Chapter A.6, Problem 1E

In Exercises 1-5, find a logic statement corresponding to the network. Determine the conditions under which current will flow from $A$ to $B$.

To determine

To find:

The logic statement corresponding to the network and write the conditions under which current can be flow from $A$ to $B$.

Answer to Problem 1E

Solution:

The logic statement corresponding to the network is $p\wedge q\wedge \left(r\vee s\right)$ and the conditions under which current can be flow from $A$ to $B$ are if and only if $p$ is closed, $q$ is closed and either $r$ or $s$ or both $r$ and $s$ are closed.

Explanation of Solution

Given:

The logic statement is

Figure(1)

Approach:

When the two circuits $p$, $q$ are in series, they will be in conjunction with each other i.e. $p\wedge q$.

When the two circuits $p$, $q$ are in parallel, they will be in disjunction with each other i.e. $p\vee q$.

Calculation:

The current will pass from point $A$ to $B$ if the following conditions are satisfied.

1. $p$ is closed.

2. $q$ is closed.

3. either $r$ or $s$ or both are closed.

Therefore, the logic statement corresponding to the network is $p\wedge q\wedge \left(r\vee s\right)$ and the conditions under which current can be flow from $A$ to $B$ are if and only if $p$ is closed, $q$ is closed and either $r$ or $s$ or both $r$ and $s$ are closed.

Conclusion:

Hence, the logic statement corresponding to the network is $p\wedge q\wedge \left(r\vee s\right)$ and the conditions under which current can be flow from $A$ to $B$ are if and only if $p$ is closed, $q$ is closed and either $r$ or $s$ or both $r$ and $s$ are closed.