Question

Two resistors of 6$\Omega$ and 3$\Omega$ are connected in parallel. Equivalent resistance is: ____.

• A. 9$\Omega$
• B. 2$\Omega$
• C. 4$\Omega$
• D. 1.5$\Omega$

Hint:

In a parallel circuit, the equivalent resistance is always smaller than the smallest individual resistor. Since 3$\Omega$ is the smallest, the answer had to be less than 3.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
When resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.

Step 2: Key Formula or Approach:
For two resistors $R_1$ and $R_2$: \[ R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2} \]

Step 3: Detailed Explanation:
Given: $R_1 = 6\Omega$ and $R_2 = 3\Omega$. 1. Apply the product-over-sum formula: \[ R_{eq} = \frac{6 \times 3}{6 + 3} \] \[ R_{eq} = \frac{18}{9} = 2\Omega \]

Step 4: Final Answer:
The equivalent resistance is 2$\Omega$.