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

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. ::contentReference[oaicite:0]{index=0}

Step 1: Write the given resistance values. \[ R_1 = R_2 = R_3 = 6\,\Omega \]

Step 2: Substitute the values in the parallel resistance formula. \[ \frac{1}{R_p} = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} \]

Step 3: Calculate the equivalent resistance. \[ \frac{1}{R_p} = \frac{3}{6} = \frac{1}{2} \] \[ R_p = 2\,\Omega \] Hence, the equivalent resistance is: \[ \boxed{2\,\Omega} \]