Question

A metallic wire of resistance 30 \( \Omega \) is bent in the form of an equilateral triangle. The resistance between any two vertices of the triangle is:

• A. \(3.67 \, \Omega\)
• B. \(6.36 \, \Omega\)
• C. \(3.36 \, \Omega\)
• D. \(6.67 \, \Omega\)

Hint:

When resistors are in parallel, the equivalent resistance decreases. If the two resistors are in series, their resistances add up.

Answer 1

The Correct Option is D

The metallic wire is bent into an equilateral triangle, so the total resistance is divided into three equal parts, each having resistance \( R = 30 \, \Omega \).

When measuring the resistance between two vertices, the two sides of the triangle not involved in the measurement are in parallel. The equivalent resistance of two parallel resistors, each of resistance \( R \), is given by:

\[ R_{{eq}} = \frac{R \cdot R}{R + R} = \frac{30 \times 30}{30 + 30} = 15 \, \Omega \]

This equivalent resistance is in series with the remaining side, which also has resistance \( 30 \, \Omega \). Therefore, the total resistance is:

\[ R_{{total}} = 15 \, \Omega + 30 \, \Omega = 45 \, \Omega \]

Thus, the equivalent resistance between the two vertices is:

\[ \frac{45}{3} = 15 \, \Omega \]