Current, Resistance, Direct-current Circuits

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Current, Resistance, Direct-current Circuits
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• 1. Electric current
• The current is the rate at which charge flows
  through this surface
• Suppose ?Q is the amount of charge that flows
  through an area A in a time interval ?t and that
  the direction of flow is perpendicular to the
  area. Then the current I is equal to the amount
  of charge divided by the time
• I ? Q/?t
• SI C/sA
• (Ampere)

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• 2. Current and voltage measuraments in circuits

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• 3. Resistance and Ohms Law
• Resistance is the ratio of the voltage across the
  conductor to the current
• R ?V/ I
• SI units 1V/A1O (Ohms)
• Ohms Law the resistance remains constant over a
  wide range of applied voltage or currents
• ?V IR

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• A resistor is a conductor that provides a
  specified resistance in an electric circuit
• The resistance is proportional to the conductors
  length l and inversely proportional to its
  cross-sectional area A
• R ? l/A
• ? resistivity of the material (ct. of
  proportionality) SI unit O m

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• 4. Electrical energy and power
• The rate at which the system loses potential
  energy as the charge passes through resistor is
  equal to the rate at which the system gains
  internal energy in the resistor.
• (?Q/ ?t) ?V I ?V
• Power P - the rate at which energy is delivered
  to the resistor
• P I ?V
• P I2R ?V2/R
• SI kilowatt-hour
• 1kWh (103W)(3600s) 3.6x106J

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• Question Some homes have light dimmers that are
  operated by rotating a knob. What is being
  changed in the electric circuit when the know is
  rotated?
• R I

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Direct-Current Circuits

• 5. Sources of EMF (electromotive force)- a
  charge pump that forces electrons to move in a
  direction opposite the electrostatic field inside
  the source
• The emf e of a source is the work done per unit
  charge (SI unit V)
• ?V e Ir
• e the terminal voltage when the current is zero
  (open circuit voltage)

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• ?V IR
• (R- the external resistance)
• e IR Ir
• I e / (Rr)
• I e I2R I2r if rltltR
• (the power delivered
• by the battery is
• transferred to the load
• resistance)

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• 6. Resistors in series

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• ?V IR1 IR2 I(R1R2)
• ?V I Req
• IReq I(R1R2)
• Req R1R2
• Req R1R2.
• The equivalent resistance of a series combination
  of resistors is the algebraic sum of the
  individual resistances and is always greater than
  any individual resistance

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• 7. Resistors in parallel

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• The potential differences across resistors are
  the same because each is connected directly
  across the battery terminals
• Because charge is conserved, the current I that
  enters point a must equal the total current I1I2
  leaving that point
• I I1I2
• I1?V /R1
• I2?V /R2
• I ?V /Req
• 1/Req 1/R1 1/R2
• The inverse of the equivalent resistance of two
  or more resistors connected in parallel is the
  sum of the inverses of the individual resistances
  and is always less than the smallest resistance
  in the group

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• 8. Kirchhoffs Rules
• 1. The sum of the currents entering any jonction
  must equal the sum of the currents leaving that
  junction (junction rule)

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• 2. The sum of the potential differences across
  all the elements around any closed circuit loop
  must be zero (loop rule)

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• a) if the resistor is traversed in the direction
  of the current, the charge in electric potential
  across the resistor is IR

• b) If a resistor is traversed in the direction
  opposite the current, the charge in electric
  potential across resistors is IR

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• c) if a source of emf is traversed in the
  direction of the emf (from to ) the charge in
  electric potential is S

• d) if a source of emf is traversed in the
  direction opposite the emf, the charge in
  electric potential is -S

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• Problem solving strategy
• 1. Assign labels and symbols to all the known and
  unknown quantities
• 2. Assign directions to the currents in each part
  of the circuit
• 3. Apply the junction rule to any junction in the
  circuit
• 4. Apply Kirchhoffs loop rule, to as many loops
  in the circuit as are needed to solve for the
  unknowns
• 5. solve the equations
• 6. Check your answers by substituting them into
  the original equations

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• Problem Find the currents in the circuit shown
  in fig. by using Kirchhoffs rules

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• 9. RC circuits

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• We consider that the capacitor is initially
  uncharged with the switch open. After the switch
  is closed, the battery begins to charge the
  plates of capacitor and the charge passes through
  resistor
• A the capacitor is being charged, the circuit
  carries a changing current. The process continues
  until the capacitor is charged to a maximum value
• QCe
• e -maximum voltage across the capacitor
• Once the capacitor is fully charged, the current
  in circuit is zero

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• qQ(1-e t/RC)
• RCs time constant
• The time constant represents the time required
  for the charge to increase from zero to 63.2 its
  maximum equilibrium value

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• Before the switch is closed the potential
  difference across the charged capacitor is Q/C
• Once the switch is closed, the charge begins to
  flow through the resistor, until the capacitor is
  fully charged
• qQe-t/RC
• The charge decreasses exponentially with time
• ?Vee-t/RC

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