Question

The correct formula to calculate the equivalent resistance of R\(_1\) and R\(_2\) when connected in parallel, is:

• A. \(\frac{R_1 + R_2}{R_1 R_2}\)
• B. \(\frac{R_1 R_2}{R_1 + R_2}\)
• C. \(\frac{R_1 - R_2}{R_1 R_2}\)
• D. \(\frac{R_1 R_2}{R_1 - R_2}\)

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", \(R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The reciprocal of the equivalent resistance of a parallel combination is the sum of the reciprocals of the individual resistances.
Step 2: Key Formula or Approach:
\[ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} \]
Step 3: Detailed Explanation:
Taking the LCM on the right side:
\[ \frac{1}{R_p} = \frac{R_2 + R_1}{R_1 \cdot R_2} \]
To find \( R_p \), take the reciprocal of the whole expression:
\[ R_p = \frac{R_1 R_2}{R_1 + R_2} \]
Step 4: Final Answer:
The equivalent resistance is the product of the two resistances divided by their sum.