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April 24, 2006
Science A52 – Section #8:
Electricity:
Electrical energy (batteries, wall sockets, etc.) is derived from the movement of electric
charges (usually electrons).
Ohm’s Law:
Voltage = Current * Resistance
V=I*R
Power:
Power = Voltage * Current
# Watts = V * I
Resistance:
Resistivity is the inverse of the conductivity of a material. Copper has a very high
conductivity – thus a low resistivity. Your body has a low conductivity, and thus a high
resistivity. Resistance is given by:
R
L
A
R = resistance {units = ohms -  }
 = resistivity {units = ohms*length}
L =length
A =area of wire
Table 2: Resistivities of select metals from The Physics Hypertextbook.
Metal
Resistivity (nΩ*m)
Copper
17.1
Silver
15.9
Aluminum
26.5
Example 1: What is the resistance of a 1 km long copper wire with a radius of 0.1 cm?
The resistance of a wire is given by
L
where  (  m) is the resistivity and depends on the material of the wire, L
A
(m) is the length of the wire and A (m2) the cross-sectional area.
R

For copper the
resistivity is
 
  17.1n m  17.1109  m
The cross-section area is
A  r 2  0.1cm   0.1102 m   3.14 106 m 2

The resistance of the wire

R
2
2
L
A
17.110
9

m 10 3 m
3.14 106 m 2
 5.4
Example 2: Voltage and current

What is the current in the wire if you apply a 110 V voltage?
The current and the voltage are related through the resistance.
I

V 110V

 20.4 Amps
R 5.4
Example 3: Power losses
What are the power losses in the wire?
The power losses are calculated from the current and resistance.
P  I 2 R  20.4 Amps  5.4  2241W
2

Magnetism:
Magnetic fields originate from the movement of electric charges. This
relationship is quantified in the Biot-Savart equation.
The magnetic field surrounding a long straight current carrying wire is given by:
o I
2 r
B =magnetic field {Teslas – use right hand rule for direction}
o =4  *10-7
I=current {Amps}
R=radius {meters}
B
This idea is used to make electro-magnets by coiling wire along a ferrous metal
(like iron) and running current through the wire.
Example: A toaster oven uses 1500 watts and plugs into a 120V outlet. Calculate the
magnitude and direction of the magnetic field 1m from the cord.
I  P / V  1500W /120V  12.5 Amps
B
o I 4 *107 *12.5 Amps

 2.5*106 Tesla
2 r
2 *1m
Transformers:
Induction of magnetic fields back to current allows one to build a transformer to
raise or lower AC voltage (think of the large plastic socket on your cell phone charger).
d m
dt
d m
V2   N 2
dt
V
V2  N 2 ( 1 )
N1
V1   N 1
V2  (
N2
)V1
N1
Example: Your Cell Phone battery is 12V, and you want to build a transformer to plug
into a wall socket at 120V. If you have a 150 turns around a ferrous core on the side
connected to your phone, how many turns must you have on the socket side?
V

 120V 
N wall   wall  N phone  
150turns  1,500turns
V

 12V 
 phone 
Semiconductors:
Transistors can be thought of as a voltage regulated valve that controls the flow of
electrons (i.e. current). Below is a simple diagram:
The height of ΔE can be modified with an applied voltage ( higher V, lower ΔE, more
current flows). If an electron has more energy than ΔE than it will flow from the emitter
to collector. Below is a plot of the logarithm of current vs. voltage.