February 16, 2017 | Author: Josh, LRT | Category: N/A
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Cha ter 1 – Electri c C rrent
Chapter 14 – Electric Current 14.1
Conduction of electricity
Consider a simple closed circuit consists of wires, a battery and a light bulb as shown in Figure A.
Figure A
From the Figure A,
Direction of electric field,
Direction of electron,
or current, : Positive to negative terminal
flows: Negative to positive terminal The electron accelerates becaus bec ausee of the electric force acted on it. It is defined as the total nett charge, flowing through the flowing through the area per unit time, . SI unit for
1 ampere of current is defined as one coulomb of charge passing through the surface area in one second.
14.2
Current density
It is defined as the current flowing through a conductor per unit cross-sectional area .
It is a vector quantity Unit = The direction of
is the same with the direction of the .
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Page 1 of 7
Cha ter 1 – Electri c C rrent
From,
( )
Electrical conductivity,
SI unit for 14.3
is
is the measure of a material’s ability to conduct electric current.
Drift velocity
The drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field. When the electric field is applied to the metal , the freely moving electron experience an electric force and tend to drift with constant average velocity (called drift velocity) towards a direction opposite to the direction of the field as shown in Figure Figu re B .
Figure B **1 The magnitude of the drift velocity is smaller than the random velocities of the free electrons .
**2 The electric current is flowing in the opposite direction of the electron flows .
Drift velocity of charges,
L = length of metal rod
cross-sectional tional area A = cross-sec J = current density e = electron
lectri ric c file fil ed E = E lect I = current
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Page 2 of 7
Cha ter 1 – Electri c C rrent
ê
ê
ê
ê
number of free electrons per volume in metal rod. the number of free electron, is given by: The total charge of the free electrons that pass pas s through the area along the rod is Q Time, required for electron move along the rod is Then, t electron ] : number of free electron per unit volume [DENSITY of free electron] : charge of the electron Set,
14.4 ê
Resistivity and Ohm’s law
Resistance, R di fferencee across an electrical component to the current passing Ratio of the potential differenc through it.
# It is a measure of the component’s opposition to the flow of the electric charge . # Scalar quantity with unit →
ê
or
Resistivity, The resistance of a unit cross-sectional area per unit length of the material .
# It is a measure of material’s ability to oppose the flow of an electric current . # Scalar quantity with unit → # Known as specific resistance # high gh resi resist stiivity] # Good conductors [low resistivity] ; Good insulator [hi
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Cha ter 1 – Electri c C rrent
ê
Conductivity, The reciprocal of the resistivity of a material .
# Scalar quantity with unit →
ê
Ohm’s Law States that the potential difference across a metallic conductor is proportional to the current flowing through it if its temperature is constant.
It can be stated in other form,
is maintained across the conductor sets up by an electric field, and this field produce a current, that is proportiona proportionall to the potential difference . If the field is assumed to be uniform, From ohm’s law, … where and ( )
or
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and
Page 4 of 7
Cha ter 1 – Electri c C rrent
Graphs of potential of potential difference,
14.5
against current, for various materials.
METAL
SEMICONDUCTOR
CARBON
ELECTROLYTE
Dependence of resistivity on temperature
Metal T) = , Number of electrons per unit volume ( n) = UNCHANGED. o Temperature ( T o Metal atoms in the crystal lattice vibrate with greater amplitude and cause the number of collisions between the free electrons and metal atoms increases. Hence the resistance in the metal increases .
Superconductor T) = o Temperature ( T
ê
The resistance decreases to 0.
Temperature coefficient of resistivity, Fractional increase in resistivity of a conductor per unit rise in temperat temperature ure
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Page 5 of 7
Cha ter 1 – Electri c C rrent
Since,
The resistivity of a conductor varies approximatel y linearly with temperature
→ or Thus,
# Unit for
Graphs of resistance, of resistance,
against temperature, for various materials.
METAL
SEMICONDUCTOR
SUPERCONDUCTOR
CARBON
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Page 6 of 7
Cha ter 1 – Electri c C rrent Problems 1.
Resistivity of a wire depends on A. B. C. D.
2.
Length Material Cross-section area Electrons
A silver wire carries a current of . Determine a) The numbers of electrons per second pass through the wire. b) The amount of charge flows through a cross-sectional area of the wire in 55 s. 9 ) (Given charge of electron,
3.
4.
A high voltage transmission line with a diameter of and a length of carries a steady current of . If the conductor is copper wire with a free charge density of 8 electrons , calculate the time taken by one electron to travel the full length of the line. 9 ) (
long and has a
When a potential difference of 240 V is applied across a wire that is 9 . radius, the current density is Calculate Answers: a) The resistivity of the wire. b) The conductivity of the wire. 1. B
2.
a)
9
b) 165 C 5.
A copper wire carries a current of . The cross section of the wire is a square of side and its length is . 8 The density ofthe free electron in the wire is . Determine a) The current density b) The drift velocity of the electrons c) The electric field intensity between both end of the wire d) The potential difference across the wire e) The resistance of the wire
(Given the resistivity of copper is
9 )
8 and
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3. 4.
8 s a) 8 b) 7 a) 6 A b) 4 c) d) e) Ω
Ω
5.
Ω
charge of electron,
Page 7 of 7
