Electric Currents and Resistance

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Electric Currents and Resistance
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• The Electric Battery
• Electric Current
• Ohms Law Resistance and Resistors
• Resistivity
• Electric Power
• Microscopic View of Electric Current Current
  Density and Drift Velocity

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Volta discovered that electricity could be
created if dissimilar metals were connected by a
conductive solution called an electrolyte. This
is a simple electric cell.
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The Electric Battery
A battery transforms chemical energy into
electrical energy. Chemical reactions within the
cell create a potential difference between the
terminals by slowly dissolving them. This
potential difference can be maintained even if a
current is kept flowing, until one or the other
terminal is completely dissolved.
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The Electric Battery
Several cells connected together make a battery,
although now we refer to a single cell as a
battery as well.
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Electric Current
Electric current is the rate of flow of charge
through a conductor
The instantaneous current is given by
Unit of electric current the ampere, A
1 A 1 C/s.
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Electric Current
A complete circuit is one where current can flow
all the way around. Note that the schematic
drawing doesnt look much like the physical
circuit!
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Electric Current
Current is flow of charge. A steady current of
2.5 A exists in a wire for 4.0 min. (a) How much
total charge passed by a given point in the
circuit during those 4.0 min? (b) How many
electrons would this be?
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Current Density and Drift Velocity
Electrons in a conductor have large, random
speeds just due to their temperature. When a
potential difference is applied, the electrons
also acquire an average drift velocity, which is
generally considerably smaller than the thermal
velocity.
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Current Density and Drift Velocity
We define the current density (current per unit
area) this is a convenient concept for relating
the microscopic motions of electrons to the
macroscopic current
If the current is not uniform
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Current Density and Drift Velocity
Charges move with a drift velocity along the
wire.
Total charge within the volume
Time taken to pass through
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Electric Current
How to connect a battery. What is wrong with each
of the schemes shown for lighting a flashlight
bulb with a flashlight battery and a single wire?
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Electric Current
By convention, current is defined as flowing from
to -. Electrons actually flow in the opposite
direction, but not all currents consist of
electrons.
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Ohms Law
Experimentally, it is found that the current in a
wire is proportional to the potential difference
between its ends
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Ohms Law Resistance and Resistors
The ratio of voltage to current is called the
resistance
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Ohms Law
In many conductors, the resistance is independent
of the voltage this relationship is called Ohms
law. Materials that do not follow Ohms law are
called nonohmic.
Unit of resistance the ohm, ? 1 ? 1 V/A.
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Ohms Law
Current and potential. Current I enters a
resistor R as shown. (a) Is the potential higher
at point A or at point B? (b) Is the current
greater at point A or at point B?
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Ohms Law
Flashlight bulb resistance. A small flashlight
bulb draws 300 mA from its 1.5-V battery. (a)
What is the resistance of the bulb? (b) If the
battery becomes weak and the voltage drops to 1.2
V, how would the current change?
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Ohms Law
Standard resistors are manufactured for use in
electric circuits they are color-coded to
indicate their value and precision.
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Ohms Law
This is the standard resistor color code. Note
that the colors from red to violet are in the
order they appear in a rainbow.
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Ohms Law

• Some clarifications
• Batteries maintain a (nearly) constant potential
  difference the current varies.
• Resistance is a property of a material or
  device.
• Current is not a vector but it does have a
  direction.
• Current and charge do not get used up. Whatever
  charge goes in one end of a circuit comes out the
  other end.

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Resistivity
The resistance of a wire is directly proportional
to its length and inversely proportional to its
cross-sectional area
Geometric property
The constant ?, the resistivity, is
characteristic of the material.
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Resistivity
This table gives the resistivity and temperature
coefficients of typical conductors,
semiconductors, and insulators.
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Current Density and Drift Velocity
The electric field inside a current-carrying wire
can be found from the relationship between the
current, voltage, and resistance. Writing R ?
l/A, I jA, and V El , and substituting in
Ohms law gives
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Electric Power
Power, as in kinematics, is the energy
transformed by a device per unit time
or
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Electric Power
The unit of power is the watt, W. For ohmic
devices, we can make the substitutions
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Electric Power
Headlights. Calculate the resistance of a 40-W
automobile headlight designed for 12 V.
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Electric Power
What you pay for on your electric bill is not
power, but energy the power consumption
multiplied by the time. We have been measuring
energy in joules, but the electric company
measures it in kilowatt-hours, kWh 1 kWh (1000
W)(3600 s) 3.60 x 106 J.
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Electric Power
Electric heater. An electric heater draws a
steady 15.0 A on a 120-V line. How much power
does it require and how much does it cost per
month (30 days) if it operates 3.0 h per day and
the electric company charges 9.2 cents per kWh?
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Electric Power
Lightning bolt. Lightning is a spectacular
example of electric current in a natural
phenomenon. There is much variability to
lightning bolts, but a typical event can transfer
109 J of energy across a potential difference of
perhaps 5 x 107 V during a time interval of about
0.2 s. Use this information to estimate (a) the
total amount of charge transferred between cloud
and ground, (b) the current in the lightning
bolt, and (c) the average power delivered over
the 0.2 s.
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Summary

• A battery is a source of constant potential
  difference.
• Electric current is the rate of flow of electric
  charge.
• Conventional current is in the direction that
  positive charge would flow.
• Resistance is the ratio of voltage to current

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Summary

• Ohmic materials have constant resistance,
  independent of voltage.
• Resistance is determined by shape and material

• ? is the resistivity.

