EMF, Terminal Voltage, and Internal Resistance Mary Grace DC. Odiamar

De La Salle University

2401 Taft Avenue, Malate, Manila, Philippines mary_grace_odiamar@dlsu.edu.ph

Abstract – This paper is generally about the inspection and

examination of voltage sources of direct-current circuits, known

otherwise as seats of emf or emf devices. The experiment aimed

to illustrate the difference between emf and terminal voltage, to

show how an ideal battery is different from a real one with an

internal resistance, to measure the electromotive force of a

battery, to calculate the internal resistance of a real battery and

to show the variants of a battery’s terminal voltage with its

current output through experimentation. In this experiment, the

internal resistance of Daniell cell (wet cell) was computed by

measuring the voltage across the circuit where the values of

resistances R were given; current I and internal resistance r were

then computed through Ohm’s Law and through the equation of

terminal voltage of a real battery, respectively. On the other

hand, the carbon battery’s internal resistance was computed by

measuring the voltage across the circuit where the values of

current were given; internal resistance r was also computed

through the equation of terminal voltage of a real battery. The

acquired results were very likely to show how a battery’s voltage

is related to current and resistance, as well as how to calculate a

battery’s internal resistance.

Keywords – Emf, Terminal Voltage, Internal Resistance, Battery,

Daniell Cell, Dry Cell, Voltmeter, Ammeter, Rheostat

I. INTRODUCTION

Electric circuits are essential means to transport electric

potential energy from one region to another. When charged

particles move within a circuit, energy is transported from a

source such as a battery to an instrument where the said

energy is stored or transformed into other form/s. Generally,

today’s modern world is heavily dependent on electric

circuits. They have been used for years because of their

effectiveness and practicality – they typically allow energy to

be conveyed without moving any parts. One should note that

electric circuits are at the heart of every electronic device.

Every electric circuit consists of components, and these

often include sources, resistors, and other circuit elements

interconnected in a network [1]. One element to be noted in

this paper is the source of the circuit, more often known as the

battery. In a battery, a chemical reaction occurs when a load

completes the circuit between the terminals. The chemical

reaction then transfers electrons from one terminal to another

terminal. The electric potential difference is caused by the

positive and negative charges on the battery terminals. The

maximum potential difference of a battery is called the

electromotive force or emf, designated by Ɛ [2].

II. THEORETICAL BACKGROUND

A. Seats of EMF and EMF

When a potential difference or voltage is applied across a

circuit, current will be allowed to flow. These devices that are

responsible for the flow of charge in circuits are called seats

of emf, emf devices or simply voltage sources. The emf is not

really a force but is the work per unit charge that an emf

device does in moving positive charges from lower potential

terminal (-) to higher potential terminal (+). Its unit is joule

per coulomb or volts. A voltage source is labeled with its emf

value, Ɛ, which is equivalent to Ɛ =

[3].

B. Emf, Terminal Voltage, and Internal Resistance

A real battery is made of matter; therefore, there is

resistance r to the flow of charge inside the battery. This

resistance inside the battery is called internal resistance r. An

ideal battery with zero internal resistance has a terminal

voltage equal to its emf, no matter how much current is drawn

from them. However, a real battery in a circuit where current

is drawn from has a terminal voltage which is not equivalent

to its emf [4]. Its terminal voltage is given by 𝑉𝑎b = ε – 𝐼𝑟. In

this equation we notice that the terminal voltage drops as we

draw more current from the battery because of the internal

resistance. In rearranging the equation, we can get a battery’s

internal resistance by r =

C. Daniell Cell and Dry Cell

John Frederick Daniell, a chemistry professor in London,

has developed an emf device that supplied constant electric

current. The Daniell cell is a type of wet cell and has also been

called as a gravity cell and crowfoot cell. In the early 1800s,

the cell became a popular power supply in the laboratories and

in the telecommunications industry. The cell is made of

copper and zinc electrodes and an electrolyte solution. This

battery converts chemical energy to electrical energy

whenever a load is present.

Nowadays, better batteries with low internal resistances

have been developed. Cars consume lead-acid batteries, which

is also a wet cell. This battery comprises of lead and lead

oxide electrodes and an electrolyte solution.

