Download Physics 212 and 222 Circuit Elements and Electric Power

Physics 212 and 222
Circuit Elements and Electric Power
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Resistors
Capacitors
Inductors
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Physics 212 and 222
Circuit Elements and Electric Power
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Physics 212 and 222
Circuit Elements and Electric Power
Resistors slow down the electrons
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Physics 212 and 222
Circuit Elements and Electric Power
Resistors slow down the electrons
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Physics 212 and 222
Circuit Elements and Electric Power
In most instances, the voltage across a piece of material is
proportional to the current that flows through it
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The constant of proportionality is called resistance, R, and
has units of Ohms (Ω)
This is known as Ohm’s law and is usually written as
V  IR
In a circuit diagram we draw resistance like this
R
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Physics 212 and 222
Circuit Elements and Electric Power
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As length increases, the electrons are
blocked for a longer time, slowing them
down even more. Thus, the current is
smaller and the resistance is greater
As area increases, more electrons
pass through it. Thus, the current is
greater and the resistance is smaller
For many materials, the resistance is proportional to the
length of the resistor and inversely proportional to the crosssectional area
L
R
A
The constant of proportionality is called resistivity, ρ, and
is different for different materials
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Table 28.2 in the text gives resistivity for some materials
Physics 212 and 222
Circuit Elements and Electric Power
Power is defined as the change in energy per unit time
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In the case of electric potential energy, we can write
U qV
P

 IV
t
t
The power may be written in different forms using Ohm’s
law
P  IV
PI R
2
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V2
P
R
Physics 212 and 222
Circuit Elements and Electric Power
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+σ
E  2k
E
Δs
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V  2kd
V  Ed
Physics 212 and 222
Circuit Elements and Electric Power
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+σ
d
V=4πkσd
Q
A
A
A
C 

 0
V 4kd 4kd
d
E
-σ
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V=0
Physics 212 and 222
Circuit Elements and Electric Power
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•V=4πkσd0/κ
•+σ
•Ed
•d0
•d
E  E0  E d 
•E0
•V=0
•-σ
E  E0
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E0
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Physics 212 and 222
Circuit Elements and Electric Power
Capacitors store the electrons
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Physics 212 and 222
Circuit Elements and Electric Power
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A capacitor is two conductors of equal but opposite charge
separated by a dielectric.
A dielectric is a substance made up of stationary dipoles.
The capacitance of a capacitor is given by the equation.
Q
C
V
Q is magnitude of the charge of one of the conductors.
V is the magnitude of the difference in potential between
them.
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The capacitance depends only on the geometry (shape and
size of the capacitor, not on Q or V because they are
proportional to each other.
Physics 212 and 222
Circuit Elements and Electric Power
For any capacitor, the electric potential energy is given by
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1 Q2 1
U  QV 
 CV 2
2
2 C 2
But where is that energy
found?
For a parallel plate
capacitor…
1
1
U  CV   0 AE 2 d
2
2
U
1
ue 
  0 E 2
Volume 2
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This is the electrostatic field energy density.
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The energy lies in the electric field!
Physics 212 and 222
Circuit Elements and Electric Power
Inductors create magnetic fields
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Physics 212 and 222
Circuit Elements and Electric Power
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Resistors
Capacitors
Inductors
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