Question

Find the equivalent resistance of three resistors of \(6\,\Omega\) each connected in parallel.

• A. \(6\,\Omega\)
• B. \(3\,\Omega\)
• C. \(2\,\Omega\)
• D. \(1\,\Omega\)

Hint:

For \(n\) identical resistors connected in parallel, the equivalent resistance is given by \(R/n\), where \(R\) is the resistance of each resistor.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to calculate the combined or effective resistance when multiple resistors are placed in a parallel arrangement.
Step 2: Key Formula or Approach:
For \(n\) resistors connected in parallel, the equivalent resistance (\(R_p\)) is given by:
\[ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots \]
Alternatively, for \(n\) identical resistors of resistance \(R\):
\[ R_p = \frac{R}{n} \]
Step 3: Detailed Explanation:
Given:
\(R_1 = R_2 = R_3 = 6\,\Omega\)
Since all three resistors are identical and connected in parallel:
Number of resistors, \(n = 3\)
Using the simplified formula:
\[ R_p = \frac{6}{3} \]
\[ R_p = 2\,\Omega \]
Step 4: Final Answer:
The equivalent resistance is \(2\,\Omega\).