Electric Circuits DC

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Electric Circuits (DC)
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Electric Circuits (DC)

• Electromotive Force and Current
• Current and Drift velocity
• An electric current, which is a flow of charge,
  occurs when there is a potential difference. For
  a current to flow also requires a complete
  circuit, which means the flowing charge has to be
  able to get back to where it starts. Current (I)
  is measured in amperes (A), and is the amount of
  charge flowing per second.
• When current flows through wires in a circuit,
  the moving charges are electrons. For historical
  reasons, however, when analyzing circuits the
  direction of the current is taken to be the
  direction of the flow of positive charge,
  opposite to the direction the electrons go. We
  can blame Benjamin Franklin for this. It amounts
  to the same thing, because the flow of positive
  charge in one direction is equivalent to the flow
  of negative charge in the opposite direction.
• When a battery or power supply sets up a
  difference in potential between two parts of a
  wire, an electric field is created and the
  electrons respond to that field. In a
  current-carrying conductor, however, the
  electrons do not all flow in the same direction.
  In fact, even when there is no potential
  difference (and therefore no field), the
  electrons are moving around randomly. This random
  motion continues when there is a field, but the
  field superimposes onto this random motion a
  small net velocity, the drift velocity. Because
  electrons are negative charges, the direction of
  the drift velocity is opposite to the electric
  field.
• Example 1 page 579

Current equals charge divided by time
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Electric Circuits (DC)

• Ohms Law
• Electrical resistance
• Voltage can be thought of as the pressure pushing
  charges along a conductor, while the electrical
  resistance of a conductor is a measure of how
  difficult it is to push the charges along. Using
  the flow analogy, electrical resistance is
  similar to friction. For water flowing through a
  pipe, a long narrow pipe provides more resistance
  to the flow than does a short fat pipe. The same
  applies for flowing currents long thin wires
  provide more resistance than do short thick
  wires.
• Resistance also depends on temperature, usually
  increasing as the temperature increases. For
  reasonably small changes in temperature, the
  change in resistivity, and therefore the change
  in resistance, is proportional to the temperature
  change. This is reflected in the equations
• At low temperatures some materials, known as
  superconductors, have no resistance at all.
  Resistance in wires produces a loss of energy
  (usually in the form of heat), so materials with
  no resistance produce no energy loss when
  currents pass through them.
• Ohm's Law
• In many materials, the voltage and resistance are
  connected by Ohm's Law
• Ohm's Law V IR
• The connection between voltage and resistance can
  be more complicated in some materials.These
  materials are called non-ohmic. We'll focus
  mainly on ohmic materials for now, those obeying
  Ohm's Law.

Ohm.its not just a good idea, its the LAW!
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Electric Circuits (DC)

• Electric Power
• Power is the rate at which work is done. It has
  units of Watts. 1 W 1 J/s
• Electric power is given by the equations
• Batteries and power supplies supply power to a
  circuit, and this power is used up by motors as
  well as by anything that has resistance. The
  power dissipated in a resistor goes into heating
  the resistor this is know as Joule heating. In
  many cases, Joule heating is wasted energy. In
  some cases, however, Joule heating is exploited
  as a source of heat, such as in a toaster or an
  electric heater.
• The electric company bills not for power but for
  energy, using units of kilowatt-hours.
• 1 kW-h 3.6 x 106 J
• One kW-h typically costs about 10 cents, which is
  relatively cheap. It does add up, though. The
  following equation gives the total cost of
  operating something electrical
• Cost (Power rating in kW) x (number of hours
  it's running) x (cost per kW-h)
• An example...if a 100 W light bulb is on for two
  hours each day, and energy costs 0.10 per kW-h,
  how much does it cost to run the bulb for a
  month?
• Cost 0.1 kW x 60 hours x 0.1/kW-h 0.6, or
  60 cents.
• The cost for power that comes from a wall socket
  is relatively cheap. On the other hand, the cost
  of battery power is much higher. 100 per kW-h, a
  thousand times more than what it costs for AC
  power from the wall socket, is a typical value.
• Although power is cheap, it is not limitless.
  Electricity use continues to increase, so it is
  important to use energy more efficiently to
  offset consumption. Appliances that use energy
  most efficiently sometimes cost more but in the
  long run, when the energy savings are accounted
  for, they can end up being the cheaper
  alternative.

