Current and Resistance
Chapter 31
Batteries
Battery
• Batteries provide
Chemical Electricity
• Electrons “bunch up” or
have the potential to
flow from the negative
end
• Electrons can’t flow in
an isolated battery
-e
+
e
e e
Chemical
Reaction
that
produces
electrons
Chemical
Reaction
that absorbs
electrons
Circuits
Drift Speed
• Electrons do not flow through wires like pipes
• Electric field gives direction to the random
motion of electrons. (vD = drift speed)
• 0.05 mm/s
• About 5 ½ hours to travel one meter (coin
waterfall at Chuck-E-Cheese)
• About a year to go 1 mile
Electron Current (ie)
ie = neAvD
ne = electron density
Calculate the electron current in a 2.0 mm diamter
copper wire if the electron drift speed is 1.0 X 10-4
m/s. (2.7 X 1019 s-1)
• Conventional Current
– Flows positive to negative
– Opposite of electron flow (electron current)
Current (I)
• Current – Net amount of charge per unit time
• 1 coulomb/second = 1Ampere
I = DQ
Dt
I = dQ
dt
I = eie
electron current
The electron current through a wire is 1.2 X 1019
electrons/s.
a. Calculate the current, I (1.9 A)
b. Calculate the amount of charge that flows each
hour (6800 C)
Current Density (J)
A 1.0 A current passes through a 1.0 mm
diameter wire.
a. Calculate the current density. (1.3 X 106 A/m2)
b. Calculate the drift speed of the electron. (0.13
mm/s)
A 5.0 A current passes through a 3.2 mm
diameter wire.
a. Calculate the current density. (6.2 X 105 A/m2)
b. Calculate the drift speed of the electron. (0.05
mm/s)
Current: Ex. 1
A steady current of 2.5 A flows through a wire for
4.0 min. How much charge passed through any
point in the circuit?
I = DQ
Dt
DQ = IDt
DQ = (2.5 A)(240 s) = 600 C
How many electrons would this be?
1 electron = 1.60 X 10-19 C
600 C
1 electron
= 3.8 X 1021electrons
1.60 X 10-19 C
Current Density (J)
Conductivity (s)
Resistivitiy (r)
Current density
A 2.0 mm diameter aluminum wire carries a
current of 800 mA.
a. Calculate the current density using J = I/A (2.55
X 105 A/m2)
b. Calculate the electric field inside the wire
(0.0072 V/m)
A copper wire has a diameter of 3.2 mm. The
current is 5.0 A.
a. Calculate the current density of the wire (6.2 X
105 A/m2)
b. Calculate the electric field inside the wire (0.01
V/m)
Ohm’s Law
V = IR
DV = IR
V = Voltage (V)
I = Current (A)
R = Resistance (Ohms, W)
(only works for metal conductors, not
semiconductors (nonohmic))
Resistors
• Color coded to determine resistance
• Devices that heat have high resistance (light
bulbs, electric stoves, toasters)
A small flashlight bulb draws 300 mA
from a 1.5 V battery.
a. Calculate the resistance of the bulb
(5.0 W)
b. If the voltage dropped to 1.2 V and the
resistance stayed at 5.0 W, what
current would flow. (0.24 A)
Resistivity
R = rL
A
R = Resistance
L = Length (longer wire, greater resistance)
A = Area (wider wire, less resistance)
r = Resistivity of the material
http://www.earthsci.unimelb.edu.au/ES304/MODULES/RES/NOTES/resistivity.html
What is the resistance of a 2.00mm diameter,
10.0 meter copper wire?
A = pr2 = (3.14)(0.001 m)2 = 3.14 X 10-6 m2
R = rL = (1.68 X 10-8 Wm)(10.0 m)
A
(3.14 X 10-6 m2)
R = 0.0535 W of 53.5 m W
A speaker wire must be 20.0 m long and have a
resistance of less than 0.100 W per wire.
a. What diameter copper wire should be used?
(2.06 mm)
b. What is the voltage drop across each wire at a
current of 4.00 A? (0.40 V)
A wire of length L is stretched to twice its
normal length.
a. Calculate the new cross sectional area (assume
the volume does not charge (Anew =1/2A)
b. Calculate the new resistance (Rnew = R)
R = rL
A
A = rL
R
A = [(1.68 X 10-8 Wm)(20.0 m)]/0.100 W
A = 3.36 X 10-6 m2
A = pr2
r = (A/p)1/2
r = (3.36 X 10-6 m2 /3.14)1/2 = 1.03 X 10-3 m
D = 2r = 2.06 X 10-3 m or 2.06 mm
Resistance and Temperature
• Metals
– Resistance increases with temp.
– Atoms more disorderly
– Interferes with flow of electrons
• Semiconductors
– Resistance sometimes decreases with temperature
– Some electrons become excited and able to flow
Superconductivity
• Superconductivity – resistance of a material
becomes zero
• No loss of current over a wire
• Generally near absolute zero
• Record as of 2007 is 138 K
• Maglev trains