Direct Current Circuits

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Chapter 18

• Direct Current Circuits

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18.1 Sources of emf

• The source that maintains the constant current in
  a circuit is called a source of emf.
• Any device (such as batteries or generators)that
  increase the potential energy of charges
  circulating in circuits are sources of emf.
• The device acts like a charge pump!
• The emf of a source is the work done per unit of
  charge, the SI unit is the volt.

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18.2 Resistors in Series

• Series circuit - only one path for the current.
• All charges must follow the same conducting path.
• The current in all resistors in a series circuit
  are the same, because any charge that passes
  through one resistor must also pass through the
  other.
• Figure 18.2

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Series cont

• Regardless of how many resistors we have in
  series, the sum of the potential differences
  across the individual resistors is equal to the
  potential difference across the combination.
• This demonstrates conservation of energy.

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Equivalent Resistance

• The equivalent resistance in a series circuit is
  equal to the sum of all the individual resistors.
• The equivalent resistance of a series combination
  of resistors is always greater than any
  individual resistance.
• Any break in the circuit creates an open circuit,
  thus the circuit is no longer complete.
• Ex 18.1

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Safety Measures

• In many circuits, fuses are used in series with
  other circuit elements for safety purposes.
• The conductor in the fuse is designed to melt and
  open the circuit at some maximum current.
• If a fuse were not used, excessive currents could
  damage circuit elements, over heat wires, and
  perhaps cause a fire.
• Modern homes have circuit breakers instead of
  fuses.
• When the current in a circuit exceeds a certain
  value (usually 15A), the breaker acts as a switch
  and opens the circuit.

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18.3 Resistors in Parallel

• A parallel circuit allows the current to travel
  in more than one path.
• When resistors are connected in parallel, the
  potential differences across them are the same.
• This must be true since the sides of the
  resistors are connected to common points (Figure
  18.4b).
• The currents vary however, unless of course the
  resistors are the same.
• Remember charge follows the path of least
  resistance!

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Parallel cont

• Because charge is conserved, the current that
  enters a junction, must equal the current
  leaving the junction!
• The potential drop across each resistor must be
  the same for each resistor and must equal the
  potential drop of the battery!

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Parallel Equivalent Resistance

• The equivalent resistance of a parallel circuit
  is defined as the reciprocal of the equivalent
  resistance equals the sum of reciprocals for each
  individual resistor.
• The equivalent resistance of two or more
  resistors connected in parallel is always less
  than the smallest resistance in the group!
• Ex 18.2
• Ex. 18.3

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18.4 Kirchoffs Rules and Complex DC Circuits

• 1. The sum of the currents entering any junction
  must equal the sum of the currents leaving that
  junction( junction rule)!
• (Conservation of charge)
• 2. The sum of the potential differences across
  all the elements around any closed circuit loop
  must be zero (loop rule)!
• (Conservation of energy)

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Kirchoffs Rules

• A real life example!

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Kirchoffs rules

• 1. You must assign symbols and direction to the
  currents in all branches of the circuit. If you
  should happen to guess the wrong direction for
  the current, the end result for that current will
  be negative but its magnitude will be correct!

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Kirchoffs rules

• 2. When applying the loop rule, you must choose a
  direction (clockwise or counter clockwise) for
  going around the loop.
• As you traverse the loop, record voltage drops
  and rises accordingly.

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Summary of voltage drops and rises

• (a) If a resistor is traversed in the direction
  of the current , the change in electric potential
  is (-IR).
• (b) If a resistor is traversed in the direction
  opposite of the current , the change in electric
  potential is (IR).
• (c) If a source of emf is traversed in the
  direction of the emf (from - to on the
  terminals), the change in the electric potential
  is E!
• (d) If a source of emf is traversed in the
  direction opposite of the emf (from to - on the
  terminals), the change in the electric potential
  is -E!

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In General

• The numbers of times the junction rule can be
  applied is one fewer than the number of junction
  points in a circuit!
• The loop rule can be applied as often as needed
  so long as a new circuit element (resistor or
  battery) or a new current appears in each new
  equation!
• You need as many independent equations as there
  are unknowns!

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Example Problems

• Ex. 18.4
• Ex. 18.5

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Household circuits

• Utility company distributes electric power to
  individual houses with a pair of wires or power
  lines.
• Electrical devices in a house are connected in
  parallel to these lines (the potential drop
  across these wires is about 120V)!
• One wire is connected to the ground, and the
  other (hot wire), has a potential of 120V.
• A meter and circuit breaker (or fuse) are
  connected in series with the wire entering the
  house.

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18.7 Safety

• A person can be electrocuted by touching a live
  wire while in contact with the ground.
• 5mA or less can cause a sensation of shock.
• Larger than 10mAcauses loss of muscle control.
• 100mA can be fatal.
• Special power outlets called ground fault
  interrupters (gfi) are used in many new homes
  that sense small amounts of currents leaking to
  the ground. This device interrupts (shuts off)
  the current.