Transcript Current and Resistance

Current and Resistance
28-10-2015
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Define the current.
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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
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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
I 


Q
t
The SI unit of current is
Ampere (A) 1 A = 1 C/s
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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

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
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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 crosssectional 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
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The drift speed, vd, is the speed at which the carriers
move
◦ vd = Δx/ Δt
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Rewritten: ΔQ = (n A vd Δt) q
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Finally, current, I = ΔQ/Δt = nqvdA

OR
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:
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
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
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
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The constant of proportionality is the resistance of
the conductor
V
R
I
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Units of resistance are ohms (Ω)
◦ 1Ω=1V/A
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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
◦
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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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