The Combination of Cells and Resistors in a Circuit

Name: Emmanuel BALOME
ID Number: 20140385
Group Number: A2
Lab Partners: * Christopher BAGME * Leandra BANIYAMAI * Amex BATEME * Kingston BOB * Natalie BROWN

Abstract

Batteries and resistors can be connected in both series and parallel circuits where the current and voltage running through them can be altered. Batteries connected in series give off large amounts of electromotive force while the reverse happens when connected in parallel. Resistors connected in series are added individually while an inverse summation results while connected in parallel. These are the effects that will be closely studied in this report.

Introduction

All electronic devices and setups require some complex form of wiring for proper functionality. To do so electricians have to understand the effects of electricity and how it can be managed. Batteries or more preferably ‘dry cells’ produce electromotive forces that create electric fields that help drive electrons around circuits. There are two common circuit arrangements; one is called the series circuit while the other is called the parallel circuit. Components in series circuits are connected one after another where the whole current flows through each component, while components in parallel circuits are arranged in a way that the current breaks up so that a fraction of it flows through a component. These type of wirings are found in common housing circuits but the more complex ones are found in electronic devices such as televisions, radios, computers, etc. Students were made aware of these effects by doing a practical that required them to construct circuits that involved batteries and resistors connected in both parallel and series. Later they were asked to compare the two circuits in terms of the current and voltage readings taken at each instances.

Theoretical Background

When moving along circuits electrons face different forms of resistance particularly peculiar to the distinct materials they are comprised of and the way they are wired such as in series or parallel, the total voltage (V), current (I) and resistance (R) through a series can be calculated as follows: * VT=V1+V2+V3+Vn
VT=V1+V2+V3+Vn
Voltage :

* Current:
I1=I2=I3=I4=In
I1=I2=I3=I4=In

1

1

* Resistance:
2

2

RT=R1+R2+R3+Rn
RT=R1+R2+R3+Rn

While in a parallel circuit the total voltage, current and resistance can be calculated as shown below: * VT=V1=V2=V3=Vn
VT=V1=V2=V3=Vn
Voltage:

* Current:
IT=I1+I2+I3+In
IT=I1+I2+I3+In

* Resistance:
1RT=1R1+1R2+1R3+1Rn
1RT=1R1+1R2+1R3+1Rn

Electromotive force (εmf) is not a force but it is simply the potential needed to drive electrons around a circuit when there is no current. The readings on the shells of batteries indicate the electromotive force, but once they are used in closed circuits they come under the stress of internal resistance (r) and terminal resistance (R), so the equation relating all of this is shown below: εmf=internal voltage+terminal voltage εmf=internal voltage+terminal voltage

εmf=Ir+IR εmf=Ir+IR But as for the case of this practical the εmf measured was initially not connected to a circuit, there were some variances in the εmf when the batteries were connected in series and parallel: * ET=E1+E2+E3+En
ET=E1+E2+E3+En
Electromotive force of the batteries in series

* ET=E1=E2=E3=En
ET=E1=E2=E3=En
Electromotive force of the batteries in parallel

A great German scientist in the 19th Century pooled the three quantities - voltage (V), current (I) and resistance (R) - in electricity together in a simple algebraic statement:

V=IR

The wirings of parallel and series present a more diverse approach that obtains unique results that are imperative to the day to day basis of electronics.

Experimental Design and Procedure

The apparatuses that were used are: * Two dry cells (1.5V each) * A multimeter * Two resistors * Five circuit wires

Methodology: 1. Students were asked to design four circuits that had a combination of dry cells in series and parallel and a combination of resistors in series and parallel. 2. After being approved by tutors on standby the students constructed the four circuits by connecting the components each at a time using the wires because the circuit board was assigned only one to a group. 3. At the first stage the students went on to measure the εmfof the dry cells connected in series and then parallel using the multimeter. 4. After that, they measured the voltage, current and resistance of the two resistors that were connected to the two dry cells in series and then parallel. (Note: the two dry cells were connected to in series and not parallel.) 5. Once the readings were taken, the students were then told to state equations that supported the results of the practical.

Analysis

The four diagrams depicting the four circuits are on the next page (page 4) while the results of the practical are shown below:

a) A combination of dry cells in a series circuit.

The total emf reading of the two 1.5V batteries for that wiring was 3.04V with individual cells at 1.52V, this simply implied that the total emf was the linear summation of the voltage of two power sources (check the diagram on page 4). Therefore the voltage reading for batteries connected in series is summed as:
(Let the total combined emf be E and the emf due to battery 1 be E1 and that due to battery 2 as E2)

E=E1+E2

So the total emf is calculated below as:

E=1.52V+1.52V
E=1.52V+1.52V
E=E1+E2
E=E1+E2
Data
E1=1.52V
E2=1.52V
E=3.04V
E=3.04V

b) A combination of dry cells in a parallel circuit.