In contrast to the batteries of the earlier centuries, modern

batteries have been constructed to be very portable and

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.005 0.01 0.015

Vab

(v

olt

s)

I (A)

maintenance-free. One of today’s primary batteries is the zinc-

carbon battery, a dry cell, and also known as the standard

carbon battery. It is a very cheap battery and comes in various

sizes – AA, AAA, C and D [3].

III. METHODOLOGY

A. Preliminary Steps

Before starting the experiment, the wires should be

checked for continuity as for the research to have fewer errors

and to yield more accurate results. The functionality of these

wires could be checked by just connecting the probes of the

voltmeter-ohmmeter-milliammeter (VOM) to the ends of the

wires. The VOM should be set to the ohmmeter function. The

batteries to be used in the experiment should be guaranteed to

be new and working as well.

B. Daniell Cell (Wet Cell)

To perform the experiment for the Daniell cell, the

voltage across the terminals of the Daniell cell was first

measured with a voltmeter. The value obtained is equal to its

emf. A series circuit involving a Daniell cell, a decade

resistance box set to 20 Ω and a voltmeter connected to the

circuit in parallel was then constructed. The first reading in

the voltmeter was recorded. The experiment was repeated

with different values of the decade resistance box – 40, 60, 80

and 100 Ω. The measured voltage values were then recorded.

Internal resistance r was computed through the equation r

=

. This experiment had two trials.

Figure 1. Setup for Daniell Cell [3].

C. Carbon Battery (Dry Cell)

For the dry cell, the voltage across the terminals of this

battery was measured first as well. The value obtained was

recorded as its emf. A series circuit was constructed as well,

with the voltmeter connected across the battery in parallel. It

should also be noted that one end terminal and the center tap

of the rheostat is connected, while the other end terminal of

the rheostat is disconnected. In getting the voltage reading, the

slider of the rheostat was adjusted until the ammeter reads

0.05 amperes. The experiment was repeated with different

values of the current. The rheostat was adjusted with the

following readings in the ammeter – 0.10, 0.15, 0.20 and 0.25

amperes. The measured voltages were logged. Internal

resistance r was then computed through the equation r =

.

Figure 2. Setup for dry cell [3].

IV. RESULTS AND DISCUSSION

A. Daniell Cell (Wet Cell)

1) First Trial:

Ɛ = 1.1 volts

TABLE 1

MEASUREMENTS

Figure 3. Vab vs. I (First trial for Daniell cell)

R (Ω) Measured Vab (Volts) I (A) Calculated r (Ω)

20 0.26 0.013 64.62

40 0.41 0.0103 66.99

60 0.52 0.00867 66.90

80 0.60 0.00750 66.67

100 0.66 0.00660 66.67

Average r = 66.37 Ω

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.002 0.004 0.006 0.008 0.01

Vab

(v

olt

s)

I (A)

0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3

Vab

(v

olt

s)

I (A)

Current I was calculated from the measured voltages and

resistances by Ohm’s Law, I =

. With the complete data, the

internal resistances r were calculated through the equation r

=

which was derived earlier. It should be noted from the

data that as the external resistance increases, the current

decreases. The internal resistance increases together with the

external resistance and the average internal resistance

obtained for trial one is 66.37 Ω. In the graph, the slope

determines the internal resistance r. It was computed through

m =

. In this trial, m=

; m = -67.86. The

negative sign in the slope indicates an inverse relationship

between the terminal voltage and the current. The internal

resistance from slope is equal to 67.86 Ω, a value which is

very close to the average r, which is 66.37 Ω. The value of

emf Ɛ can also be obtained from the graph through the

equation y = mx + b. Y-intercept b is equal to the emf Ɛ.

Getting emf Ɛ, 0.52 = (-67.86)(8.67 x10-3) + b. The equation

yielded b = 1.11, a value equivalent to the measured emf 1.10

V.

