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The Starting Point: Elements, Atoms and Charge
Electrons and protons have, in addition totheir mass, a quantity called charge
Charge (unlike mass) can be either positive(protons) or negative (electrons)
Like charges repel, unlike charges attract
Ions External force can cause an electron to
leave its orbit -atom is referred to as a positive ion
External force can cause an atom to gain an electron -atom is referred to as a negative ion
Electric Current Whenever electric charges, 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
QI
t
Electric Current, cont 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
Current and Drift Speed 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
Charge Carrier Motion in a Conductor
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
Current and Drift Speed
Charged particles move through a conductor of cross-sectional area A
n is the number of charge carriers per unit volume
nAΔx is the total number of charge carriers
Current and Drift Speed 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
Quiz 1 Consider positive and negative charges moving
horizontally through the four regions in the following Figure. Rank the magnitudes of the currents in these four regions from lowest to highest.
(a) Id , Ia , Ic , Ib (b) Ia , Ic , Ib , Id (c) Ic , Ia , Id , Ib (d) Id , Ib , Ic , Ia (e) Ia , Ib , Ic , Id (f) none of these
Answer Quiz 1
(d). Negative charges moving in one direction are equivalent to positive charges moving in the opposite direction. Thus, Ia, Ib, Ic and Id
are equivalent to the movement of 5, 3, 4, and 2 charges respectively, giving Id < Ib < Ic< Ia
A copper wire of cross-sectional area 3.00x10-6 m2 carries a current of 10 A. Assuming that each copper atom contributes one free electron to the metal, find the drift speed of the electron in this wire. The density of copper is 8.95 g/cm3.
22 3 19 6 2
6
10.0 /
8.48 10 1.6 10 3.00 10
2.46 10 /
d
I C sv
nqA electrons m C m
m s
Example
Electrons in a Circuit The drift speed is much smaller than the
average speed between collisions When a circuit is completed, the electric
field travels with a speed close to the speed of light
Although the drift speed is on the order of 10-4 m/s the effect of the electric field is felt on the order of 108 m/s
Quiz 2 Suppose a current-carrying wire has a cross-
sectional area that gradually becomes smaller along the wire, so that the wire has the shape of a very long cone. How does the drift speed vary along the wire?
(a) It slows down as the cross section becomes smaller.
(b) It speeds up as the cross section becomes smaller.
(c) It doesn’t change. (d) More information is needed.
Answer Quiz 2
(b). Under steady-state conditions, the current is the same in all parts of the wire. Thus, the drift velocity, given by vd = I/nqA, is inversely proportional to the cross-sectional area
Meters in a Circuit – Ammeter
An ammeter is used to measure current In line with the bulb, all the charge passing
through the bulb also must pass through the meter
Meters in a Circuit – Voltmeter
A voltmeter is used to measure voltage (potential difference) Connects to the two ends of the bulb
Voltage
The electrical potential difference is what causes current to flow.
The basic unit of voltage is the volts . ~
Current flow-Amperes (Amps)
Ampere: unit of measurement for electrical current.
One volt across aresistance of one ohm will produce a flow of one amp. ~
Exercise The capacity of a car battery is usually
specified in ampere-hours. A battery rated at, say, 100 A-h should be able to supply 100 A for 1 h, 50 A for 2 h, 25 A for 4 h, 1 A for 100 h, or any other combination yielding a product of 100 A-h. a. How many coulombs of charge should we be
able to draw from a fully charged 100 A-h battery?
b. How many electrons does your answer to part a require?
Answer
100 1 100 (1 ) 3600 360000C s
A hr hr Cs hr
322
19
360 10224.7 10
1.602 10
Assumptions:Battery fully charged.
a)
b) charge on electron: -1.602 ´ 10-19 Cno. of electrons =
Ohm’s Law German Physicist – George Simon Ohm
Found that current is inversely proportional to resistance for a given voltage
Known as Ohm’s law The Relationship Between Current and Voltage The Relationship Between Current and Resistance
Basic Circuit Calculations
Using Ohm’s Law to Calculate Current
where R = the circuit resistanceV = the applied voltage
R
VI
Basic Circuit Calculations Using Ohm’s Law to Calculate
Voltage
where I = the circuit currentR = the circuit resistance
IRV
Basic Circuit Calculations
Using Ohm’s Law to Calculate Resistance
whereV = the circuit voltage I = the circuit current
I
VR
Ohm’s Law 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
Ohm’s LawOhm’s LawConductivity and resistivity
VL
AI
EA
IJ
1
A
LIV
IRV
AR
is resistivity
is current density
Example
A nichrome wire of radius 0.321 mm has resistivity of 1.5 x 10-6 Ωm. If a potential difference of 10.0 V is maintained across a 1 m length of the nichrome wire, what is the current?
Cross section: 22 3 7 20.321 10 3.24 10A r m m 6
7 2
1.5 104.6
3.24 10m
R m
l A m
Resistance/unit length:
10.02.2
4.6
V VI A
R
Ohm’s Law, cont
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
Ohm’s Law, final 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
Quiz 4 In Figure, does
the resistance of the diode (a) increase or (b) decrease as the positive voltage ΔV increases?
Answer Quiz 4
(b). The slope of the line tangent to the curve at a point is the reciprocal of the resistance at that point. Note that as increases, the slope (and hence ) increases. Thus, the resistance decreases.
Temperature Dependence of Temperature Dependence of ResistanceResistance
Define temp coefficient of resistivityDefine temp coefficient of resistivity
dTd1
If If is small and constant is small and constant
oo TT1
Units of Units of is ( is (ooC)C)-1-1
Platinum Resistance ThermometerA resistance thermometer, which measures temperature by measuring the change in the resistance of a conductor, is made of platinum and has a resistance of 50 Ω at 20oC. When the device is immersed in a vessel containing melting indium, its resistance increases to 76.8 Ω. Find the melting point of Indium.
CR
RRTT o
o
oo 137
CT o157
Example
αα=3.92x10=3.92x10-3-3((ooC)C)-1-1
Since the To= 20oc then
Why do old light bulbs give less light than when new?
The filament of a light bulb, made of tungsten, is kept at high temperature when the light bulb is on.
It tends to evaporate, i.e. to become thinner, thus decreasing in radius, and cross sectional area.
Its resistance increases with time. The current going though the filament then decreases with time – and so does its luminosity.
Tungsten atoms evaporate off the filament and end up on the inner surface of the bulb.
Over time, the glass becomes less transparent and therefore less luminous.
Low temperature behavior of Low temperature behavior of resistanceresistance
SuperconductivitySuperconductivitySemiconductorSemiconductor
Exercise 1 If a current of 80.0 mA exists in a
metal wire, how many electrons flow past a given cross section of the wire in 10.0 min? Sketch the direction of the current and the direction of the electrons’ motion.
Exercise 2 If 3.25 × 10−3 kg of gold is
deposited on the negative electrode of an electrolytic cell in a period of 2.78 h, what is the current in the cell during that period? Assume that the gold ions carry one elementary unit of positive charge.
Exercise 3 An aluminum wire with a cross-
sectional area of 4.0 × 10−6 m2 carries a current of 5.0 A. Find the drift speed of the electrons in the wire. The density of aluminum is 2.7 g/cm3. (Assume that one electron is supplied by each atom.)