Question

The equivalent resistance between points A and B in a circuit with two resistors of 6 \(\Omega\) each connected in parallel is:

• A. 12 \(\Omega\)
• B. 6 \(\Omega\)
• C. 3 \(\Omega\)
• D. 4 \(\Omega\)

Hint:

For parallel resistors, the equivalent resistance is less than the smallest individual resistance.

Answer 1

The Correct Option is C

Step 1: For resistors in parallel, use the formula: \[ \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} \] Given: \( R_1 = 6 \, \Omega \), \( R_2 = 6 \, \Omega \).
\[ \frac{1}{R_{\text{eq}}} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \] \[ R_{\text{eq}} = 3 \, \Omega \] Step 2: Verify: For identical resistors, \( R_{\text{eq}} = \frac{R}{2} = \frac{6}{2} = 3 \, \Omega \). Matches option (3).