# Resistance and Current

```Ch. 17 Current and Resistance
concept #1, 4, 5, 6, 8, 10
Problems #1, 2, 3, 7, 11, 13, 17, 21,
25, 27, 31, 33, 43
Static electricity devices, such as a Van de Graaf
generator, produced small flow of charge for short
time intervals.
When it was learned how to produce a continuous
flow for longer times, electricity became an
important part of human technology.
For example run a light bulb, use to power a
refrigerator.
The continuous flow of charge leads up to electric
current.
Take a wire and cut a cross sectional area
through it. The charges move in a direction
perpendicular to the surface.
Current – the rate at which charge flows
through the surface.
The current is the amount of charge Q that
flows through a cross-sectional area in a time
interval t.
Current: I = Q/ T
SI unit of current is the Ampere (A)
1 Ampere = 1 coulomb/second
A = C/s
Direction of current: The direction of the
current is the direction in which positive
charges flow.
Remember that in a conductor, the charges
that move are the negative electrons. So in a
copper wire, the current is in the opposite
direction of the electron’s motion.
e
current
Take the example of a current loop. If the
electrons flow clockwise. The current is
counterclockwise.
A particle accelerator shoots a beam of protons.
The current is in the same direction of the
protons’ motion.
see example problem 17.1
Microscopic view of current
The current depends on the average speed of
the charge carriers. Not all the electron will
move with the same speed.
I = Q/ t
Q = number of carriers x charge per carrier
= (nA x)q
n charge density (#/volume)
A = cross-sectional area
x = length along wire
q = charge of individual carrier
for electron (q = 1.6 x 10-19 C)
Q = (nA x)q
a distance x = vd t
vd = drift velocity (average velocity along
direction of motion) see picture (pg 570)
Q = (nA vd t)q
I = Q/ t = (nA vd t)q / t = (nA vd)q
I = nqvdA
Work example 17.2.
As charges flow through a conductor (wire), they
are constantly colliding with each other and the
walls of the conductor. It is the net movement of
charge that produces the current.
Think of water through a pipe. If a drop of water
is forced into an already filled pipe, a drop will be
pushed out the other end.
A current flow at one end produces a similar flow
at the other end very quickly.
Current and voltage measurement in circuits.
circuit – closed loop of some sort around
which current circulates
Basic circuit – battery hooked to a light bulb.
The battery pushes the charges through the
light bulb and around the loop.
Circuits need closed loops for current to flow.
Current won’t flow through a ‘dead end’.
The battery increases the potential energy of
the charges. Then the charges lose the PE as
they go around the circuit.
Think of the circuit as a roller coaster that the
charges ride. The initial ‘lift’ that the charges
need to get over the hill is provided by the
battery.
measuring devices
voltmeter – measures voltages (potential
differences)
ammeter – measures the current
See fig 17.5
voltmeters always need to be in parallel
ammeters always need to be in series
Resistance and Ohm’s law
When a voltage is applied across a conductor,
current will flow and will be proportional to the
potential difference.
I~ V
The proportionality constant is known as the
resistance.
Resistance is defined as the ratio of the voltage
across a conductor to the current it carries.
R = V/I
resistance has units of volts per ampere
Called Ohm’s ( )
1 V/1 A = 1
Ohm’s Law: V = I R
Can compare electrical current to current in a river.
- as river’s change in elevation increases, the
current increases
(the potential difference increases)
- if river is blocked up with rock, the flow decreases
(similar to having a larger resistance)
Resistor
Symbol is a zigzag
material is ohmic if the resistance is constant
over a large range of voltages
nonohmic – resistance changes with voltage
see graphs on pg 574
example 17.3
Resistivity
Resistance depends on the length and width
of the conductor.
As electrons move through the conductor,
they bounce into the atoms in the material.
The more collisions, the higher the resistance.
if you want to minimized the collisions, use a
short and wide conductor.
wider – lower resistance
longer – higher resistance.
Resistance is proportional to the length and
inversely proportional to the cross-sectional
area.
The proportionality constant is the resistivity.
R = L/A
The resistivity has units of m
Resistivity depends on what the conductor is
Switching to a high
resistance.
material will increase
Good conductors have small resitivities.
see table 17.1 (pg 576)
example 17.4
Temperature variation of resistance.
Resistance depends on resistivity.
Resistivity depends on atomic structure.
Atomic spacing depends on temperature.
= 0{1 + (T – T0)}
= temperature coefficient of resistivity (how
the resistivity changes with temperature)
Second column of table on page 576.
Sine resistivity changes with temperature,
so does resistance.
R = R0{1 + (T – T0)}
and R0 are the resistivity and resistance at a
reference temperature T0.
0
When you increase the temperature of a resistor,
the resistance increases.
Superconductors
Resistance increases with temperature.
Low temp, low resistance.
For some metals, there is a critical temperature, Tc,
where the resistance drops to zero.
If R = zero, then an established current will flow
without an applied voltage.
Goal is to produce superconductors at higher and
higher temperatures.
Electrical Energy and Power
As charge moves around circuit, it increases in
potential as it goes through battery, then loses
potential as it goes through resistor. When it
returns to original point it is back at original
potential.
Remember that there are collisions between the
charge and the atoms in the resistor. This causes
the resistor to gain thermal energy.
The potential energy is turned into thermal
energy.
As charge passes through resistor, the charge,
Q, loses an amount of potential energy Q V.
If it takes time, t, to pass through the resistor,
the rate that the charge loses potential energy
is:
Q V/ t
=
( Q/ t)DV = I V
power is current x potential difference
P=IV
Using Ohm’s law we can make subtitutions and
see:
P = I V = I2R = V2/R
Do examples 17.6 and 17.7a
units
SI unit of energy is the Joule (J)
SI unit of power is the Watt (W)
Power = energy/time
Unit used by electric companies is the: kilowatt-hour.
This is a unit of energy.
1 kWh = using 1000 W for 1 hour of time
1kWh = (103 W)(3600 s) = 3.6 x 106 J
```