**Internal Resistance of a Battery**

Introduction

By Moses, Keith, Ron and Chukiang

Summary and Resutls

Support For Hypothesis

The hypothesis is supported by the results.

Using Logger Pro

Data

Analysis

In Conclusion

Despite the potential error in our data involving the variance in reported voltages and current, the error is very minimal. This leads us to believe our data and results are solid, accurate and repeatable.

Questions

Purpose

Our Purpose was to analyze the effect of the internal resistance (r) and the EMF of a battery, by treating it as if it is in series with the circuit and find their values.

Hypothesis

The Internal Resistance (r) is predicted to be much smaller than the external resistance (R) and the EMF is predicted to be less than the terminal voltage. Thus, enabling us to ignore the resistance for this battery in real world application.

Procedure

Observations

1. As the Resistance increased, the voltage increased and current dropped which is what we expected.

2. Additionally, the fluctuations in the voltage readings become more pronounced as we decreased the resistance.

Data Tables

Sample Calculations and Random error

1. Error could originate from a constant drop in Voltage due to the on going chemical processes in the battery. A switch is thus added to reduce it.

2. The error for this lab would be a failure to take instantaneous readings. In the case of reading the ammeter, the average values of the fluctuations have been taken.

3. Equation used is modeled as R=(EMF/I)-r instead of V= -Ir+EMF thus eliminating random error reading the voltmeter.

Graphs

Things would improve if

Logger-pro could have been utilized to obtain the instantaneous data thus reducing the human error.

Error Analysis

Yes

1. The Internal Resistance of the battery is 12.237 Ohms. This is indeed much smaller than the resistance we used.

2. The EMF is greater than the terminal voltage (rating) of the battery. The obtained electromagnetic force being 6.495V and the given battery voltage rated at 6 Volts. We speculate that the 6Volts on the battery is a rounded figure.

Also,

We can now choose to ignore the internal resistance in day to day engineering calculations.

Based on Jim Harvey's speech structures

Independent variabel is the Variable Resistance [R].

Dependent Variables are the Current and Terminal Voltage.

Variables

Procedure

Analysis Plan

We set up the circuit above with the ammeter in series and Volt meter in parallel. Then setting the Variable resistance as the independent variable, current and voltage are recorded in the data table given below.

r=Internal resistance I=Current

R=Variable Resistor

EMF = Voltage of the battery

The Electro Motive Force for the circuit, according to Kirchoff's second law, can be modeled as; R= (EMF)/I - r.

Plotting Variable Resistance (R) vs 1/Current (I^-1), should result in a best fit line with an equation; Y=mX+C. Where Y=R, X=(1/I). Therefore we can say R=m(1/I)+C

Comparing the above equations, we can say that m= EMF and Y-intercept=-r=Internal Resistance.

0 = Ɛ – Ir - IR

Ɛ = IR + Ir

Ɛ(/I) = IR + Ir

R = Ɛ/I - r

0 = Ɛ – Ir - IR

Ɛ = IR + Ir

Ɛ = V + Ir

V = Ɛ – Ir

Derivation of Formula

and thus compensate for Moses's bad eye sight

.

1. Vertical Error

Error for Resistance was found to be

1% from the variable resistance machine website. Thus the error bars reflected this on the graph. Thus taking the calculated error was 0.41%

2. Horizontal Error

Error for Ammeter came from the fluke meter and from reading error. We found to it be 1.5% error for the fluke meter. This reading error was estimated to be 1%. The combined error came up to be 1.04%.

Systematic Error % Calculation

Final equation corresponding to

R = Ɛ /I- r

R = 6.495/I - 12.237

The EMF found = 6.49V+ .064V or -0.065

The internal resistance = r = 12.237+/- 0.122 Ohms

We tried using the logger pro to record data.

However, the data wasn't consistent. As a result, we chose to ignore the data recorded through logger pro.