Download Chapter 27

Chapter 27: Current and Resistance
Reading assignment:
Chapter 27
Homework 27.1, due Monday, Feb. 27: OQ1, 5, 14
Homework 27.2, due Wednesday, March 1: OQ3, OQ6, 15, 21, 25, 26, 31, 33, 39, 44, 48, 53
• Begin our study of charges in motion --> electric current
•  Electrodynamics
• Invention of battery, Alessandro Volta, 1800 --> production of steady electric current
• Electrical current and circuits are omnipresent in today’s technological world
• Electric current, Ohm’s law, resistance, resistivity, electric power
Batteries
• There is a potential difference (voltage) between the terminals of
a battery:
• Series connection:
-
+ -
+ -
+
• Voltages add up in a series connection. The voltage between the
ends of three 1.5 V batteries connected in series is 3x1.5V = 4.5V.
• Symbol of battery in a circuit:
Electric current
• When a continuous conducting path is
connected between the terminals of a
battery, we have an electrical circuit.
• When such a circuit is formed, charge can
flow through the wires of the circuit, from
one terminal of the battery to the other. A
flow of charge, such as this is called an
Symbol for battery
electrical current.
• The electrical current, I, in a wire is defined as the amount of charge that passes
through it per unit time.
Q
I
t
dQ
I
dt
Instantaneous
current
Q is the amount of charge that passes through the conductor at any location during time interval t.
• The direction of current is the direction in which positive charges flow
• Unit of electrical current is Ampere (1A) (Coulomb/second).
How to connect a battery
What’s wrong with each of the schemes shown in the Figure for lighting a flashlight with a
flashlight battery and a single wire?
(a) There is no loop for the current to flow
around.
(b) There is loop to and from the light bulb, but
there is no potential difference.
(c) Nothing wrong here. The bulb will light up.
-
-
-
(a)
(b)
(c)
i-clicker:
Current flow of charge. A steady current of 2.5 A flows in a wire for 4.0
minutes (Be careful to use SI units).
1) How much charge passes through any point in the circuit?
A) 0 C
C) 600 C
B) 10 C
D) 1000 C
2) How many electrons would this be?
Ohm’s Law
• To produce an electrical current I in a wire, a difference in potential V is required (set
up by a battery, power supply or outlet).
• Ohm’s law: The current in the wire is proportional to the potential difference applied to
its ends:
I  V
The amount of current flowing in a wire for a given voltage depends on the resistance
of the wire, R. The higher the resistance the less current will flow for a given voltage.
V
I
R
Or:
V  IR
Resistance: R 
V
I
Ohm’s Law
Unit of resistance: 1 Ohm (1 W)
Georg Simon Ohm
1789 – 1854
White board example
Ohm’s law. Flashbulb light resistance.
A small light bulb draws 300 mA from its
1.5 V battery
(A) What is the resistance of the light
bulb?
(B) If the voltage dropped to 1.2 V how
would the current change?
Resistors
• All electric devices offer
resistance to the flow of
current (filaments of light
bulbs or electric heaters,
etc.)
• Resistors are used to
control the amount of
current. They have a
resistance ranging from
less than on Ohm to
millions of Ohms.
• Symbol in a circuit is
How to read the code (four band code):
• First find the tolerance band, it will typically be gold ( 5%) and
sometimes silver (10%).
• Starting from the other end, identify the first band - write down
the number associated with that color.
• Now 'read' the next color
• Now read the third or 'multiplier' band
• If the resistor has one more band past the tolerance band it is a
quality band. Read the number as the '% failure rate per 1000 hour'
This is rated assuming full wattage being applied to the resistors.
Resistivity and Resistance of a wire
• The resistance of a wire is
proportional to its length L and
inversely proportional to its crosssectional area A.
L
R 
A
• The proportionality constant  is called the resistivity.
• It depends on the material and has units of W·m.
• There is a huge range of values across different materials.
• Typically metals (the best is silver  = 1.6x10-8 W·m) have a
very low resistivity (are good conductors).
• Insulators have a very high resistivity (glass: 1010 – 1014 W·m).
Effect of temperature on resistivity and resistance
• Typically (but not always!) the resistivity (and thus the resistance)
of metals increases with increasing temperature.
• At higher temperatures the atoms are moving more rapidly and
thus interfere with the flow of the electrons.
T  0  1   T  T0 
RT  R0  1   T  T0 
T0
RT and R0 are resistance at temperature T and reference temperature T0 (usually 20°C)
 is the temperature coefficient of resistivity (see Table 27-2)
•  can be negative for semiconductors, i.e. resistance
decreases with increasing temperature! Why?
Semiconductors
Toughened glass
insulator on high voltage
power line
http://www.parsmaghare
h.com/En/index.htm
White board example
Resistance thermometer. The variation in electrical resistance with
temperature can be used to make precise temperature measurements.
Suppose at 20oC the resistance of a platinum resistance thermometer is
164.2 W. When placed in a particular solution, the resistance is 187.4 W.
What is the temperature of this solution?
Electric power
• Electric energy is useful, because it can be easily transformed into other
forms of energy (heat, light, mechanical).
• Electrons lose all their energy (potential) as they travel through the circuit
from one terminal of the battery to the other terminal
• Remember: electric potential energy: Uel = QV
P = power =
energy QV

time
t
P  I V
Power is measured in Watt
• By using Ohm’s law, V = IR, the power in a resistor can be written as:
P  I V  I ( IR )  I 2 R
 V
P  I V  
 R
V 2

 V 
R

Black board example
Electric heater. An electric heater draws 15.0 A on a 120V line
(regular household outlet; this is alternating current (AC), but all equations are still valid).
A) How much power does it us?
B) How much does it cost to operate it for 90 hours if the
electric company charges 10.5 cents per kWh? (Assume
steady current flow in one direction)
Black board example
Lightning bolt.
In a typical lightning event, 109 J of energy are transferred
across a potential difference of 5 x 107 V during a time
interval of 0.2 seconds.
Use this information to estimate
A) the total amount of charge transferred,
B) the current
C) and the average power over the 0.2 seconds.
Microscopic model of current and Ohm’s law again
I avg  nqvd A
I … current
n … density of charge carriers
q … charge per carrier
vd … drift velocity
A … cross-sectional area
J E
Ohm’s law
J… current density, I/A
… conductivity,  = 1/; … resistivity, (material constant)
E … electric field
Review
Q
t
Definition of current:
I
Ohm’s Law (common def.):
V  IR
Resistance of a wire:
R 
I
dQ
dt
L
A
Temp. dependence of
T  0  1   T  T0 
RT  R0  1   T  T0 
energy QV
P = power =

time
t
P  I V
P  I V  I ( IR )  I 2 R
Microscopic definition of
current, I, and Ohm’s law
I avg  nqvd A
resistivity , Resistance, R:
 V
P  I V  
 R
J E
V 2


V


R
