Transcript Chapter 17 Current and Resistance 17.1 Electric Current Whenever electric charges move, an electric current is said to exist  The current is the.

Chapter 17
Current and Resistance
17.1 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
17.2 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
17.3 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 17.2
Look at the four “circuits” shown below and
select those that will light the bulb.
17.4 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
I
Unit: V/A=W (ohm)
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