Turn that light off!
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Electric Circuits (DC)

• Series Circuits
• A series circuit is a circuit in which resistors
  are arranged in a chain, so the current has only
  one path to take.
• The current is the same through each resistor.
  The total resistance of the circuit is found by
  simply adding up the resistance values of the
  individual resistors
• equivalent resistance of resistors in series R
  R1 R2 R3 ...
• A series circuit is shown in the diagram above.
  The current flows through each resistor in turn.
• The values of the two resistors are 6 and 3 ohms
• With a 12 V battery, using V I R the total
  current in the circuit is
• I V / R 12 / 9 1.33 A. The current through
  each resistor would be 1.33 A.

Series resistors just add up
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Electric Circuits (DC)

• Parallel Circuits
• The current in a parallel circuit breaks up, with
  some flowing along each parallel branch and
  re-combining when the branches meet again. The
  voltage across each resistor in parallel is the
  same.
• The total resistance of a set of resistors in
  parallel is found by adding up the reciprocals of
  the resistance values, and then taking the
  reciprocal of the total
• equivalent resistance of resistors in parallel 1
  / R 1 / R1 1 / R2 1 / R3 ...
• Dont forget to take the reciprocal after adding
  the 1/R terms!
• A parallel circuit is shown in the diagram below.
  In this case the current supplied by the
  amplifier splits up, and the amount going through
  each speaker (resistor) depends on the
  resistance.

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Electric Circuits (DC)

• Kirchhoffs Rules
• Junctions and Branches.
• A junction is a point where at least three
  circuit paths meet.
• A branch is a path connecting two junctions.

B and E are junctions
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Electric Circuits (DC)

• Kirchhoffs Rules
• In a circuit involving one voltage source and a
  number of resistors in series and/or parallel,
  the resistors can generally be reduced to a
  single equivalent resistor.
• With more than one voltage source, the situation
  is trickier. If all the voltage sources are part
  of one branch they can be combined into a single
  equivalent battery. Generally, If the voltage
  sources are part of different branches, another
  method has to be used to analyze the circuit to
  find the current in each branch. Circuits like
  this are known as multi-loop circuits.
• Finding the current in all branches of a
  multi-loop circuit (or the emf of a battery or
  the value of a resistor) is done by following
  guidelines known as Kirchoff's rules. These
  guidelines also apply to very simple circuits.
• Kirchoff's first rule the junction rule. The
  sum of the currents coming in to a junction is
  equal to the sum leaving the junction. (this is
  conservation of charge)
• Kirchoff's second rule the loop rule. The sum
  of all the potential differences around a
  complete loop is equal to zero. (Conservation of
  energy)

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Electric Circuits (DC)

• Kirchhoffs Rules
• The branch current method
• To analyze a circuit using the branch-current
  method involves three steps
• Label the current and the current direction in
  each branch. Sometimes it's hard to tell which is
  the correct direction for the current in a
  particular loop. That does NOT matter. Simply
  pick a direction. If you guess wrong, you¹ll get
  a negative value. The value is correct, and the
  negative sign means that the current direction is
  opposite to the way you guessed. You should use
  the negative sign in your calculations, however.
• Use Kirchoff's first rule to write down current
  equations for each junction that gives you a
  different equation. For a circuit with two inner
  loops and two junctions, one current equation is
  enough because both junctions give you the same
  equation.
• Use Kirchoff's second rule to write down loop
  equations for as many loops as it takes to
  include each branch at least once. To write down
  a loop equation, you choose a starting point, and
  then walk around the loop in one direction until
  you get back to the starting point. As you cross
  batteries and resistors, write down each voltage
  change. Add these voltage gains and losses up and
  set them equal to zero.
• When you cross a battery from the - side to the
  side, that's a positive change. Going the other
  way gives you a drop in potential, so that's a
  negative change.
• When you cross a resistor in the same direction
  as the current, that's also a drop in potential
  so it's a negative change in potential. Crossing
  a resistor in the opposite direction as the
  current gives you a positive change in potential.
  

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Electric Circuits (DC)

• Kirchhoffs Rules (Example 13 page 597)