DC CIRCUITS AND INSTRUMENTS

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DC CIRCUITS AND INSTRUMENTS
Chapter 18 Problems 18-1/18-3
5,6,7,8,9,12,14 18-4
15,17,21,23 18-5 29,31,33
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DC CIRCUITS AND INSTRUMENTS

• OBJECTIVES
• 1. Determine the equivalent resistance of
  resistors arranged in series or in parallel or
  the equivalent resistance of a series-parallel
  combination.
• 2. Use Ohm's law and Kirchhoff s rules to
  determine the current through each resistor and
  the voltage drop across each resistor in a single
  loop or multiloop dc circuit.
• 3. Distinguish between the emf and the terminal
  voltage of a battery and calculate the terminal
  voltage given the emf internal resistance of the
  battery and external resistance in the circuit.
• 4. Determine the equivalent capacitance of
  capacitors arranged in series or in parallel or
  the equivalent capacitance of a series-parallel
  combination.

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Objectives

• 5. Determine the charge on each capacitor and the
  voltage drop across each capacitor in a circuit
  where capacitors are arranged in series, parallel
  or a series-parallel combination.
• 6. Calculate the time constant of a RC circuit.
  Determine the charge on the capacitor and the
  potential difference across the capacitor at a
  particular moment of time and the current through
  the resistor at a particular moment in time.
• 7. Describe the basic operation of a
  galvanometer and calculate the resistance which
  must be added to convert a galvanometer into an
  ammeter or a voltmeter.
• 8. Describe how a slide wire potentiometer can be
  used to determine the emf of a source of
  emf.Given the emf of a standard cell, use the
  slide wire potentiometer to calculate the emf of
  the unknown.
• 9. Describe how a Wheatstone bridge circuit can
  be used to determine the resistance of an unknown
  resistor. Given three known resistors and a
  Wheatstone bridge circuit, calculate the
  resistance
• of an unknown resistor.

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RESISTORS IN SERIES

• A simple SERIES CIRCUIT is shown in the diagram
  below. The current (I) at every point in a
  series circuit equals the current leaving the
  battery.

I1 I2I3ITotal
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RESISTORS IN SERIES

• Assuming that the connecting wires offer no
  resistance to current flow, the potential
  difference between the terminals of the battery
  (V) equals the sum of the potential differences
  across the resistors, i.e.,
• VVl V2 V3

• The equivalent electrical resistance (R) for this
  combination is equal to the sum of the individual
  resistors, i.e.,
• RR1 R2 R3

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RESISTORS IN PARALLEL

• In a simple PARALLEL CIRCUIT, the current leaving
  the battery divides at junction point A in the
  diagram shown below and recombines at point B.
  The battery current (I) equals the sum of the
  currents in the branches. In general
• I I1 I2 I3

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RESISTORS IN PARALLEL

• If no other resistance is present, the potential
  difference across each resistor equals the
  potential difference across the terminals of the
  battery.
• The equivalent resistance (R) of a parallel
  combination is always less than the smallest of
  the individual resistors. The formula for the
  equivalent resistance is as follows
• 1/R
  1/RI 1/R2 1/R3

• The potential difference across each resistor in
  the arrangement is the same, i. e.
• V VI V2 V3

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RESISTORS IN PARALLEL

• In a simple PARALLEL CIRCUIT, the current leaving
  the battery divides at junction point A in the
  diagram shown below and recombines at point B.
  The battery current (I) equals the sum of the
  currents in the branches. In general
• I I1 I2 I3

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EMF AND TERMINAL VOLTAGE

• All sources of emf have what is known as
  INTERNAL RESISTANCE (r) to the flow of electric
  current. The internal resistance of a fresh
  battery is usually small but increases with use.
  Thus the voltage across the terminals of a
  battery is less than the emf of the battery.
• The TERMINALVOLTAGE (V) is given by the equation
  V ? - Ir, where ? represents the emf
  of the source of
• potential in volts, I the current leaving the
  source of emf in amperes and r the internal
  resistance in ohms.
• The internal resistance of the source of emf is
  always considered to be in a series with the
  external resistance present in the electric
  circuit.

