What is the equivalent resistance of a circuit consisting of two identical resistors, each of resistance R, connected in parallel?

The equivalent resistance of two identical resistors connected in parallel can be calculated using the formula for parallel resistors. When two resistors (with resistance R) are connected in parallel, the equivalent resistance ( R_{eq} ) can be determined via the following equation:

[

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

]

Simplifying this equation leads to:

[

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

]

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

[

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

]

This shows that the equivalent resistance of two identical resistors in parallel is half of the resistance of one resistor. Therefore, if each resistor has a resistance of R, the equivalent resistance will be R/2.

Understanding this concept is important because it illustrates how the total resistance decreases when resistors are arranged in parallel, which is a fundamental principle in circuit design and analysis.