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Grade = 10/10 V. Good! Lab Partners: Ainsworth Kiffin & Sammir Condezo Gonzales Online Lab 7 - Resistors in Series and Parallel University Name PHYS 1110 - 01 21 March 2021 Dr. Nader Copty
Objectives: The objective of this activity is to investigate the relationship between the equivalent resistance and individual resistors connected in series and parallel. We will also investigate the voltage across and current through resistors connected in series and parallel using simulation software. Theory: Before starting the experiment, there are a few concepts and equations that need to be known in order to perform the lab: •A combination of resistors in a circuit can be replaced with an equivalent (total) resistor that does not alter the circuit and has the same total current and potential difference as the actual resistors. •The relationship between the current, voltage, and resistance is given by Ohm’s law:
𝑽 = 𝑰𝑹
•
Where: o
V = voltage or potential difference (V) o
I = current (A) o
R = resistance (Ω) •Re
sistors connected in series
have the same current flowing through them. The equivalent (total) resistance, current, and voltage of series combination are given by: •
𝑹
𝑻
= 𝑹
?
+ 𝑹
?
+ 𝑹
?
+ ⋯
•
𝑰
𝑻
= 𝑰
?
= 𝑰
?
= 𝑰
?
= ⋯
•
𝑽
𝑻
= 𝑽
?
+ 𝑽
?
+ 𝑽
?
+ ⋯
•Resistors connected in parallel
have the same voltage applied across them. The equivalent (total) resistance, current, and voltage of parallel combination are given by: •
?
𝑹
𝑻
=
?
𝑹
?
+
?
𝑹
?
+
?
𝑹
?
+ ⋯
•
𝑰
𝑻
= 𝑰
?
= 𝑰
?
= 𝑰
?
= ⋯
•
𝑽
𝑻
= 𝑽
?
+ 𝑽
?
+ 𝑽
?
+ ⋯
•In this activity, we w
ill simulate three resistors in various combinations in a circuit. We will measure the current through the resistors, and the voltage cross the resistors. •We will determine the experimental value of the equivalent resistance (
RT Exp
) using Ohm’s law and the accepted value of the equivalent resistance (
RT Acc
) using the given equations.
Equipment and Materials: •
Computer •
Scientific Calculator •
PhET Circuit Construction Kit: DC –
Virtual Lab Simulation
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Data: •
Part A- Resistor in Series Trial 1
: R
1
= 15.0 Ω, R
2
= 33.0 Ω, R
3
= 100.0 Ω
Voltmeter & Ammeter Across: V (Volts) I (Amps) R
1 V
1
=
12.2 V I
1
=
0.81 A R
2 V
2 =
26.8 V I
2 =
0.81 A R
3 V
3
=
81.1 V I
3
=
0.81 A Battery V
T Acc
= 120.0 V I
T Acc
=
0.81 A Trial 2:
R
1
= 100.0 Ω, R
2
= 15.0 Ω, R
3
= 33.0 Ω
Voltmeter & Ammeter Across: V (Volts) I (Amps) R
1 V
1
=
81.1 V I
1
=
0.81 A R
2 V
2 =
12.2 V I
2 =
0.81 A R
3 V
3
=
26.8 V I
3
=
0.81 A Battery V
T Acc
= 120.0 V I
T Acc
=
0.81
•
Part B- Resistor in Parallel Trial 1:
R
1
= 15.0 Ω, R
2
= 33.0 Ω, R
3
= 100.0 Ω
Voltmeter & Ammeter Across: V (Volts) I (Amps) R
1 V
1
=
120.0 V I
1
=
8.00 A R
2 V
2 =
120.0 V I
2 =
3.64 A R
3 V
3
=
120.0 V I
3
=
1.20 A Battery V
T Acc
= 120.0 V I
T Acc
=
12.8 A Trial 2:
R
1
= 100.0 Ω, R
2
= 15.0 Ω, R
3
= 33.0 Ω
Voltmeter & Ammeter Across: V (Volts) I (Amps) R
1 V
1
=
120.0 V I
1
=
1.20 A R
2 V
2 =
120.0 V I
2 =
8.00 A R
3 V
3
=
120.0 V I
3
=
3.64 A Battery V
T Acc
= 120.0 V I
T Acc
=
12.8 A
Graphs: Part A Trial 1 Trial 2 Part B Trial 1 Trial 2
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Calculations: Part A Trial 1
: R
1
= 15.0 Ω R
2
= 33.0 Ω R
3
= 100.0 Ω
V
T Exp
= V
1
+ V
2
+ V
3
= 12.2 + 26.8 + 81.1 = 120.1 V % Error = ( (120 V - 120.1 V) / 120 V ) x 100% = 0.08% I
T Exp
= (I
1
+ I
2
+ I
3
) / 3 = (0.81 + 0.81 + 0.81) / 3 = 0.81 A % Error = ( (0.81 A - 0.81 A) / 0.81 A ) x 100% = 0.00% R
T Acc
= R
1
+ R
2
+ R
3
= 15.0 + 33.0 + 100.0 = 148 Ω
R
T Exp
= (V
T Exp
) / (I
T Exp
) = (120.1 V) / (0.81 A) = 148 Ω
% Error = ( (148 Ω - 148 Ω) / 148 Ω ) x 100% = 0.00% Trial 2:
R
1
= 100.0 Ω, R
2
= 15.0 Ω, R
3
= 33.0 Ω
V
T Exp
= V
1
+ V
2
+ V
3 = 81.1 + 12.2 + 26.8 = 120.1 V % Error = ( (120 V - 120.1 V) / 120 V ) x 100% = 0.08% I
T Exp
= (I
1
+ I
2
+ I
3
) / 3 = (0.81 + 0.81 + 0.81) / 3 = 0.81 A % Error = ( (0.81 A - 0.81 A) / 0.81 A ) x 100% = 0.00% R
T Acc
= R
1
+ R
2
+ R
