The correct formula to calculate the equivalent resistance of R\(_1\) and R\(_2\) when connected in parallel, is:
Show Hint
For resistors in series, you add them: \(R_{eq} = R_1 + R_2\). For two resistors in parallel, remember the shortcut: "product over sum", \(R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2}\).
Step 1: Understanding the Question:
The question asks for the standard formula for the equivalent resistance (\(R_{eq}\)) of two resistors, R\(_1\) and R\(_2\), connected in a parallel arrangement. Step 2: Key Formula or Approach:
For resistors connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots \]
Step 3: Detailed Explanation:
For two resistors R\(_1\) and R\(_2\) in parallel, the formula is:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \]
To find \(R_{eq}\), we first need to combine the fractions on the right side. The common denominator is \(R_1 R_2\).
\[ \frac{1}{R_{eq}} = \frac{R_2}{R_1 R_2} + \frac{R_1}{R_1 R_2} \]
\[ \frac{1}{R_{eq}} = \frac{R_2 + R_1}{R_1 R_2} \]
Now, to solve for \(R_{eq}\), we take the reciprocal of both sides of the equation:
\[ R_{eq} = \frac{R_1 R_2}{R_1 + R_2} \]
This is often referred to as the "product over sum" rule for two parallel resistors.
Comparing this result with the given options, it matches option (B). Step 4: Final Answer:
The correct formula for the equivalent resistance of two resistors in parallel is the product of their resistances divided by the sum of their resistances.
