Transcript File

Chapter 21-part1
Current and Resistance
1 Electric Current
Whenever electric charges move, an
electric current is said to exist
 The current is the rate at which the

charge flows through a certain crosssection

For the current definition, we look at
the charges flowing perpendicularly to a
surface of area A
Definition of the current:
+
-
Charge in motion
through an area A.
The time rate of the
charge flow through
A defines the current
(=charges per time):
I=DQ/Dt
Units: C/s=As/s=A
SI unit of the current:
Ampere
Electric Current, cont

The direction of current flow is the direction
positive charge would flow

This is known as conventional (technical) current
flow, i.e., from plus (+) to minus (-)


However, 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
2 Current and Drift Speed
Charged particles
move through a
conductor of crosssectional area A
 n is the number of
charge carriers per
unit volume V
(=“concentration”)
 nADx=nV is the total
number of charge
carriers in V

Current and Drift Speed, cont
The total charge is the number of carriers times
the charge per carrier, q (elementary charge)
 ΔQ = (nAΔx)q [unit: (1/m3)(m2 m)As=C]
 The drift speed, vd, is the speed at which the
carriers move




vd = Δx/Δt
Δx
Rewritten: ΔQ = (nAvdΔt)q
Finally, current, I = ΔQ/Δt = nqvdA
Current and Drift Speed, final
If the conductor is isolated, the
electrons undergo (thermal) 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 electric field force F
imposes a drift on an
electron’s random motion
(106 m/s) in a conducting
material. Without field the
electron moves from P1 to
P2. With an applied field
the electron ends up at
P2’; i.e., a distance vdDt
from P2, where vd is the
drift velocity (typically
10-4 m/s).
Does the direction of the
current depend on the
sign of the charge? No!
(a)
Positive charges
moving in the same
direction of the field
produce the same
positive current as
(b) negative charges
moving
in
the
direction opposite to
the field.
qvd
E
vd
E
vd
(-q)(-vd) = qvd
Current density:
The current per unit cross-section is called the
current density J:
J=I/A= nqvdA/A=nqvd
In general, a conductor may contain several different
kinds of charged particles, concentrations, and drift
velocities. Therefore, we can define a vector
current density:
J=n1q1vd1+n2q2vd2+…
Since, the product qvd is for positive and negative
charges in the direction of E, the vector current
density J always points in the direction of the field E.
Example:
An 18-gauge copper wire (diameter
1.02 mm) carries a constant current
of 1.67 A to a 200 W lamp. The
density of free electrons is 8.51028
per
cubic
meter.
Find
the
magnitudes of (a) the current
density and (b) the drift velocity.
Solution:
(a) A=d2p/4=(0.00102 m)2p/4=8.210-7 m2
J=I/A=1.67 A/(8.210-7 m2)=2.0106 A/m2
(b) From J=I/A=nqvd, it follows:
J
2.0  10 A / m
vd 

28
3
19
nq (8.5  10 m )(1.60  10 C)
6
vd=1.510-4 m/s=0.15 mm/s
2
3 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

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 (in series!)
Meters in a Circuit - Voltmeter

A voltmeter is used to measure voltage
(potential difference)

Connects to the two ends of the bulb (parallel)
QUICK QUIZ
Look at the four “circuits” shown below and
select those that will light the bulb.
4 Resistance and Ohm’s
law

In a homogeneous
conductor,
the
current density is
uniform over any
cross section, and
the electric field is
constant along the
length.
b
a
V=Va-Vb=EL
Resistance
The ratio of the potential drop to the
current is called resistance of the segment:
V
R
Unit: V/A=W (ohm) I
Resistance, cont

Units of resistance are ohms (Ω)


1Ω=1V/A
Resistance in a circuit arises due to
collisions between the electrons
carrying the current with the fixed
atoms inside the conductor
Ohm’s Law
V

 I  V=const.I  V=RI
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
 I=V/R
 R, I0, open circuit; R0, I, short circuit
Ohm’s Law, final
Plots of V versus I
for (a) ohmic and (b)
nonohmic materials.
The resistance R=V/I
is independent of I
for ohmic materials,
as is indicated by the
constant slope of the
line in (a).
Ohmic
Nonohmic
5 Resistivity


Expected: RL/A
The resistance of an ohmic
conductor is proportional
to its length, L, and
inversely proportional to its
cross-sectional area, A
L
Rρ
A

ρ (“rho”) in Wm is the
constant of
proportionality and is
called the resistivity of
the material
Example
Determine the required length of
nichrome (=10-6 Wm) with a radius
of 0.65 mm in order to obtain R=2.0 W.

R=L/AL=RA/

(2.0W)p (0.00065m)
L

2
.
65
m
6
10 Ωm
2

The resistivity
depends on the
material and the
temperature
6 Temperature Variation of
Resistivity

For most metals, resistivity increases
with increasing temperature
With a higher temperature, the metal’s
constituent atoms vibrate with increasing
amplitude
 The electrons find it more difficult to pass
the atoms (more scattering!)

Temperature Variation of
Resistivity, cont

For most metals, resistivity increases
approximately linearly with temperature over
a limited temperature range
ρ  ρo [1  α(T  To )]

ρo is the resistivity at some reference temperature
To
 To is usually taken to be 20° C
  is the temperature coefficient of resistivity
[unit: 1/(C)]
Temperature Variation of
Resistance

Since the resistance of a conductor with
uniform cross sectional area is
proportional to the resistivity, the
temperature variation of resistance can
be written
R  Ro [1  α(T  To )]
Example

The material of the wire has a resistivity of
0=6.810-5 Wm at T0=320C, a temperature
coefficient of =2.010-3 (1/C) and L=1.1 m.
Determine the resistance of the heater wire at
an operating temperature of 420C.
Solution
=0[1+(TT0)]
 =[6.810-5 Wm][1+(2.010-3 (C)-1) 


(420C-320C)]=8.210-5 Wm
R=L/A
 R=(8.210-5 Wm)(1.1 m)/(3.110-6 m2)
 R=29 W

7 Superconductors

A class of materials and
compounds whose
resistances fall to virtually
zero below a certain
temperature, TC
 TC is called the critical
temperature (in the
graph 4.1 K)
“normal”
Superconductors, cont

The value of TC is sensitive to
Chemical composition
 Pressure
 Crystalline structure


Once a current is set up in a
superconductor, it persists without any
applied voltage

Since R = 0
Superconductor Timeline

1911


1986



High-temperature superconductivity discovered by
Bednorz and Müller
Superconductivity near 30 K
1987


Superconductivity discovered by H. Kamerlingh
Onnes
Superconductivity at 92 K and 105 K
Current

More materials and more applications
 Tc
values for
different materials;
note the high Tc
values for the
oxides.
 It’s
magic!
8 Electrical Energy and
Power

In a circuit, as a charge moves through the
battery, the electrical potential energy of the
system is increased by ΔQΔV [AsV=Ws=J]


The chemical potential energy of the battery
decreases by the same amount
As the charge moves through a resistor, it
loses this potential energy during collisions
with atoms in the resistor

The temperature of the resistor will increase
Electrical Energy and Power,
cont
The rate of the
energy transfer is
power (P):
DW ΔQ
P

V  IV
Dt
Δt
Units: (C/s)(J/C) =J/s=W
1J=1Ws=1Nm
W=AV
V
Electrical Energy and Power,
cont
 From
Ohm’s Law, alternate forms
of power are (use V=IR and I=V/R)
2
V
P  IV  I R 
R
Joule heat (I R losses)
2
2
Electrical Energy and Power,
final

The SI unit of power is Watt (W)


I must be in Amperes, R in Ohms and V in
Volts
The unit of energy used by electric
companies is the kilowatt-hour
This is defined in terms of the unit of
power and the amount of time it is
supplied
 1 kWh =(103 W)(3600 s)= 3.60 x 106 J

9 Electrical Activity in the
Heart
Heart beat Initiation



Every action involving
the body’s muscles is
initiated by electrical
activity
Voltage pulses cause
the heart to beat
These voltage pulses
(1 mV) are large
enough to be detected
by equipment attached
to the skin
Electrocardiogram (EKG)




A normal EKG
P occurs just before the
atria begin to contract
The QRS pulse occurs in
the ventricles just
before they contract
The T pulse occurs
when the cells in the
ventricles begin to
recover
Abnormal EKG, 1
The QRS portion is
wider than normal
 This indicates the
possibility of an
enlarged heart

Abnormal EKG, 2



There is no constant relationship between P and QRS
pulse
This suggests a blockage in the electrical conduction
path between the SA and the AV nodes
This leads to inefficient heart pumping
Abnormal EKG, 3

No P pulse and an irregular spacing between the QRS
pulses
Symptomatic of irregular atrial contraction, called

The atrial and ventricular contraction are irregular

fibrillation
Implanted Cardioverter
Defibrillator (ICD)
Devices that can
monitor, record and
logically process
heart signals
 Then supply
different corrective
signals to hearts
that are not beating
correctly

Dual chamber
ICD
Monitor lead