Resistive DC Circuits
Experiment 1 (Revised)
Lucas Tay
J. Kubby
Jan 16, 2016
Section 05: Thursday 2:00PM – 4:00PM
Partner: Kevin Beher
Note: Revisions comments on the last page.
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Introduction
The overall purpose of this lab is to allow students to familiarize themselves with the lab kit (proto board,
various fixed and variable resistors, etc.), some of the lab equipment (primarily the digital multimeter and
power source), and for students to get a feel for very simple resistor-only circuits. Each of these circuits
has no more than 5 resistors arranged in a variety of series and parallel configurations. The series ones
will have two or more resistors in a row along the same path, while parallel connections will have the
resistors connected on each end (all positives on one side, all negatives on the other) at the same nodes
while all being hooked up to a single voltage source. Through this, Ohm’s Law and Kirchhoff’s Laws will
be used and verified throughout the experiments. Ohm’s Law states that V=IR, Kirchhoff’s Current Law
essentially states that sum of currents entering a node is equal to the sum of currents leaving the same
node, and Kirchhoff’s Voltage law states that the sum of voltages around any closed loop is equal to zero.
In one of the circuits, the power dissipation when of a current flowing through a resistor will be measured
as well. This power dissipated in this case is primarily done so in the forms of heat and light.
Basic Resistive Circuits
Create the circuit displayed in Figure 1 on the circuit board using the power supply, two 1 kΩ resistors,
and a 5 kΩ resistor, having one of the 1 kΩ and the 5 kΩ resistor in parallel.
Note: Since a 5 kΩ was not available, a 2 kΩ and a 3 kΩ resistor were used in series instead, giving us an
equivalent resistance of 5 kΩ.
Figure 1
Resistor Circuit Schematic for Lab 1, Part 1
The resistances of each of the resistors were all measured before setting up the circuit was put together,
using the digital multimeter, the values of each shown on the table, Figure 2, below. Set the power
source, VS, to 5 V, as confirmed by having the multimeter as having a potential difference of 5.002 V.
Once the current was flowing through the circuit, the voltage drops across each resistor, V1, V2, and V3
were measured, followed by the currents I1, I2, I3, and I4 flowing through the resistors.
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Resistors
Resistor
R1
R2
R3
Nominal
[kΩ]
1
1
5
Measured
[kΩ]
0.990
0.990
4.969
Absolute Difference
[kΩ]
0.010
0.010
0.031
Figure 2
Relative Difference
1.00%
1.00%
0.62%
Values of the Resistors for circuit shown in Figure 1
Voltages
Voltage
VS
V1
V2
V3
Currents
Value
[V]
5.002
2.726
2.275
2.275
Current
I1
I2
I3
I4
Value
[mA]
2.75
2.30
0.46
2.76
Figures 3 and 4
Measured values for the voltages and currents across the circuit shown in Figure 1
Kirchhoff’s Current Law states that the current entering a node is equal to the current leaving that same
node, so we know that I1 should be equal to I2 + I3 and I2 + I3 should be equal to I4, giving us I1 = I2 + I3 =
I4, and this is all confirmed through the values recorded in Figure 4. The split of the currents into I2 and I3
is also inversely proportional to the difference in resistances as well (About a 5:1 split of the current, as
one has roughly 5 times less than the resistance of the other)
Light Bulb Circuits
Create a circuit on the bread board using a voltage source and two lightbulbs in two ways – one in series
(as shown in Figure 5), then again in parallel (as shown in Figure 6).
Figure 5 and 6
Circuit with Light Bulbs in Parallel and in Series for Lab 1, Part 2
Before turning on the circuit, the resistances of each lightbulb was measured and recorded below in
Figure 7, and then once the voltage source was turned on, the potential difference across the power
source and the current flowing through the system was measured. The approximate resistance of the
system was calculated using Ohm’s Law, or 𝑉 = 𝐼𝑅, and the power dissipated can be found using 𝑃 =
𝐼𝑉. The measured and calculated values are all shown in Figure 8.
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Cold Resistances (Off)
Resistance
[Ω]
5.03
4.94
Resistors:
R1
R2
Figure 7
Resistances measure before circuits were turned on.
Hot Circuit (On)
Circuit
Series
Parallel
Voltage
[V]
1.501
1.501
Current
Resistance
[A]
[Ω]
0.027
55.59
0.075
20.01
Figure 8
Power
[W]
0.041
0.113
Measured values for series/parallel lightbulbs, along with derived resistance and power
When there was no current flowing through, each of the lightbulbs were roughly 5 Ω each. When the
voltage source was turned on and there was a current flowing through, however, the resistances rose
greatly, as the resistance of each light bulb is proportional to its own temperature. In the series circuit, the
overall resistance of the lightbulbs turned out to be roughly 27.8 Ω each, while in the parallel circuit, they
turned out to be closer to 40.0 Ω each. This makes sense because a parallel circuit has the same voltage
across each path and ends up drawing more current towards them overall, and as a direct result, more
power is dissipated. This can be seen in the forms of light (brighter) and heat (increases resistance even
further).
Note: Neither of the bulbs were dead, but one was behaving abnormally. While one bulb in both circuits
lit up as soon as the current was flowing, the other bulb took a good 20-30 seconds before it finally lit up.
