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Question

(B) The given circuit consists of two parallel branches connected in series with a battery and a lamp $L$. Let the switches be represented by variable

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) The given circuit consists of two parallel branches connected in series with a battery and a lamp $L$. Let the switches be represented by variables $S_1, S_2, S_3$. The first branch is $S_1 \land (S_2' \lor S_3')$. The second branch is $S_2 \land S_3 \land S_1$. The total circuit expression is $P = [S_1 \land (S_2' \lor S_3')] \lor (S_2 \land S_3 \land S_1)$. Using the distributive law,we can factor out $S_1$: $P = S_1 \land [(S_2' \lor S_3') \lor (S_2 \land S_3)]$. By De Morgan's law,$(S_2' \lor S_3')$ is equivalent to $(S_2 \land S_3)'$. So,$P = S_1 \land [(S_2 \land S_3)' \lor (S_2 \land S_3)]$. Since $(X' \lor X)$ is always true (a tautology),the expression simplifies to $P = S_1 \land T = S_1$. Thus,the equivalent circuit is just a single switch $S_1$ in series with the lamp. The number of switches in the equivalent circuit is $1$.

The number of switches in the alternative equivalent simple circuit for the given circuit is:

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