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Potential Difference (1)
1. The Concept of Potential Difference
If two identical metallic balls A and B are charged differently (for example q A > q B ), the two balls are said to be in different electric states.
If these two balls are connected with a conducting wire, the total electric charge on these balls is redistributed equally on each of these balls
(remember that they are identical, so there is no reason for the charge not
to be redistributed equally), then these two balls are said to be in identical
electric states.
In general, the displacement of electric charges from an object to another takes place only if the two objects are connected by a conductor and
they are in different electric states.
The electric state of an object is characterized by a physical quantity
called electric potential.
So, we can say that electric charges may move between two objects
only if there is a potential difference between them.
The electric potential of a point A (or ball A) is generally written as VA ,
and the electric potential of a point B (or ball B) is VB .
The potential difference between two points A and B is written as:
VAB = VA − VB
(1)
The potential difference between the two points A and B is often called
the voltage VAB .
1.1. The sign of the potential difference
The potential difference between two points A and B can be positive or
negative, depending on whether VA > VB or VB > VA . So the potential
difference is an algebraic quantity.
VAB = VA − VB
and
VBA = VB − VA
Therefore
VAB = −VBA
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(2)
1.2. Measurement of potential difference
The potential difference or voltage, can be measured by means of a
voltmeter or an oscilloscope.
A digital multimeter is an istrument that can function as a voltmeter,
as an ammeter, as an ohmmeter, etc.., according the mode you choose. In
voltmeter mode, we use V and COM terminals. In ammeter mode, we use
A and COM.
Figure 1. Multimeter
To measure the potential difference between two points A and B, which
is VAB , you should switch the multimeter in V mode, then connect the
V terminal (or positive terminal) to the point A, and connect the COM
terminal (or negative terminal) to the point B. The voltmeter displays the
value of the voltage VAB .
The symbol of the voltmeter is shown in Figure 2.
Figure 2. Symbo of voltmeter
1.3. Some special cases of potential difference
The potential difference across the terminals of a connection wire is
zero (neglecting wire resistance).
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Figure 3. A voltmeter connected across the terminals of a connection wire
The potential difference across the terminals of an open switch is non-zero.
Actually, it is approximately equal to the voltage of the voltage source
(battery).
Figure 4. A voltmeter connected across the terminals of an open switch
The potential difference across a closed switch is zero. A closed switch
behaves as a connection wire.
Figure 5. A voltmeter connected across the terminals of a closed switch
In an electric circuit, the potential difference across the terminals of a
battery in an open circuit is usually greater than when it is in a closed
circuit.
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Figure 6. A voltmeter connected across the terminals of a battery
2. Laws of potential difference:
2.1. The law of addition of potential differences in a series circuit
In a series circuit, the total potential difference across all the components is equal to the sum of the potential differences across the individual
components:
V = V1 + V2 + V3 + ...
(3)
As an application, Figure 7 shows three lamps connected in series across
a battery. So, the voltage of the battery is distributed over the three lamps
according to Equation 3. So the total voltage of the three lamps (V1 + V2 +
V3 ) is equal to the voltage of the battery Vt . That is, Vt = V1 + V2 + V3 .
Figure 7. Three lamps are connected in series across a battery
2.2. Law of uniqueness of potential difference in a parallel circuit
In a parallel circuil, the potential difference is the same across all branches:
V = V1 = V2 = V3 = ...
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(4)
Figure 8. Three lamps are connected in parallel across a battery
3. Reference Potential
The potential difference VAB = VA − VB is the potential of the point A
minus the potential of the point B, or can be considered as the potential of
A with respect to B. (It is kind of like the position of a point in space. You
can define its position with respect to a reference). So we can say that VAB
as the potential of A with respect to B.
In an electric circuit, it is useful to consider one sigle point with respect
to which the potentials of all other points are defined.
Figure 9.
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For example, in the circuit of Figure 9, we arbitrarily choose the point
G as the reference point. So the potentials of other points are defined as:
VA
VB
VC
VD
VF
VH
=
=
=
=
=
=
VA − VG
VB − VG
VC − VG
VD − VG
VF − VG
VH − VG
For the above equations to be true, we must consider the potential of G
to be zero (VG = 0). Nothing wrong with this assumption, since potential
is a relative quantity, like position. So we always consider the reference
potential in a circuit to be zero. We call this point “Ground”, in analogy to
the ground (Earth) since the potentialof the Earth is considered zero.
In Figure 9, The points E, F, G and H are actually the same point, since
there are nothing in between them but connecting wires. So we can consider them as the same point G. The above equations reduce to:
VA
VB
VC
VD
=
=
=
=
VA − VG
VB − VG
VC − VG
VD − VG
The symbol of the ground is shown in Figure 10.
Figure 10.
We mark the chosen reference point with this symbol on the schematic
diagram of the circuit. For example, the circuit of Figure 9 is redrawn in
Figure 11, with the symbol of ground on the point G.
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Figure 11.
The use of ground reference potential is usually used in electronic engineering, where the electric circuits are usually complicated.
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