copyright 2013, 2010, 2007, pearson, education, inc. section 3.7 switching circuits
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Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Electrical CircuitsElectrical circuits can be expressed as logical statements.
T (true) represents a closed switch (or current flow).
F (false) represents an open switch (or no current flow).
In a series circuit the current can take only one path.
In a parallel circuit there are two or more paths the current can take.
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Series Circuit
Case 1: Both switches are closed; that is, p is T and q is T. The light is on, T.
Case 2: Switch p is closed and switch q is open; that is, p is T and q is F. The light is off, F.
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Series Circuit
Case 3: Switch p is open and switch q is closed; that is, p is F and q is T. The light is off, F.
Case 4: Both switches are open; that is, p is F and q is F. The light is off, F.
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Series Circuit
Switches in series will always be represented with a conjunction . ⋀In summary,
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Parallel Circuit
Case 1: Both switches are closed; that is, p is T and q is T. The light is on, T.
Case 2: Switch p is closed and switch q is open; that is, p is T and q is F. The light is on, T.
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Parallel Circuit
Case 3: Switch p is open and switch q is closed; that is, p is F and q is T. The light is on, T.
Case 4: Both switches are open; that is, p is F and q is F. The light is off, F.
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Parallel Circuit
Switches in parallel will always be represented with a disjunction .⋁In summary,
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Example 2: Representing a Switching Circuit with Symbolic Statementsa. Write a symbolic statement that represents the circuit.
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p and q are in parallel: p ⋁ q q and r are in series: q ⋀ rtogether we get: (p q⋀ ) ⋁ (q ⋀ r)
Example 2: Representing a Switching Circuit with Symbolic StatementsSolution
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Example 2: Representing a Switching Circuit with Symbolic Statements
b. Construct a truth table to determine when the light will be on.
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Example 2: Representing a Switching Circuit with Symbolic StatementsSolution
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Example 3: Representing a Symbolic Statement as a Switching CircuitDraw a switching circuit that represents
[(p ~⋀ q) (⋁ r ⋁ q)] ⋀s.
Solution
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Equivalent Circuits
Equivalent circuits are two circuits that have equivalent corresponding symbolic statements.
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Equivalent Circuits
Sometimes two circuits that look very different will actually have the exact same conditions under which the light will be on.The truth tables have identical answer columns.
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Example 4: Are the Circuits Equivalent?Determine whether the two circuits are equivalent.
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Example 4: Are the Circuits Equivalent?
p (⋁ q ⋀ r)
(p ⋁ q) (⋀ p ⋁ r)
Solution
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Example 4: Are the Circuits Equivalent?
The answer columns are identical.
Solution
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