3 = 100.0 + 15.0 + 33.0 = 148 Ω
R
T Exp
= (V
T Exp
) / (I
T Exp
) = (120.1 V) / (0.81 A) = 148 Ω
% Error = ( (148 Ω - 148 Ω) / 148 Ω ) x 100% = 0.00% Part B Trial 1
: R
1
= 15.0 Ω R
2
= 33.0 Ω R
3
= 100.0 Ω
V
T Exp
= (V
1
+ V
2
+ V
3
) / 3 = (120.0 + 120.0 + 120.0) / 3 = 120.0 V % Error = ( (120 V - 120 V) / 120 V ) x 100% = 0.00% I
T Exp
= I
1
+ I
2
+ I
3 = 8.00 + 3.64 + 1.20 = 12.8 A % Error = ( (12.8 A - 12.8 A) / 12.8 A ) x 100% = 0.00% R
T Acc
= 1 / (1/R
1
+ 1/R
2
+ 1/R
3
) = 1 / ( (1/15.0) + (1/33.0) + (1/100.0)) = 9.35 Ω
R
T Exp
= (V
T Exp
) / (I
T Exp
) = 120 V / 12.8 A = 9.38 Ω
% Error = ( (9.35 Ω - 9.38 Ω) / 9.35 Ω ) x 100% = 0.32%
Trial 2
: R
1
= 100.0 Ω, R
2
= 15.0 Ω, R
3
= 33.0 Ω
V
T Exp
= (V
1
+ V
2
+ V
3
) / 3 = (120.0 + 120.0 + 120.0) / 3 = 120.0 V % Error = ( (120 V - 120 V) / 120 V ) x 100% = 0.00% I
T Exp
= I
1
+ I
2
+ I
3 = 1.20 + 8.00 + 3.64 = 12.8 A % Error = ( (12.8 A - 12.8 A) / 12.8 A ) x 100% = 0.00%
R
T Acc
= 1 / (1/R
1
+ 1/R
2
+ 1/R
3
) = 1 / ( (1/100.0) + (1/15.0) + (1/33.0)) = 9.35 Ω
R
T Exp
= (V
T Exp
) / (I
T Exp
) = 120 V / 12.8 A = 9.38 Ω
% Error = ( (9.35 Ω - 9.38 Ω) / 9.35 Ω ) x 100% = 0.32%
Conclusions: In Trial 1 of Part A, the total experiment voltage was 120.1 V. This resulted in a 0.08% error. The total experimental current was calculated to be 0.81 A with a 0.00% error. The accepted value of the total resistance was 148 Ω, which I successfully calculated with a 0.00% error. For trial 2 we yielded the same results despite the same placement of each resistor. We yielded a voltage of 120.1 V, an experimental current of 0.81 A and the total resistance of 148 Ω.
In Trial 1 of Part B, the total experiment voltage was 120.0 V. This resulted in a 0.00% error. The total experimental current was calculated to be 12.8 A with a 0.00% error. The total accepted resistance was calculated to be 9.35 Ω while the total experimental resistance was calculated to be 9.38 Ω, which I successfully calculated with a 0.32% error. For both trials we yielded the same results despite the same placement of each resistor. So I conclude that the position of the resistor doesn’t have any effect on the results as long as the values are the same in each trial. The final results obtained from the simulation do agree with the theory of this lab. The theory stated that through Ohm’s Law voltage, the current is directly proportional to the voltage, and inversely proportional to the resistance. When calculating our percent error for current and resistance, it remained low, ranging from 0% - 2.21%. The low percent proved that the experiment was accurate and precise. The placement and order of resistors has a great effect overall on all parts of the experiment. Because they control the control of energy, similar to a dam, the remaining electricity that can move throughout the system differs. This also depends on the strength of each resistor.
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Sources of Error: The sources of error in this experiment maybe from: •
Inaccurate measurements of the voltmeter and ammeter. •
The quality of wires could greatly affect the measured conductivity. •
The uneven placement of the battery and resistors can also have an effect on the readings. •
The battery’s output would affect the proper voltage to perform the lab.
References. •
Copty
, Nader. “Online Lab Experiment: Electric Charges and Fields” Handout. Online •
Walker, Jearl, Robert Resnick, and David Halliday. Halliday & Resnick Fundamentals of Physics. 11th ed. Hoboken, NJ: Wiley, 2018. Print. •
https://phet.colorado.edu/sims/html/circuit-construction-kit-dc-virtual-lab/latest/circuit-
construction-kit-dc-virtual-lab_en.html Contributions: Ainsworth Kiffin:
•
Title Page •
Objective •
Theory Part A •
Equipment •
Part A: Data, Calculations and Graphs •
Part A: Analysis
Sammir Condezo Gonzales: •
Theory Part B •
Part B: Data, Calculations and Graphs •
Part B: Analysis
•
Part A and B- Analysis •
Sources of Error
•
References
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