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Summary

• Power in an electric circuit

• Direct current is constant.
• Relation between drift speed and current

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DC Circuits
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• EMF and Terminal Voltage
• Resistors in Series and in Parallel
• Kirchhoffs Rules

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EMF and Terminal Voltage
Electric circuit needs battery or generator to
produce current these are called sources of emf
(Electromotive force). Battery is a nearly
constant voltage source, but does have a small
internal resistance, which reduces the actual
voltage from the ideal emf
emf
Terminal Voltage
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EMF and Terminal Voltage
This resistance behaves as though it were in
series with the emf.
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EMF and Terminal Voltage
Battery with internal resistance. A 65.0-O
resistor is connected to the terminals of a
battery whose emf is 12.0 V and whose internal
resistance is 0.5 O. Calculate (a) the current
in the circuit, (b) the terminal voltage of the
battery, Vab, and (c) the power dissipated in
the resistor R and in the batterys internal
resistance r.
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Resistors in Series
A series connection has a single path from the
battery, through each circuit element in turn,
then back to the battery.
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Resistors in Series

• The current through each resistor is the same
• The voltage depends on the resistance.
• The sum of the voltage drops across the resistors
  equals the battery voltage

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Resistors in Parallel
A parallel connection splits the current the
voltage across each resistor is the same
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Resistors in Parallel
The voltage across each resistor is the same
The total current is the sum of the currents
across each resistor
,
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Resistors in Parallel
This gives the reciprocal of the equivalent
resistance
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Resistors
Series or parallel? (a) The lightbulbs in the
figure are identical. Which configuration
produces more light? (b) Which way do you think
the headlights of a car are wired? Ignore change
of filament resistance R with current.
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Resistors
An illuminating surprise. A 100-W, 120-V
lightbulb and a 60-W, 120-V lightbulb are
connected in two different ways as shown. In each
case, which bulb glows more brightly? Ignore
change of filament resistance with current (and
temperature).
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Resistors
Circuit with series and parallel resistors. How
much current is drawn from the battery shown?
What is the current through each of the resistor?
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Resistors in Series and in Parallel
Bulb brightness in a circuit. The circuit shown
has three identical lightbulbs, each of
resistance R. (a) When switch S is closed, how
will the brightness of bulbs A and B compare
with that of bulb C? (b) What happens when
switch S is opened? Use a minimum of mathematics
in your answers.
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Resistors
Analyzing a circuit. A 9.0-V battery whose
internal resistance r is 0.50 O is connected in
the circuit shown. (a) How much current is drawn
from the battery? (b) What is the terminal
voltage of the battery? (c) What is the current
in the 6.0-O resistor?
a
b
d
c
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Kirchhoffs Rules
Some circuits cannot be broken down into series
and parallel connections. For these circuits we
use Kirchhoffs rules.
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Kirchhoffs Rules
Junction rule The sum of currents entering a
junction equals the sum of the currents leaving
it.
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Kirchhoffs Rules
Loop rule The sum of the changes in potential
around a closed loop is zero.
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Kirchhoffs Rules

• Junction rule
• Loop rule

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Kirchhoffs Rules

1. Label each current, including its direction.
2. Identify unknowns.
3. Apply junction and loop rules you will need as
   many independent equations as there are unknowns.
4. Solve the equations, being careful with signs. If
   the solution for a current is negative, that
   current is in the opposite direction from the one
   you have chosen.

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Kirchhoffs Rules
Using Kirchhoffs rules. Calculate the currents
I1, I2, and I3 in the three branches of the
circuit in the figure.
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Calculate the equivalent resistance
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I
I-I1
I1
I1-I2
I-I2
I2
I
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Solution
Solving the coupled equations and express I1 and
I2 in terms of I, R1, R2 and R3
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Solution
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Summary

• A source of emf transforms energy from some
  other form to electrical energy.
• A battery is a source of emf in parallel with an
  internal resistance.
• Resistors in series

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Summary

• Resistors in parallel

• Kirchhoffs rules
• Sum of currents entering a junction equals sum of
  currents leaving it.
• Total potential difference around closed loop is
  zero.

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Summary

• RC circuit has a characteristic time constant

• Ammeter measures current.
• Voltmeter measures voltage.