Transcript Slide 1

Circuits
Resistors, Capacitors and Inductors
Resistors
Capacitors
Inductors
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Circuits
Resistors, Capacitors and Inductors
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Circuits
Resistors, Capacitors and Inductors
Resistors slow down the electrons
I
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Circuits
Resistors, Capacitors and Inductors
Resistors slow down the electrons
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-
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Circuits
Resistors, Capacitors and Inductors
In most instances, the voltage across a piece of material is
proportional to the current that flows through it
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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Circuits
Resistors, Capacitors and Inductors
As area increases, more electrons
pass through it. Thus, the current is
greater and the resistance is smaller
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
For many materials, the resistance is proportional to the length of
the resistor and inversely proportional to the cross-sectional 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
Circuits
Resistors, Capacitors and Inductors
Power is defined as the change in energy per unit time
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
Circuits
Resistors, Capacitors and Inductors
+σ
E  2k
E
Δs
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V  2kd
V  Ed
Circuits
Resistors, Capacitors and Inductors
+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
Circuits
Resistors, Capacitors and Inductors
V=4πkσd0/κ
+σ
Ed
d0
d
E  E0  E d 
E0
V=0
-σ
E  E0
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E0

Circuits
Resistors, Capacitors and Inductors
Capacitors store the electrons
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Circuits
Resistors, Capacitors and Inductors
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.
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.
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Circuits
Resistors, Capacitors and Inductors
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
2
U  CV   0 AE 2 d
2
2
U
1
ue 
  0 E 2
Volume 2
This is the electrostatic field energy density.
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The energy lies in the electric field!
Circuits
Resistors, Capacitors and Inductors
Inductors create magnetic fields
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