Question

Write the symbolic form of the following switching circuits construct its switching table and interpret it.

(i) 

(ii)

(iii)

Answer 1

(i) Let p : the switch S₁ is closed 

q : the switch S₂ is closed 

~p : the switch S₁' is closed or the switch S₁ is open 

~ q : the switch S₂' is closed or the switch S₂ is open.

Then the symbolic form of the given circuit is :

(p ∨ ~q) ∨ (~p ∧ q)

Since the final column contains all' 1′,

The lamp will always glow irrespective of the status of switches.

(ii) Let p : the switch S₁ is closed 

q : the switch S₂ is closed 

~p : the switch S₁ is closed or the switch S₁ is open. 

~q : the switch S₁ is closed or the switch S₂ is open. 

Then the symbolic form of the given circuit is :

p ∨ (~p ∧ ~q) ∨ (p ∧ q)

Since the final column contains '0' when p is 0 and q is '1', otherwise it contains ‘1′. 

Hence,

The lamp will not glow when S₁ is OFF and S₂ is ON, otherwise the lamp will glow.

(iii) Let p : the switch S₁ is closed 

q : the switch S₂ is closed

r : the switch S₃ is closed 

~q : the switch S₂' is closed or the switch S₂ is open 

~r: the switch S₃' is closed or the switch S₃ is open. 

Then,

The symbolic form of the given circuit is : 

[p ∨ (~q) ∨ r)] ∧ [p ∨ (q ∧ r)]

From the switching table, 

The ‘final column’ and the column of p are identical. 

Hence,

The lamp will glow which S₁ is ‘ON’.