Define the current.
Understand the microscopic description of
current.
Discuss the rat at which the power transfer to a
device in an electric current.
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2-1 Electric current
2-2 Resistance and Ohm’s Law
2-3 Current density, conductivity and
resistivity
2-4 Electrical Energy and Power
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Whenever electric charges of like signs move, an
electric current is said to exist.
The current is the rate at which the charge flows
through this surface
◦ Look at the charges flowing perpendicularly to a surface of
area A
The SI unit of current is
Ampere (A) 1 A = 1 C/s
4
QI
t
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∆Q is the amount of charge that
passes through this area in a
time interval ∆ t,
the average current Iav is equal to the
charge that passes through “A” per
unit time
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We define the instantaneous current I as
the differential limit of average current:
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The direction of the current is the direction
positive charge would flow
◦ This is known as conventional current direction
In a common conductor, such as copper, the current is
due to the motion of the negatively charged electrons
It is common to refer to a moving charge as a mobile
charge carrier . A charge carrier can be positive or
negative. For example, the mobile charge carriers in a
metal are electrons.
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Charged particles move
through a conductor of cross-
sectional area A
n is the number of charge
carriers per unit volume
n A Δx is the total number of
charge carriers
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The total charge is the number of carriers times the charge
per carrier, q
◦ ΔQ = (n A Δx) q
The drift speed, vd, is the speed at which the carriers move
◦ vd = Δx/ Δt
Rewritten: ΔQ = (n A vd Δt) q
Finally, current, I = ΔQ/Δt = nqvdA
OR
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the average current in the conductor
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If the conductor is isolated, the electrons undergo
random motion
When an electric field is set up in the conductor, it
creates an electric force on the electrons and
hence a current
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The zig-zag black line represents the motion of charge carrier in a conductor The net drift speed is small
The sharp changes in direction are due to collisions
The net motion of electrons is opposite the direction of the electric field
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Consider a conductor of cross-sectional area
A carrying a current I. The current density J in
the conductor is defined as the current per unit
area. Because the current I = nqvdA,
the current density is:
11
the current density is proportional to the electric field:
Where σ the constant of
proportionality & is called the
conductivity of the conductor.
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If the field is assumed to be uniform,
the potential difference is related to
the field through the relationship
12
express the magnitude of the current
density in the wire as
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Where ,J = I/A, we can write the potential
difference as
13
The quantity R = ℓ/σA is called the resistance of
the conductor. We can define the resistance as
the ratio of the potential difference across a
conductor to the current in the conductor:
,
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1. Material property—each material will oppose the flow of
current differently.
2. Length—the longer the length , the more is the
probability of collisions and, hence, the larger the
resistance.
3. Cross-sectional area—the larger the area A, the easier
it becomes for electrons to flow and, hence, the lower the
resistance.
4. Temperature—typically, for metals, as temperature
increases, the resistance increases
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Thus, the resistance R of any material with a uniform cross-
sectional area A and length (as shown in Fig) is directly
proportional to the length and inversely proportional to its
cross-sectional area. In mathematical form,
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In a conductor, the voltage applied across the
ends of the conductor is proportional to the current
through the conductor
The constant of proportionality is the resistance of
the conductor
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VR
I
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Units of resistance are ohms (Ω)
◦ 1 Ω = 1 V / A
Resistance in a circuit arises due to collisions
between the electrons carrying the current with
the fixed atoms inside the conductor
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Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents
This statement has become known as Ohm’s Law
◦ ΔV = I R
Ohm’s Law is an empirical relationship that is valid only for certain materials ◦ Materials that obey Ohm’s Law are said to be Ohmic
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An ohmic device
The resistance is
constant over a wide
range of voltages
The relationship
between current and
voltage is linear
The slope is related to
the resistance
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Non-Ohmic materials are
those whose resistance
changes with voltage or
current
The current-voltage
relationship is nonlinear
A diode is a common
example of a non-Ohmic
device
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The electric current I in a conductor is defined as
The average current in a conductor is related to the motion of
the charge carriers through the relationship
The magnitude of the current density J in a conductor is the
current per unit area:
The current density in an ohmic conductor is proportional to
the electric field according to the expression
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