The total emf reading for the two 1.5V batteries for that wiring was 1.52V, this simply implied that total emf is the same as the individual emfs (check the diagram on page 4). Therefore the total emf for batteries of the same voltage that are connected in parallel is summed below:
(Let the total combined emf be E and the emf due to battery 1 be E1 and that due to battery 2 as E2)
3

3

E=E1=E2
E=E1=E2

5

5

So, the total emf can be calculated as:

E=1.52V
E=1.52V
E=1.52V=1.52V
E=1.52V=1.52V
E=E1=E2
E=E1=E2
Data
E1=1.52V
E2=1.52V

c) A combination of resistors in a series circuit.

The voltage and current through each of the resistors is show below with the values of the resistors themselves in the series circuit (check the diagram on page 4).
I2=3.5mA
I2=3.5mA
I1=3.5mA
I1=3.5mA

V2=1.92V
V2=1.92V
V1=1.11V
V1=1.11V

R2=564Ω
R2=564Ω
R1=326Ω
R1=326Ω

The equation used to calculate the electric resistance in the series circuit is given below:
RT=R1+R2
RT=R1+R2

Thus the value of the overall combined resistance is:
RT=R1+R2
RT=R1+R2

RT=326Ω+564Ω
RT=326Ω+564Ω

RT=890Ω
RT=890Ω

d) A combination of resistors in a parallel circuit.

The voltage and current through each of the resistors is show below with the values of the resistors themselves in the parallel circuit: (check the diagram on page 4)
I2=5.4mA
I2=5.4mA
I1=9.2mA
I1=9.2mA

V2=3V
V2=3V
V1=3V
V1=3V

R2=564Ω
R2=564Ω
R1=326Ω
R1=326Ω

The total combined resistance can be calculated as follows in a parallel circuit:
1RT=1R1+1R2
1RT=1R1+1R2

RT=R1R2R1+R2
RT=R1R2R1+R2

6

6

RT=326Ω×564Ω326Ω+564Ω
RT=326Ω×564Ω326Ω+564Ω

RT=206.59Ω
RT=206.59Ω

Clearly, the arrangement of components in circuits did present a big deal of alteration in the overall current and voltage running through the circuit. When the voltage broke up the current remained the same and vice versa, this attribute is an inherent property of all dynamic electric charges. Another relative property seen was that when the batteries or resistors were connected in parallel the voltage remained the same and consequentially the current increased, as seen in the comparison between the last two cases where a dramatic increase in the current is noted when the resistors were connected in parallel. The experiment turned out well as there were no complications. By using V=IR in the last two cases, it turned out that the reading was accurate: * The total emf of the resistors arranged series.
V=3.1V
V=3.1V
V=(3.5×10-3A)(890Ω)
V=(3.5×10-3A)(890Ω)
V=IRT
V=IRT
Data
I=3.5mA
RT=890Ω
V=?

* The total emf of the resistors arranged in parallel.
V=3.0V
V=3.0V
V=(1.4×10-2A)(206.95Ω)
V=(1.4×10-2A)(206.95Ω)
V=ITRT
V=ITRT
Data
IT=14.6mA
RT=206.95Ω
V=?

Conclusion

On the whole, it can be appreciated that when dry cells are connected in series, their total combined emf is the sum of all the emfs of the batteries connected, while the total combined emf of batteries of the same emf connected in parallel is the emf value of a single dry cell. Furthermore, the voltage entering a parallel circuit is the same throughout, whereas voltage in series is not maintained all through. Additionally, current in series is the same throughout, however it changes in a parallel circuit. Likewise, the total combined resistance in a series is obtained by adding it up linearly while the total combined resistance in a parallel is obtained by calculating the summation of its inverse.

Acknowledgements:

I would firstly like to acknowledge and thank GOD for guiding me right through this report because without Him nothing can be accomplished. And as for these students who have helped me in carrying out the experiment I would like to say thankyou, and they are: * Christopher BAGME * Leandra BANIYAMAI * Amex BATEME * Kingston BOB * Natalie BROWN
And those people who have helped in whatever ways they had, I am greatful and appreciate their contributions.

References:

* Openstax College (2013) College Physics. USA: Rice University, Connexions. * Serway, R. A and Jewett Jr, J.W (2014) Physics for Scientists and Engineerss with Modern Physics. 9th ed. USA: Brooks/Cole.

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PHYSICS 1 REPORT
Combination of Cells and Resistors
PHYSICS 1 REPORT
Combination of Cells and Resistors

Tutor: Mr Rawali
Tutor: Mr Rawali

M

Name: Emmanuel BALOME
ID Number: 20140385
Group: A2
Course: Science Foundation Year

Name: Emmanuel BALOME
ID Number: 20140385
Group: A2
Course: Science Foundation Year

Tutor: Mr Felix Gitai
Tutor: Mr Felix Gitai