Chapter 27 DC Circuits

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Chapter 27 DC Circuits

• The circuit
• Resistance in combinations
• Kirchhoffs Rules
• RC transient circuits

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Work done by a battery on charge
Here
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Real Battery and Single Loop circuits Whats
the current ?
Conservation of energy Kirchoffs first Law Sum
of voltages in a closed loop is zero.
Real Circuit with ammeter and voltmeter
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Equivalent ResistanceResistors in Series

• Series requirements
• Conservation of energy
• Potential differences add
• Current is constant

Apply Ohms Law to each resistor
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Resistors in parallel

• Parallel requirements
• Charge conservation
• Currents must add
• Potential difference is same across each resistor

Apply Ohms Law to each resistor
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Example 27-2
What is current through battery?
What is current through i2 ?
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Kirchhoffs Rules
Signs for Rule 2 The direction of travel when
traversing the loop is from a to b.

• The algebraic sum of the currents entering a
  junction is zero. (Conservation of Charge)
• The algebraic sum of the changes in electric
  potential difference around any closed circuit
  loop is zero. (Conservation of Energy)

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Problem 27-3
Find the currents in each of the three legs of
the circuit,
Three unknowns, need three equations. Also since
batteries are in there cannot reduce the
resistances since none in parallel or series
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Example Applying Kirchhoffs Rules
Apply Kirchhoffs second rule to the closed path
in red, traversing it clockwise
Apply Kirchhoffs second rule to the closed path
in green, traversing it clockwise Note the sign
changes for some of the elements

• Apply Kirchhoffs first rule to the three wire
  junction at the bottom of the diagram

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Another, example applying Kirchhoffs Rules

• Solve the equations simultaneously for the
  values if I. If I is negative the current is in
  the opposite direction

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RC Circuits and Time dependence
Time dependence Recall Lab 7! Resistor slows
down the charging of the capacitor

• Time dependent behavior (transient) 2 cases
  switch at
• a or at b
• Charging
• discharging

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In position a Charging the Capacitor

• Use Kirchhoffs Loop rule

Or the voltage across capacitor is ..
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Whats VR across resistor?Find the current and
multiply by R
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Discharging Position b
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Example RC circuit
R10? C1F

• How long does it take the capacitor to reach ½
  its final charge, if the capacitor is uncharged
  at t 0?

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1. Charging the Capacitor