physics lab

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)

•Resistors connected in series have the same current flowing through them. The equivalent

(total) resistance, current, and voltage of series combination are given by:

• 𝑹𝑻 = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑 +⋯

• 𝑰𝑻 = 𝑰𝟏 = 𝑰𝟐 = 𝑰𝟑 = ⋯

• 𝑽𝑻 = 𝑽𝟏 + 𝑽𝟐 + 𝑽𝟑 +⋯

•Resistors connected in parallel have the same voltage applied across them. The equivalent

(total) resistance, current, and voltage of parallel combination are given by:

• 𝟏

𝑹𝑻 =

𝟏

𝑹𝟏 +

𝟏

𝑹𝟐 +

𝟏

𝑹𝟑 +⋯

• 𝑰𝑻 = 𝑰𝟏 = 𝑰𝟐 = 𝑰𝟑 = ⋯

• 𝑽𝑻 = 𝑽𝟏 + 𝑽𝟐 + 𝑽𝟑 +⋯

•In this activity, we will 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

Data:

• Part A- Resistor in Series

Trial 1: R1 = 15.0 Ω, R2 = 33.0 Ω, R3 = 100.0 Ω

Voltmeter & Ammeter

Across:

V (Volts) I (Amps)

R1 V1 = 12.2 V I1 = 0.81 A

R2 V2 = 26.8 V I2 = 0.81 A

R3 V3 = 81.1 V I3 = 0.81 A

Battery VT Acc = 120.0 V IT Acc

= 0.81 A

Trial 2: R1 = 100.0 Ω, R2 = 15.0 Ω, R3 = 33.0 Ω

Voltmeter & Ammeter

Across:

V (Volts) I (Amps)

R1 V1 = 81.1 V I1 = 0.81 A

R2 V2 = 12.2 V I2 = 0.81 A

R3 V3 = 26.8 V I3 = 0.81 A

Battery VT Acc = 120.0 V IT Acc

= 0.81

• Part B- Resistor in Parallel

Trial 1: R1 = 15.0 Ω, R2 = 33.0 Ω, R3 = 100.0 Ω

Voltmeter & Ammeter

Across:

V (Volts) I (Amps)

R1 V1 = 120.0 V I1 = 8.00 A

R2 V2 = 120.0 V I2 = 3.64 A

R3 V3 = 120.0 V I3 = 1.20 A

Battery VT Acc = 120.0 V IT Acc

= 12.8 A

Trial 2: R1 = 100.0 Ω, R2 = 15.0 Ω, R3 = 33.0 Ω

Voltmeter & Ammeter

Across:

V (Volts) I (Amps)

R1 V1 = 120.0 V I1 = 1.20 A

R2 V2 = 120.0 V I2 = 8.00 A

R3 V3 = 120.0 V I3 = 3.64 A

Battery VT Acc = 120.0 V IT Acc

= 12.8 A

Graphs:

Part A

Trial 1 Trial 2

Part B

Trial 1 Trial 2

Calculations:

Part A

Trial 1:

R1 = 15.0 Ω R2 = 33.0 Ω R3 = 100.0 Ω

VT Exp = V1 + V2 + V3

= 12.2 + 26.8 + 81.1

= 120.1 V

% Error = ( (120 V - 120.1 V) / 120 V ) x 100% = 0.08%

IT Exp = (I1 + I2 + I3) / 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%

RT Acc = R1 + R2 + R3

= 15.0 + 33.0 + 100.0

= 148 Ω

RT Exp = (VT Exp) / (IT Exp)

= (120.1 V) / (0.81 A)

= 148 Ω

% Error = ( (148 Ω - 148 Ω) / 148 Ω ) x 100% = 0.00%

Trial 2:

R1 = 100.0 Ω, R2 = 15.0 Ω, R3 = 33.0 Ω

VT Exp = V1 + V2 + V3

= 81.1 + 12.2 + 26.8

= 120.1 V

% Error = ( (120 V - 120.1 V) / 120 V ) x 100% = 0.08%

IT Exp = (I1 + I2 + I3) / 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%

RT Acc = R1 + R2 + R3

= 100.0 + 15.0 + 33.0

= 148 Ω

RT Exp = (VT Exp) / (IT Exp)

= (120.1 V) / (0.81 A)

= 148 Ω

% Error = ( (148 Ω - 148 Ω) / 148 Ω ) x 100% = 0.00%

Part B

Trial 1:

R1 = 15.0 Ω R2 = 33.0 Ω R3 = 100.0 Ω

VT Exp = (V1 + V2 + V3) / 3

= (120.0 + 120.0 + 120.0) / 3

= 120.0 V

% Error = ( (120 V - 120 V) / 120 V ) x 100% = 0.00%

IT Exp = I1 + I2 + I3

= 8.00 + 3.64 + 1.20

= 12.8 A

% Error = ( (12.8 A - 12.8 A) / 12.8 A ) x 100% = 0.00%

RT Acc = 1 / (1/R1 + 1/R2 + 1/R3)

= 1 / ( (1/15.0) + (1/33.0) + (1/100.0))

= 9.35 Ω

RT Exp = (VT Exp) / (IT 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:

R1 = 100.0 Ω, R2 = 15.0 Ω, R3 = 33.0 Ω

VT Exp = (V1 + V2 + V3) / 3

= (120.0 + 120.0 + 120.0) / 3

= 120.0 V

% Error = ( (120 V - 120 V) / 120 V ) x 100% = 0.00%

IT Exp = I1 + I2 + I3

= 1.20 + 8.00 + 3.64

= 12.8 A

% Error = ( (12.8 A - 12.8 A) / 12.8 A ) x 100% = 0.00%

RT Acc = 1 / (1/R1 + 1/R2 + 1/R3)

= 1 / ( (1/100.0) + (1/15.0) + (1/33.0))

= 9.35 Ω

RT Exp = (VT Exp) / (IT 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.

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