What is the equivalent resistance in a parallel circuit with two equal resistors each of value R?

In a parallel circuit, the equivalent resistance can be calculated using the formula for two resistors: ( \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} ). When both resistors are equal, such as in this case where both are of value R, the equation simplifies to ( \frac{1}{R_{eq}} = \frac{1}{R} + \frac{1}{R} ).

By combining the fractions, we find:

[

\frac{1}{R_{eq}} = \frac{2}{R}

]

To find ( R_{eq} ), we take the reciprocal of both sides, resulting in:

[

R_{eq} = \frac{R}{2}

]

This shows that the equivalent resistance of two equal resistors in parallel is half the value of one of the resistors. Therefore, the correct answer reflects this principle of parallel circuits, demonstrating how parallel connections effectively reduce the total resistance compared to individual resistors.

Other options do not adhere to the rules of resistor combinations in parallel; while R represents a single resistor value, 2R and R² do not exhibit