Electric Circuits
Physics 102
Lecture 2
14 February 2002
HAPPY
VALENTINE’S
DAY
14 Feb 2002
Physics 102 Lecture 2
1
LAURA HELLER - WEDNESDAY LAB
14 Feb 2002
Physics 102 Lecture 2
2
Capacitors
Two parallel conducting plates with equal but
opposite charges form a capacitor.
Neglecting “fringing” near the edges:
The field inside is uniform with E = σ / ε 0
(σ is the charge per unit area on the plate q/a)
The field outside vanishes.
d
A
The charge on each plate of a capacitor is
proportional to the potential difference
between the plates, q = CV .
Capacitance has units farad=coulomb/volt.
For this geometry C = ε 0 A / d , so ε 0
has units of farads/meter.
2
Capacitors store energy
14 Feb 2002
= CV / 2
2
= Q / 2C
Physics 102 Lecture 2
3
Capacitors and Dielectrics
A dielectric material in a capacitor
will reduce the field strength by a
factor κ = E0 / E (dielectric constant).
The voltage is also reduced
because V = Ed .
Since q = CV = const. , C must
increase when the dielectric is
inserted.
For parallel plates: C = κε 0 A / d
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Physics 102 Lecture 2
4
Energy in Capacitor with Dielectric
2
Without a dielectric:
With a dielectric:
2
C0V0
Q0
=
=
2
2C0
2
0 0
2
0
CV
Q
=
=
2κ
2κC0
If we charge up a capacitor with a dielectric
nearby, what will happen?
A) Nothing, dielectrics are electrically neutral.
B)The dielectric is repelled.
C)The dielectric is sucked in.
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Physics 102 Lecture 2
5
A dielectric is inserted between the plates
of a capacitor. The system is then charged
and the dielectric is removed. The electrostatic
energy stored in the capacitor is
A. greater than
B. the same as
C. smaller than
it would have been if the dielectric were left
in place.
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Physics 102 Lecture 2
6
A parallel-plate capacitor is attached to a
battery that maintains a constant potential
difference V between the plates. While the
battery is still connected, a glass slab is inserted
so as to just fill the space between the
plates. The stored energy
A. increases.
B. decreases.
C. remains the same.
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Physics 102 Lecture 2
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Electromotive Force and Currents
I
I
I
Chemical reactions can
transfer charge from one
place to another
Charge separation creates
an electrical potential
difference, or emf
(electromotive force)
Sustained emf creates a
current in a conducting
wire: I = ∆q / ∆t
[unit of current
ampere=coulomb/second]
14 Feb 2002
Biochemical
Dry cell battery
Auto battery
Van de Graaff
Lightning
1-100 mV
1.5 V
12 V
4.5 MV
108-109 V
Potential DIFFERENCES
Physics 102 Lecture 2
8
Voltage Vs. Current
The voltage is the energy per charge.
In a fluid analogy, voltage is like a pressure difference.
Batteries produce voltage differences. Pumps, for
example, produce pressure differences.
Water
reservoir
Pressure difference
from height of
reservoir corresponds
to voltage.
Current is the number of
charges through a cross
section per second.
Current corresponds to the
flow of water in the fluid
analogy.
Av → I
∆P → ∆V
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Physics 102 Lecture 2
9
Ohm’s Law
In many materials, the current that flows
is proportional to the voltage across
(potential difference) the material: I ∝ V
The proportionality constant is the resistance
R, a property of the particular piece of
material
Ohm’s Law: V = IR
I
∆V
Note that Ohm’s “Law” is only an approximation that holds true
over a particular range of currents and voltages, and it is not at
all correct for some materials; it is not a fundamental law.
14 Feb 2002
Physics 102 Lecture 2
10
Series and Parallel Circuits
When multiple resistors are connected in a circuit,
we use two simple rules:
I
I
Resistors in series
R = R1 + R2
I
i
Resistors in parallel
1
1
1
=
+
R R1 R2
I
More complex circuits are broken into simple pieces
14 Feb 2002
Physics 102 Lecture 2
11
Resistive Properties of Materials
I
Resistivity is an intrinsic property of a material
N
N
N
I
L is length of object
A is cross sectional area of objectFF
ρ is the resistivity (units ohms·meters)
L
R=ρ
A
Resistivity (and resistance) often depend on
temperature (increasing with T in metals)
ρ = ρ0 [1 + α (T − T0 )]
R = R0 [1 + α (T − T0 )]
14 Feb 2002
Physics 102 Lecture 2
Cool
12
•Recall that power is energy
per unit time.
•As charges move (or currents
flow), the electric field does
work on the particles (changes
their energies).
∆E ∆qV
P=
=
= IV
∆t
∆t
2
= I ( IR) = I R
•Recall that a watt is the SI
power unit, so kilowatt-hour is
a unit of energy.
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Physics 102 Lecture 2
2
V
V

=
V=
 R
R
13
A. I
B. They’re the same
C. II
•The resistance of circuit I is smaller than of circuit II
•Hence more current flows through battery in I
•P=IV, hence power is greater in circuit I
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Physics 102 Lecture 2
14
AC Circuits
I
I
I
Outlets supply 120V 60 Hz “AC” (alternating
current) which is generated by a local power plant.
There are three wires a)a ground [green], b)a neutral
[white], and c) a HOT wire [black].
Why do we get power from an alternating current?
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Physics 102 Lecture 2
15
RC Circuits
I
Circuits with both
capacitors and resistors
have time variable currents
q = q0 (1 − e − t / RC )
V = V0 (1 − e − t / RC )
I = I0 e − t / RC
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Physics 102 Lecture 2
16
RC Puzzler
This is called a “relaxation oscillator.”
Why does the light blink?
14 Feb 2002
Physics 102 Lecture 2
17