inner
signal wire and an outer concentric shielding braided cylindrical wire. The outside shell of each
coaxial connected is screwed to the case of the breadboard box and therefore is at ground potential.
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ON OFF
GND
15
5
-15
BNC terminals at the bottom of the breadboard
Figure 1. Sample of a Breadboard box. (The one we have in the lab is slightly different)
1.4 - Digital Multi meter (DM)
Resistance, voltage and current measurements can be made with this instrument. Connections to
the instrument are made through three labeled binding posts. The instrument has a number of buttons
some of which are used to set the instrument function, i.e., to make it read dc volts, and others are for
range control, i.e., to set it to read voltages that under 2 volts.
1.5 - Dual Power Supply (DPS)
It is a supply of variable voltage that has two independent outputs. Both current and voltage could
be set. The two outputs could be connected either in series or in parallel. A fixed positive 5 volts is also
available. The instrument has an on-off switch, and voltage control knobs for each power supply.
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2 - Background
2.1 – Resistors-Sets Equivalence
Having the v-i relationship of a resistor as v(t) = i(t).R, we can show that the resistor equivalent to
a set of resistors connected in series, could be obtained by simply summing the quantities of each resistor
in the set (Figure 2). For the set of resistors in parallel the replica of the equivalent resistor would be equal
to sum of the replication of each resistor in the set (Figure 3).
R1
a
a
R2
R = R1+R2 +R3
=
b
b
R3
Figure 2. The equivalent of the resistors connected in series.
a
a
R1
R2
R3
=
1/R = (1/R1) + (1/R2) + (1/R3)
b
b
Figure 3. The equivalent of the resistors connected in parallel.
A set of resistors could be replaced by its equivalent without affecting the KCL and KVL equations
applied at, and between the terminals where the replacement is done, respectively.
For -connected resistors, there is an equivalent Y-connected resistors set, by which the analysis of the
circuits containing -connected resistors could be simplified, dramatically. The resistors in the Yconnected set are related to the combination of resistors in the -connected resistors set as follows:
a
a
R2
Ra
R1
b
c
R3
Rb
Rc
b
c
Figure 4. The  and Y-connected resistors sets.
The above two  and Y-connected resistors are equivalent when:
R1R2
RR
,
Rb  2 3 ,


  R1  R2  R3
Ra 
EGR 2402 Laboratory Manual
Rc 
R1R3

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2.2 - LIGHT EMITTING DIODE CHARACTERISTICS
(A Graphical Analysis Approach)
In order to solve a circuit in terms of its node-voltages and branch-currents, we have to consider
two kinds of equations applying to the circuit simultaneously. One set of equations is extracted from the
circuit topology, using KVL and KCL laws. Theses equations, therefore, reflects the specifications of the
circuit in terms of the way in which the various components of the circuit are connected to each other.
The other group of equations originates from the intrinsic electrical behavior of each component,
showing the physical specification of the components, irrespective the way that they are connected to each
other.
In the circuit analysis procedure, there are many cases in which solving the simultaneous
equations is very difficult unless we use sophisticated computer programs. There is still a relatively simple
graphical approach to solve the simultaneous equations that works properly in many cases.
In Figure 5 the LED is connected in series with load resistor R across the power supply. Since the
LED is a non-linear device it is not easy to analytically determine the voltages and current in this single
loop circuit. However, a graphical method using what is called a “load line” can be applied to give the
LED operating voltage and current (called the operating point) for particular values of power supply
voltage and load resistance (Figure 6).
100 
+
Vs
+
-
-
Figure 5. A simple circuit with Light Emitting Diod.
The load line equation is obtained by applying KVL to the single loop circuit (Figure 5), giving
vd=Vs - Rid
This linear equation can be plotted on to the graph containing the LED vi-curve. Note that Vs is the
voltage axis intercept value and the line has the slope -R. The intersection of the load line with the vicurve yields a solution for the LED operating point. Figure 6 illustrates the method and shows the LED
operating voltage (vdo) and operating current (ido) for particular values of Vs and R. If either Vs or R is
changed, the operating point will change too.
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3
Vs
2.25
LED curve
Vd
1.5
Slope - R
id0
0.75
Load line
0
0
0.01
0.02
0.03
id
Figure 6. Load line solution for the LED operating point.
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PreLab Handout
1- Show that the relation of Ra = R1R2/ ( R1+R2+R3) is valid for the resistor network in Figure 4.
2- Obtain the relation that is valid between R1 and the resistors of the Y-connected set.
Hint: To obtain the requested relations, notice that two resistor sets are equivalent if and only if they show
same circuit behavior, i.e., we will have the same result if we apply a test voltage source on the same
terminal on resistor sets as shown below.
IT
a
IT
a
R2
+
Ra
+
R1
VT
VT
-
-
b
c
R3
Rb
Rc
c
b
Figure 7. Circuit diagrams used to calculate the resistors of each set in terms of the resistors of the other
set.
Write the input resistance seen by the test supply in each circuit and make them equal to each other, i.e.
for the circuits shown in Figure 7 we have:
Ra + Rb = R2 || (R1+R3)
Apply the test supply to other terminals of both circuits correspondingly and obtain the equations similar
to the above one. Solving three simultaneous equations, obtained in the way explained, the resistors of
each set could be calculated in terms of the resistors of the other set.
3 – a) Calculate the resistance observed in the terminal x-x of the circuit shown in Figure 8 below given
that R = 4.7 K Use the fact that a -connection of three equal resistors R is equivalent to a Yconnection of three equal resistors RY when 3RY=R.
c
x
R/3
3R
R
b
a
R
R
x
Figure 8. Resistor network
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10
Rxx theoretical = ____________ 

b) Calculate the equivalent resistance seen across c-b terminals.
R cb = _______________
The following section might be done using circuit analysis or circuit simulation with workbench.
4 - Considering the circuit shown in Figure 8, assume that we apply a dc power supply across terminals xx having 10 volts magnitude. Calculate the voltages across terminals a-b. Having known all voltages of
the circuit nodes, calculate the current passing through each resistor.
V ad Theoretical) = _______________
V bdTheoretical) = ________________
I 3R Theoretical) = _______________
IR/3Theoretical) = _______________
IR-LeftTheoretical) = _______________
IR-RightTheoretical) = ________________
IR-BridgeTheoretical) = _______________
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