2) Second Trial:

Ɛ = 1.08 volts

TABLE 2

MEASUREMENTS

Figure 4. Vab vs. I (Second trial for Daniell cell)

Current I was calculated from the measured voltages and

resistances by Ohm’s Law, I =

. With the complete data, the

internal resistances r were calculated through the equation r

=

which was derived earlier. It should be noted from the

data that as the external resistance increases, the current

decreases. The internal resistance increases together with the

external resistance and the average internal resistance

obtained for trial one is 107.54 Ω. In the graph, the slope

determines the internal resistance r. It was computed through

m =

. In this trial, m=

; m = -100. The

negative sign in the slope indicates an inverse relationship

between the terminal voltage and the current. The internal

resistance from slope is equal to 100 Ω, a value which is very

close to the average r, which is 107.54 Ω. The value of emf Ɛ

can also be obtained from the graph through the equation y =

mx + b. Y-intercept b is equal to the emf Ɛ. Getting emf Ɛ,

0.39 = (-100)(6.5x10-3) + b. The equation yielded b = 1.04, a

value equivalent to the measured emf 1.08 V. It is noted that

the first and second trials have precise results.

B. Carbon Zinc (Dry Cell)

Ɛ = 1.08 volts TABLE 3

MEASUREMENTS

I (A) Measured Vab (Volts) Calculated r (Ω)

0.07 2.37 4.00

0.10 2.25 4.00

0.15 2.05 4.00

0.20 1.85 4.00

0.25 1.65 4.00

Average r = 4.00 Ω

Figure 5. Vab vs. I (First trial for carbon zinc)

With the complete data, the internal resistances r were

calculated through the equation r =

which was derived

earlier. It should be noted from the data that as the external

resistance increases, the current decreases. The internal

resistance increases together with the external resistance and

the average internal resistance obtained is 4.00 Ω, which is

generally lower than that of a Daniell cell’s. In the graph, the

slope determines the internal resistance r. It was computed

through m =

. In this trial, m=

; m = -4. The

negative sign in the slope indicates an inverse relationship

between the terminal voltage and the current. The internal

resistance from slope is equal to 4 Ω, a value which is

R (Ω) Measured Vab

(Volts)

I (A) Calculated r (Ω)

20 0.17 0.0085 107.06

40 0.29 0.00753 108.97

60 0.39 0.00650 106.15

80 0.46 0.00575 107.83

100 0.52 0.00520 107.69

Average r = 107.54 Ω

equivalent to the average r, which is 4 Ω. The value of emf Ɛ

can also be obtained from the graph through the equation y =

mx + b. Y-intercept b is equal to the emf Ɛ. Getting emf Ɛ,

1.65 = (-4)(0.25) + b. The equation yielded b = 2.65, a value

equivalent to the measured emf 2.65 V.

V. CONCLUSION

The results obtained in the two parts of the experiment

yielded very small discrepancies between the values measured

and calculated. This proves that the equations verify the

theories and laws formulated by renowned physicists. From

the beginning of the experiment, it was expected that the

Daniell cell would have a higher internal resistance than the

carbon zinc battery, and it was confirmed in the experiment.

Therefore, a dry cell is seen as a better battery than a Daniell

cell. It was also verified that as the current increases, the

terminal voltage decreases across both cells. Through the

experiment, it is concluded that the terminal voltage Vab is less

than its emf whenever current is flowing through the battery,

because an internal resistance is present in the battery.

ACKNOWLEDGMENT

The author wishes to thank Ms. Katrina Vargas, first

and foremost, for imparting with the author the necessary

knowledge in simple circuits and thermodynamics. She also

wishes to acknowledge her group mates for the term, Nel

Aguilar and Darlene Campado. Lastly, she also gives her

thanks for the assistance and support of the DLSU Physics

department.

REFERENCES

[1] H. D. Young, et al., “Current, Resistance, and Electromotive Force,” in

Sears and Zemansky’s University Physics with Modern Physics, 13th ed.

San Francisco, CA: J. Smith, 2004, pp. 814-831.

[2] J. D. Cutnell and K. W. Johnson, “Circuits,” in Physics, 7th ed. Danvers,

MA: Wiley, 2007, p. 603.

[3] De La Salle University Physics Department, Experiment 7: EMF,

Terminal Voltage, and Internal Resistance. Manila, Philippines: De La

Salle University, 2013.

[4] R. Serway and J. Jewett, “Direct-Current Circuits,” in Physics for

Scientists and Engineers with Modern Physics, 9th ed. Boston, MA: M.

Finch and C. Hartford, 2008, pp. 833-834.