That’s probably not intended, but the results were similar to other groups nonetheless.
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The Voltage Divider
Create a circuit as shown below in Figure 9, where V2/Vs =3/5. Use two 1k Ohm resistors and a variable
resistor.
Figure 9
Circuit with resistors in series, one of which is variable.
By having the voltage source at a default of 5 V, the potential differences across the variable resistor ends
up being a whole number, or in this case, 3 V, while V1 and V3 should be 1 V each. As the circuit only
has resistors in series, the current is equal through each and every component as well, and by doing some
basic algebra in conjunction with Ohm’s Law, it can be found that if there are two 1 kΩ resistors already
in the circuit and the goal is to have a V2/Vs = 3/5, the resistance of the variable resistor should be
roughly 3 Ω. Once the circuit was completed, the following voltages in Figure 11 were measured by
running the voltmeter across each component in order to verify that the voltages were around the desired
values.
Resistances
Resistor
R1
R2
R3
Voltages
Resistance
[kΩ]
0.996
2.980
0.996
Location
Vs
V1
V2
V3
Voltage
[V]
5.003
1.002
2.998
1.002
Figure 11
Values of each resistor, and voltages across each component.
Once the circuit was set up and tested, the values of each component ended up being around the intended
values. Since the same current is going through every element, the potential difference across each
resistor ended up being directly proportional to the resistances, essentially showing that the voltage is
directly divided among each component in a series circuit.
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The Wheatstone Bridge
Create a circuit like the one below using two 1 kΩ resistors, a potentiometer, and a random resistor
arranged as shown below in Figure 11. The goal of this assignment is to create a Wheatstone bridge, or a
diamond-shaped circuit in which no current flows through the middle because the resistances on either
side should be roughly the same.
Figure 11
Circuit for a Wheatstone Bridge for Part 4
Once set up, have the voltage source set to 5V and tune R3 until the current flowing the ammeter, Ig,
becomes zero. Having the ammeter placed in the middle between R1/3 and R2/x while in series with a
resistor accomplishes a number of things first of all, the goal is to make a balanced circuit in which the
current through the middle path (with the ammeter) is zero, so in the case that the current was not yet
balanced, having the resistor there would hopefully stop the ammeter from getting burnt out. At the same
time, since there’s going to be no current, by having a resistor there, the potential difference across the
resistor can be taken to check if the potential difference is equal to zero as well, as both sides should be
relatively equal.
Once the bridge was finally balanced and the current flowing through the ammeter was shown to be zero,
the individual resistances of each component was recorded as shown in Figure 12 below.
Resistances (Wheatstone)
Resistance
[kΩ]
0.996
0.993
0.671
0.674
Resistor
R1
R2
R3
Rx
Figure 12
Recorded Values for Resistors in Wheatstone Bridge
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Using 𝑅𝑥 =
𝑅2 𝑅3
,
𝑅1
since R1 and R2 were measured to be roughly the same, the equation can be simplified
down to 𝑅𝑥 ≅ 𝑅3 , which makes sense because the goal of this is to have two paths of equal current to
flowing (One through R1/R3, and the other through R2/RX), resulting in a current of zero in the middle. In
addition, if one resistor was more or less than the other, then the current would want to cut across through
the middle path, Ig, where the ammeter has very little resistance, in order to get to the path of least
resistance, or the lesser between Rx and R3.
Conclusion
All in all, this lab was an overall success, as it allowed students to familiarize themselves with most of the
equipment and practice working with simple circuits in a way that helps to develop a better intuition.
The first circuit was pretty straightforward in letting us see KCL in action, by having the currents in the
parallel resistors summing up to the one they were in series with. The second circuit with the light bulbs, I
believe, helped the students develop a better intuition as to how the parallel and series circuits work. For
example, if you wanted to light up a room brightly, you would have most of the light bulbs in parallel in
order to have it as bright as possible, but if you had a limited power source and/or wanted to conserve
energy, then a series connection could be used in order to be efficient and have it last longer, similar to
Christmas lights – one would want to have something in between.
The third circuit was pretty straightforward in showing the direct relationship between the voltage and the
resistances of a series circuit, and how it’s divided pretty evenly, while the fourth circuit showed us how
even when there’s a path in the very middle with almost negligible resistance, a circuit can be designed in
order to have no current flowing through there at all, and a way to measure the resistance of a random
resistor without having to measure it directly.
Revisions:

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
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Added 2-4, the descriptions of KCL/KVL, series vs. parallel circuits, and power dissipation into
the introduction. Originally had a description of KCL somewhere in the Light Bulb Circuit only.
Added “using digital multimeter” into the paragraph describing the resistances of the first circuit.
I originally said that they had been measured, just not with what.
Added the intended values of V1 and V3 being 1 V for the Voltage Divider into the first
paragraph. I originally assumed that it was pretty obvious, but it seems safer with it in than not.
Fixed the first paragraph of the Wheatstone Bridge, as was an incomplete paragraph at the time of
initial submission. I guess I cut most of it off to revise it and just forgot to actually put something
there before submitting.
Added 19, a few sentences explaining how the experimental circuit verified what was originally
planned out.
Added an extra line break in the conclusion just so it looks nicer to me.
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