Question

Three 2 \(\Omega\) resistors are connected to form a triangle. The resistance between any two corners is

• A. \(\dfrac{4}{3}\ \Omega\)
• B. \(\dfrac{3}{4}\ \Omega\)
• C. 6 \(\Omega\)
• D. \(\dfrac{2}{3}\ \Omega\)

Hint:

In a triangular network, the resistance between any two nodes = (one side) in parallel with (sum of the other two sides).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Between any two corners of the triangle, one resistor (2 \(\Omega\)) is in parallel with two resistors in series (4 \(\Omega\)).
Step 2: Detailed Explanation:
\[ R_{eq} = \frac{2 \times 4}{2 + 4} = \frac{8}{6} = \frac{4}{3}\ \Omega \]
Step 3: Final Answer:
Resistance between any two corners \(= \mathbf{\dfrac{4}{3}\ \Omega}\).