Physics - Current Electricity Question with Solution | TestHub

Let $p$ and $q$ represent the closed states of switches $S_1$ and $S_2$ respectively.

The switches $S_1^{\prime }$ and $S_2^{\prime }$ represent the states $\sim p$ and $\sim q$.

The given circuit consists of two parallel branches.

The upper branch has switch $S_1$ in series with a parallel combination of $S_2$ and $S_1$. Its boolean expression is:

$p\wedge (q\vee p)$

By the absorption law, this simplifies to:

$p\wedge (q\vee p)=p$

The lower branch has switches $S_1^{\prime }$, $S_2^{\prime }$, and $S_1$ in series. Its boolean expression is:

$\sim p\wedge \sim q\wedge p$

Since $p\wedge \sim p=F$ (False), this simplifies to:

$F\wedge \sim q=F$

The total expression for the circuit is the disjunction (OR) of the upper and lower branches:

$p\vee F=p$

This means the entire circuit is equivalent to a single switch $S_1$.

Therefore, the simplified circuit corresponds to the option with only switch $S_1$.

Answer: