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Chapter 23
Electric Circuits
Regents Physics
Mr. Rodriguez
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There are 3 basic things that you note when thinking
about electric circuits:
Voltage
Current
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Resistance
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Voltage: a force that pushes
and pulls the current through
the circuit (in this picture it
would be equivalent to gravity)
Current: the actual
“substance” that is flowing
through the wires of the circuit
(electrons!)
Resistance: friction that
impedes flow of current
through the circuit (rocks in
the river)
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Circuit Characteristics
Electrical current flows in a loop, or a circuit. The image
shows a simple electrical circuit. The circuit has four
important parts: a power source (a battery, in this case), a
conductor (the wire), the load (the light bulbs), and a switch.
Current flows from the positive side of the battery, through
the bulbs, and back to the negative side of the battery. As the
electric current makes a complete loop, both bulbs will
light. The complete loop condition is known as a closed
circuit. A current that flows continuously in one direction is
called a steady state current and is abbreviated DC. An open
circuit condition occurs when the path of current flow is
interrupted. This can happen if the wire is severed at any
point on the circuit, or if the wire is disconnected from
either side of the battery. With an open circuit, current will
not flow, and the bulb will not light
A switch is a device that enables a person to open or close
the circuit whenever they choose.
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Producing Electric Current
In the last unit, you learned that when two
conducting spheres touch charges flow from the
sphere at a high potential to the one at a lower
potential. The flow continues until there is no
potential difference between the two spheres.
A flow of charged particles is an electric
current.
I = q/t
The SI unit of current is the Ampere.
Since one ampere is the flow of one
coulomb of charge per second, it is a
current in which 6.25 x 1018 electrons
pass through the circuit per second.
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Direction of Current
Conventional Current:
Flow of current from positive terminal
to the negative terminal.
Electron Current:
Flow of current from the negative
terminal to the positive terminal.
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Current and Voltage Defined
Think of voltage as what pushes
the electrons along in the circuit,
and current as a group of
electrons that are constantly
trying to reach a state of
equilibrium.
If there is no voltage, electrons
don’t move, therefore there is no
current.
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Difference in electrical charge
between two points creates
difference in potential energy,
which causes electrons to flow
from an area with lots of electrons
(negative terminal) to an area
with few electrons (positive
terminal), producing an electric
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current.
Electric Circuits
Sample Problem
A current of 5.00 A flowed in a copper wire for 20.0s.
(a) How many coulombs of charge passed through the
wire at this time? (b) how many electrons flowed
through this wire at this time?
Solution
(a)
I = Q/t
5.00 = Q / 20.0 s
Q = 100 C
(b) Number of electrons per sec is (5)(6.25 x 1018 electrons/s )= 3.12 x 1019 electrons
per sec.
Multiply 3.12 x 1019 electrons by 20 sec = 6.25 x 1020 electrons/s
OR use Ne = Q/e
100 C / 1.6 x 10-19 = 6.25 x 1020 electrons
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Relation between Current and Resistance
Suppose two conductors have a potential difference between
them. If they are connected with a copper rod, a large current
is created. On the other hand, putting a glass rod between
them creates no current. The property of determining how
much current will flow is called resistance.
In this diagram, Let the amount of
liquid passing through the neck of
the container be the current, and
let the pressure of the water above
the neck be the voltage and let the
resistance depend upon the
charateristics of the container
(width of the neck of the
container).
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Resistance
The resistance depends on material and
geometry (shape). For a wire, we have:
R=rL/A
where r is called the resistivity . The
units of resistance is Ohms () and
measures how hard it is for current to
flow through the material, L is the length
of the wire, and A is the cross-sectional
area of the wire.
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Definition of Resistance
By experiment we find that if we increase the voltage,
we increase the current: V is proportional to I. When a
metal wire is connected to a battery supplying a
constant difference of potential, the current flowing
through it depends on the degree of opposition which
the electrons encounter in the wire conductor as they
collide with the atoms in their paths. This opposition is
called the resistance of the wire. The total resistance
of a circuit can be related to the ratio of the potential
difference applied to the ends of the wire to the current
flowing through it, or R = r L / A = V/I
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Resistance
Just as with fluid flow, the amount of
resistance does not depend on the
voltage (pressure) or the current
(volume flow). The formula V=IR
relates voltage to current. If you double
the voltage, you will double the current,
not change the resistance. As was the
case in fluid flow, the amount of
resistance depends on the materials
and shapes of the wires.
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Ohm’s Law
If a series of increasing potential differences is
applied to a given wire whose temperature is kept
constant, the current in the wire increases in
direct proportion to the difference in potential.
Plotting the currents I against the corresponding
differences in potential V gives a straight line.
This means that the ratio V/I is constant, and
therefore that the resistance R of the metal wire
also remains constant in spite of the change in V
and I.
