Question

Three resistors $R_1,R_2$, and $R_3$ are connected as shown below.
The resistance of $R_3$ is $1\Omega$ and it is known that the value of $R_3$ is smaller than the values of $R_1$ or $R_2$. The resistances of $R_1$ and $R_2$ are unknown.
Select the best statement describing the equivalent resistance of this combination:

• A. The equivalent resistance of this combination must be lower than $1\Omega$.
• B. The equivalent resistance of this combination may be lower than $1\Omega$.
• C. The equivalent resistance of this combination must be greater than $1\Omega$.
• D. The equivalent resistance of this combination may be greater than $1\Omega$.
• E. The equivalent resistance of this combination cannot be estimated without additional information.

Answer 1

The correct option is A The equivalent resistance of this combination must be lower than $1\Omega$.

The resistances in given diagram are in parallel combination , therefore equivalent resistance of the given combination ,

$1/R=1/R_1+1/R_2+1/R_3$ ,

it is clear from the equation that value of $R$ is less than $R_1$ or$R_2$ or $R_3=1$ , therefore equivalent resistance of this combination is less than 1 ohm .