Electric Potential Difference
In the previous section of Lesson 1, the concept of electric potential was introduced. Electric potential
is a location-dependent quantity that expresses the amount of potential energy
per unit of charge at a specified location. When a Coulomb of charge (or any
given amount of charge) possesses a relatively large quantity of potential
energy at a given location, then that location is said to be a location of high
electric potential. And similarly, if a Coulomb of charge (or any given amount
of charge) possesses a relatively small quantity of potential energy at a given
location, then that location is said to be a location of low electric
potential. As we begin to apply our concepts of potential energy and electric
potential to circuits, we will begin to refer to the difference in electric potential
between two points. This part of Lesson 1 will be devoted to an understanding
of electric potential difference and its application to the movement of charge
in electric circuits.
Consider the task of moving a positive test charge within a uniform electric
field from location A to location B as shown in the diagram at the right. In
moving the charge against the electric field from location A to location B,
work will have to be done on the charge by an external force. The work done on
the charge changes its potential energy to a higher value; and the amount of
work that is done is equal to the change in the potential energy. As a result
of this change in potential energy, there is also a difference in electric
potential between locations A and B. This difference in electric potential is
represented by the symbol ΔV and is
formally referred to as the electric potential difference. By definition, the electric potential difference is the difference in
electric potential (V) between the final and the initial location when work is
done upon a charge to change its potential energy. In equation form, the
electric potential difference is
The standard metric unit on electric potential difference is
the volt, abbreviated V and named in honor of
Alessandro Volta. One Volt is equivalent to one Joule per Coulomb. If the
electric potential difference between two locations is 1 volt, then one Coulomb
of charge will gain 1 joule of potential energy when moved between those two
locations. If the electric 
potential difference between two locations is 3 volts, then one coulomb
of charge will gain 3 joules of potential energy when moved between those two
locations. And finally, if the electric potential difference between two
locations is 12 volts, then one coulomb of charge will gain 12 joules of
potential energy when moved between those two locations. Because electric
potential difference is expressed in units of volts, it is sometimes referred
to as the voltage.
Electric
Potential Difference and Simple Circuits
Electric circuits, as we shall see, are all about the
movement of charge between varying locations and the corresponding loss and
gain of energy that accompanies this movement. In the previous part of Lesson
1, the concept of electric potential was applied to a simple battery-powered
electric circuit. In that
discussion, it was
explained that work must be done on a positive test charge to move it through
the cells from the negative terminal to the positive terminal. This work would
increase the potential energy of the charge and thus increase its electric
potential. As the positive test charge moves through theexternal circuit from the
positive terminal to the negative terminal, it decreases its electric potential
energy and thus is at low potential by the time it returns to the negative
terminal. If a 12 volt battery is used in the circuit, then every coulomb of
charge is gaining 12 joules of potential energy as it moves through the
battery. And similarly, every coulomb of charge loses 12 joules of electric
potential energy as it passes through the external circuit. The loss of this
electric potential energy in the external circuit results in a gain in light
energy, thermal energy and other forms of non-electrical energy.
With a clear understanding of electric potential difference,
the role of an electrochemical cell or collection of cells (i.e., a battery) in
a simple circuit can be correctly understood. The cells simply supply the
energy to do work upon the charge to move it from the negative terminal to the
positive terminal. By providing energy to the charge, the cell is capable of
maintaining an electric potential difference across the two ends of the
external circuit. Once the charge has reached the high potential terminal, it
will naturally flow through the wires to the low potential terminal. The
movement of charge through an electric circuit is analogous to the movement of
water at a water park or the movement of roller coaster cars at an amusement
park. In each analogy, work must be done on the water or the roller coaster
cars to move it from a location of low gravitational potential to a location of high
gravitational potential. Once the water or the roller coaster cars reach high
gravitational potential, they naturally move downward back to the low potential
location. For a water ride or a roller coaster ride, the task of lifting the
water or coaster cars to high potential requires energy. The energy is supplied
by a motor-driven water pump or a motor-driven chain. In a battery-powered
electric circuit, the cells serve the role of the charge pump to supply energy
to the charge to lift it from the low potential position through the cell to
the high potential position.
It is often convenient to speak of an electric circuit such
as the simple circuit discussed here as having two parts - an internal circuit
and an external circuit. The internal circuit is the
part of the circuit where energy is being supplied to the charge. For the
simple battery-powered circuit that we have been referring to, the portion of
the circuit containing the electrochemical cells is the internal circuit. The external
circuit is the part of the circuit where charge is moving outside the cells
through the wires on its path from the high potential terminal to the low
potential terminal. The movement of charge through the internal circuit
requires energy since it is an uphill movement
in a direction that is against the electric field. The movement of charge through the external circuit is natural since
it is a movement in the direction of the electric field. When at the positive
terminal of an electrochemical cell, a positive test charge is at a high electric pressurein the same manner that water at a water
park is at a high water pressure after being pumped to the top of a water
slide. Being under high electric pressure, a positive test charge spontaneously
and naturally moves through the external circuit to the low pressure, low
potential location.
As a positive test charge moves through the external circuit,
it encounters a variety of types of circuit elements. Each circuit element
serves as an energy-transforming device. Light bulbs, motors, and heating
elements (such as in toasters and hair dryers) are examples of
energy-transforming devices. In each of these devices, the electrical potential
energy of the charge is transformed into other useful (and non-useful) forms.
For instance, in a light bulb, the electric potential energy of the charge is transformed
into light energy (a useful form) and thermal energy (a non-useful form). The
moving charge is doing work upon the light bulb to produce two different forms
of energy. By doing so, the moving charge is losing its electric potential
energy. Upon leaving the circuit element, the charge is less energized. The
location just prior to entering the light bulb (or any circuit element) is a
high electric potential location; and the location just after leaving the light
bulb (or any circuit element) is a low electric potential location. Referring
to the diagram above, locations A and B are high potential locations and
locations C and D are low potential locations. The loss in electric potential
while passing through a circuit element is often referred to as avoltage drop. By the time that the positive test charge has
returned to the negative terminal, it is at 0 volts and is ready to be
re-energized and pumped back up to the high
voltage, positive terminal.
Electric
Potential Diagrams
An electric potential diagram is a convenient tool for
representing the electric potential differences between various locations in an
electric circuit. Two simple circuits and their corresponding electric
potential diagrams are shown below.
In Circuit A, there is a 1.5-volt D-cell and a single light
bulb. In Circuit B, there is a 6-volt battery (four 1.5-volt D-cells) and two
light bulbs. In each case, the negative terminal of the battery is the 0 volt
location. The positive terminal of the battery has an electric potential that
is equal to the voltage rating of the battery. The battery energizes the charge
to pump it from the low voltage terminal to the high
voltage terminal. By so doing the battery establishes an electric potential
difference across the two ends of the external circuit. Being under
electric pressure, the charge will now move through the external
circuit. As its electric potential energy is transformed into light energy and
heat energy at the light bulb locations, the charge decreases its electric
potential. The total voltage drop across the external circuit equals the
battery voltage as the charge moves from the positive terminal back to 0 volts
at the negative terminal. In the case of Circuit B, there are two voltage drops
in the external circuit, one for each light bulb. While the amount of voltage
drop in an individual bulb depends upon various factors (to be discussed later), the cumulative amount of drop must equal the 6 volts gained when
moving through the battery.
Check Your Understanding
1. Moving an electron within an electric field would change
the ____ the electron.
a. mass of
b. amount of
charge onc. potential
energy of
Answer: C
When a force is
required to move an electron in the direction of an electric field, its
electrical potential energy increases. On the other hand, an electron moving
opposite the direction of the electric field will decrease its electrical
potential energy. This is because the electric field direction is in the
direction which a positive charge spontaneously moves. An electron is negatively
charged.
2. If an electrical circuit were analogous to a water circuit
at a water park, then the battery voltage would be comparable to _____.
a. the rate at which water flows through the
circuit
b. the speed at
which water flows through the circuit
c. the distance
that water flows through the circuit
d. the water
pressure between the top and bottom of the circuit
e. the hindrance
caused by obstacles in the path of the moving water
Answer: D
The battery
establishes an electric potential difference across the two ends of the
external circuit and thus causes the charge to flow. The battery voltage is the
numerical value of this electric potential difference. In an analogous manner,
it is the difference in water pressure between the top of the water slide and
the bottom of the water slide that the water pump creates. This difference in
water pressure causes water to flow down the slide. Because of the similarity
between electric potential difference in an electric circuit and water pressure
in a water park, the quantity electric potential difference is sometimes
referred to as electric pressure.
3. If the electrical circuit in your Walkman were analogous
to a water circuit at a water park, then the battery would be comparable to
_____.
a. the people that slide from the elevated
positions to the ground
b. the obstacles
that stand in the path of the moving water
c. the pump that
moves water from the ground to the elevated positions
d. the pipes
through which water flows
e. the distance
that water flows through the circuit
Answer: C
The
electrochemical cells in an electric circuit supply the energy to pump the
charge from the low energy terminal to the high energy terminal, thus providing
a means by which the charge can flow. In an analogous manner, a water pump in a
water park supplies the energy to pump the water from the low energy position
to the high energy position. Because of the similarity between the battery in
an electric circuit and a water pump in a water park, the battery is sometimes
referred to as a charge pump.