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KIRCHHOFF'S RULES

• KIRCHHOFF'S RULES are used in conjunction with
  Ohm's law in solving problems involving complex
  circuits
• KIRCHHOFF'S FIRST RULE or JUNCTION RULE The sum
  of all currents entering any junction point
  equals the sum of all currents leaving the
  junction point. This rule is based on the law of
  conservation of electric charge.
• KIRCHHOFF'S SECOND RULE or LOOP RULE The
  algebraic sum of all the gains and losses of
  potential around any closed path must equal zero.
  This law is based on the law of conservation of
  energy.

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SUGGESTIONS FOR USING KIRCHHOFF'S LAWS
1. Place a () sign next the long line of the
battery symbol and a (-) sign next to the short
line. Start choosing a direction for conventional
current flow ( flow of positive charge ) If you
choose the wrong direction for the flow of
current in a particular branch, your final
answer for the current in that branch will be
negative. The negative answer indicates that the
current actually flows in the opposite direction.

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SUGGESTIONS FOR USING KIRCHHOFF'S LAWS

• 2. Assign a direction to the circuit in each
  independent branch of the circuit. Place a
  positive sign on the side of each resistor where
  the current enters and a negative sign on the
  side where the current exits, e.g. This
  indicates that a drop in potential occurs as the
  current passes through the resistor .

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SUGGESTIONS FOR USING KIRCHHOFF'S LAWS

• Notice how the directions of the currents are
  labeled in each branch of the circuit

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SUGGESTIONS FOR USING KIRCHHOFF'S LAWS

• 3. Select a JUNCTION POINT and apply the junction
  rule, e.g., at point A in the diagram

The junction rule may be applied at more than one
junction point. In general, apply the junction
rule to enough junctions so that each branch
current appears in at least one equation.
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SUGGESTIONS FOR USING KIRCHHOFF'S LAWS

• 4. Apply Kirchhoffs loop rule by first taking
  note whether there is a gain or loss of potential
  at each resistor and source of emf as you trace
  the closed loop. Remember that the sum of the
  gains and losses of potential must add to zero.

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SUGGESTIONS FOR USING KIRCHHOFF'S LAWS

• For example, for the left loop of the sample
  circuit above start at point B and travel
  clockwise around the loop. Because the direction
  chosen for the loop is also the direction
  assigned for the current, there is a gain in
  potential across the battery (- to ), but a
  loss of potential across each resistor ( to -).

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SUGGESTIONS FOR USING KIRCHHOFF'S LAWS

• Following the path of the current shown in the
  diagram and using the loop rule, the following
  equation can be written

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SUGGESTIONS FOR USING KIRCHHOFF'S LAWS

• The direction taken around the loop is
  ARBITRARY. Tracing a counterclockwise path
  around the circuit starting at B, as shown in the
  above right diagram, there is gain in potential
  across each resistor to (- to ) and a drop in
  potential across the battery ( to -). The loop
  equation would then be

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SUGGESTIONS FOR USING KIRCHHOFF'S LAWS

• Multiplying both sides of the above equation by -
  1 and algebraically rearranging, it can be shown
  that the two equations are equivalent. Be sure to
  apply the loop rule to enough closed loops so
  that each branch current appears in at least one
  loop equation. Solve for each branch current
  using standard algebraic methods.

Solve simultaneous equations
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CAPACITORS IN SERIES AND PARALLEL

• A circuit with CAPACITORS IN PARALLEL is shown
  in the diagram below. According to Kirchhoff s
  loop rule, the potential difference (V) of the
  source of emf
• V VI V2 V3

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CAPACITORS IN PARALLEL

• The total charge stored on the capacitor plates
  (Q) equals the amount of charge which left the
  source of
• Q Ql Q2 Q3 ( Charge is additive)
• and since Q CV then
• CV CV1 CV2 CV3
• C C1 C2 C3 (Capacitance is additive)

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CAPACITORS IN SERIES

• For CAPACITORS IN SERIES, the amount of charge
  (Q) that leaves the source of emf equals the
  amount of charge that forms on each capacitor
• Q Ql Q2 Q3

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CAPACITORS IN SERIES
From Kirchhoffs loop rule, the potential
difference across the source of emf (V) equals
the sum of the potential differences across the
individual capacitors

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Circuits containing resistors and capacitors

• An RC CIRCUIT consists of a resistor and a
  capacitor connected in series to a de power
  source.When switch 1 (S1), shown in the diagram
  below, is closed, the current will begin to flow
  from the source of emf and charge will begin to
  accumulate on the capacitor. Using Kirchhoff s
  loop rule it can be shown that