George Simon Ohm discovered that this
constancy of resistance is true for all metal
conductors provided their temperatures are also
kept constant. His discovery, known as Ohm’s
Law, is written:
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V/I = R = constant
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Ohm’s Law
Current through an ideal conductor is
proportional to the applied voltage
– Conductor is also known as a resistor
– An ideal conductor is a material whose resistance does not change
with temperature
For an ohmic device,
Voltage  Current  Resistance
V  I R
V = Voltage
I = Current
R = Resistance
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(Volts = V)
(Amperes = A)
(Ohms = Ω)
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Ohm’s Law
Sample Problem
(a) What current flows through a 80 coil of wire when
it is connected to the terminal of a generator supplying a
potential difference of 120 V? (b) How many electrons
are passing through the coil per second?
Solution
(a) I = V/R = 120V/ 80 = 1.5 A
(b) 1 A = 1 C/s = 6.25 x 1018 electrons/s
I = 1.5 A = (1.5) (6.25 x 1018 electrons/s) = 9.4 x 1018 electrons
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Electrical Power
The change of electrical potential energy
(W) of a charge is:
DPE = W = qV .
Power is the change in energy with respect
to time: Power = DPE / Dt .
Putting these two concepts together we
have:
Power = (qV) / t = V q / t = VI.
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Electrical Power
Besides this basic equation for power:
P = I*V
remember we also have Ohm’s Law:
V = I*R .
Thus we can write the following equations for
power: P = I2*R = V2/R = I*V .
The units of power are watts.
From our previous knowledge, Power is also
defined as Work(Energy)/Time. Thus:
P = W/t = I2*R = V2/R = I*V .
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Electrical Power
Sample Problem
Calculate the resistance of a 40W automobile headlight
designed for 12V.
Solution
Since we are given P=40W and V=12V, we can use the
equation P = I2R and solve for R:
R= V2/P = (12V)2/(40W) = 3.6
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Ohm’s Law Formula Chart
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Heat Generated in Resistors
The heat, Q, (electrical energy) generated
in a resistor in t seconds is equal to the
power funished by the resistor during that
time:
QEnergy = Pt = IVt =I2Rt = V2/Rt
The units of Q are Joules or Wattseconds
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The Light Bulb and its Components
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• Has two metal contacts at
the base which connect
to the ends of an
electrical circuit
• The metal contacts are
attached to two stiff wires,
which are attached to a
thin metal filament.
• The filament is in the
middle of the bulb, held
up by a glass mount.
• The wires and the
filament are housed in a
glass bulb, which is filled
with an inert gas, such as
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argon.
Light bulbs do not obey Ohm’s Law
• Bulbs are non-linear conductors
(R increases with temperature)
R  Ro  1   T  To  


R  Conductor resistance at temperature T []
Ro  Conductor resistance at reference To []
  Temperature coefficient of resistance [C 1]
T  Conductor temperature [C ]
To  Reference temperature  specified for [C ]
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Light bulbs do not obey Ohm’s Law
The filaments of light bulbs are made of Tungsten, which is a very
good conductor. It heats up easily.
 Tungsten  0.004403 / C at 20C (i.e. To  20C )
As light bulbs warm up, their resistance increases. If the
current through them remains constant:
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P  I R
They glow slightly dimmer when first plugged in.
Why?
R increases but I remains constant  P increases
Most ohmic resistors will behave non-linearly outside of a given
range of temperature, pressure, etc.
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Voltage versus Current for
Constant Resistance
The light bulb does not have a linear relationship. The resistance
of the bulb increases as the temperature of the bulb increases.
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Superconductivity
As the temperature of certain
materials approaches absolute
zero, their resistance drops to zero.
The property whereby a metal
loses its electrical resistance when
cooled to a sufficiently low
temperature is called
superconductivity. The metals
known to be superconductive
include aluminum, lead, titanium,
niobium, vanadium, and
technecium.
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What the heck is going
on?
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Conclusion
• The flow of charged particles is called the an electric
current. It is defined as I = Q/t
• Ohmic resistors obey Ohm’s Law: V =IR
• The resistance of a metal varies directly with its length
and inversely with its cross section: R = rL/A where r is
the resistivity of the wire.
• Resistance is affected by temperature. The resistance of
a conductor increases as its temperature increases
• Light bulbs do not obey Ohm’s Law
– Tungsten is such a good conductor that their
resistance depends on their temperature
– As their temperature increases, the power dissipated
by the bulb increases
• i.e. They are brighter when they are hotter
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Conclusion
• The power of a resistor in a circuit is given as
P = IV = V2/R = I2R
• A superconductor is a perfect conductor of electricity; it carries direct
current with 100% efficiency because no energy is dissipated by
resistive heating. Once induced in a superconducting loop, direct
current can flow undiminished forever.
• The Energy or Heat generated by a resistor in a gvien time t is Q =
Pt.
• Conventional current is defined as the direction opposite the flow of
electrons in a closed circuit
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