4. Which of the following is true about the electrical
circuit in your flashlight?
a.
Charge moves around the circuit very fast - nearly as fast as the speed of
light.
b. The battery supplies the charge (electrons) that moves
through the wires.
c. The battery supplies the charge (protons) that moves
through the wires.
d. The charge becomes used up as it passes through the light
bulb.
e. The battery supplies energy that raises charge from low to
high voltage.
f. ... nonsense! None of these are true.
Answer: E
As
emphasized on this page, the battery supplies the energy to move the charge
through the battery, thus establishing and maintaining an electric potential
difference. The battery does not supply electrons nor protons to the circuit;
those are already present in the atoms of the conducting material. In fact,
there would be no need to even supply charge at all since charge does not get
used up in an electric circuit; only energy is used up in an electric circuit.
5. If a battery provides a high voltage, it can ____.
a. do a lot of work over the course of its
lifetime
b. do a lot of
work on each charge it encounters
c. push a lot of
charge through a circuit
d. last a long time
Answer: B
The electric
potential difference or voltage of a battery is the potential energy difference
across its terminals for every Coulomb of charge. A high voltage battery
maximizes this ratio of energy/charge by doing a lot of work on each charge it
encounters.
The diagram below at the right shows a light bulb connected by wires to
the + and - terminals of a car battery. Use the diagram in answering the next
four questions.
6. Compared to point D, point A is _____ electric potential.
a.
12 V higher in
b. 12 V lower in
c. exactly the same
d. ... impossible to tell
Answer: A
The positive
terminal of a battery is higher in electric potential than the negative
terminal by an amount which is equal to the battery voltage.
7. The electric potential energy of a charge is zero at point
_____.
Answer: D
The negative
terminal of the battery is the low voltage location on a circuit. It is
considered to be at 0 Volts.
8. Energy is required to force a positive test charge to move
___.
a. through the wire from point A to point B
b. through the
light bulb from point B to point C
c. through the
wire from point C to point D
d. through the
battery from point D to point A
Answer: D
Energy
is required to cause a positive test charge to move against the electric field
between the negative and the positive terminal.
close
9. The energy required to move +2 C of charge between points
D and A is ____ J.
a.
0.167
b. 2.0c. 6.0d. 12e. 24
Answer: E
A 12 volt
battery would supply 12 Joules of electric potential energy per every 1 Coulomb
of charge which moves between its negative and positive terminals. The ratio of
the change in potential energy to charge is 12:1. Thus, 24 Joules would be the
difference in potential energy for 2 Coulombs of charge.
10. The following circuit consists of a D-cell and a light
bulb. Use >, <, and = symbols to compare the electric potential at A to B
and at C to D. Indicate whether the devices add energy to or remove energy from
the charge.
The electrochemical cell adds energy to the charge to move it
from the low potential, negative terminal to the high potential, positive
terminal. The light bulb removes energy from the charge. Thus, the charge is at
lower energy and a lower electric potential when at locations C and A. Since
there is no energy-consuming circuit element between locations B and D, these
two locations have roughly the same electric potential. The same can be said of
locations C and A.
11. Use your understanding of the mathematical relationship
between work, potential energy, charge and electric potential difference to
complete the following statements:
a.
A 9-volt battery will increase the potential energy of 1 coulomb of charge by
____ joules.
b. A 9-volt battery will increase the potential energy of 2
coulombs of charge by ____ joules.
c. A 9-volt battery will increase the potential energy of 0.5
coulombs of charge by ____ joules.
d. A ___-volt battery will increase the potential energy of 3
coulombs of charge by 18 joules.
e. A ___-volt battery will increase the potential energy of 2
coulombs of charge by 3 joules.
f. A 1.5-volt battery will increase the potential energy of
____ coulombs of charge by 0.75 joules.
g. A 12-volt battery will increase the potential energy of
____ coulombs of charge by 6 joules.
This question targets your mathematical understanding of the
relationship between the electrical potential difference, the voltage and the
amount of charge. The relationship is expressed by the following equation:
a.
A 9-Volt battery will increase the potential energy of 1 Coulomb of charge
by 9 Joules.
b. A 9-Volt battery will increase the potential energy of 2
Coulombs of charge by 18 Joules.
c. A 9-Volt battery will increase the potential energy of 0.5
Coulombs of charge by 4.5 Joules.
d. A 6 -Volt battery will increase the potential energy of 3 Coulombs
of charge by 18 Joules.
e. A 1.5 -Volt battery will increase the potential energy of 2 Coulombs
of charge by 3 Joules.
f. A 1.5 Volt battery will increase the potential energy
of 0.5 Coulombs of charge by
0.75 Joules.
g. A 12 Volt battery will increase the potential energy of 0.5 Coulombs of charge by
6 Joules.