Question

Number of switches in alternative equivalent simple circuit for the circuit is (are)

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

Use $p \lor \sim p \equiv T$ and $p \land \sim p \equiv F$ to reduce complex switching circuits.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to convert the switching circuit into its logical expression, simplify it, and count the resulting unique switches.
Step 2: Detailed Explanation:
From the diagram:
Top branch: \( p \) (representing \( S_1 \)).
Bottom branch: \( q \) (representing \( S_2 \)) in series with a parallel block of \( \sim q \) (representing \( S_2' \)) and \( \sim r \) (representing \( S_3' \)).
The logical statement is \( L \equiv p \lor [q \land (\sim q \lor \sim r)] \).
Simplify using distribution:
\[ L \equiv p \lor [(q \land \sim q) \lor (q \land \sim r)] \] \[ L \equiv p \lor [F \lor (q \land \sim r)] \text{ (where F is Contradiction)} \] \[ L \equiv p \lor (q \land \sim r) \] The simplified circuit has 3 switches: \( S_1 \), \( S_2 \), and \( S_3' \).
Step 4: Final Answer:
The alternative circuit has 3 switches.