Question

A uniform metallic wire of length L is mounted in two configurations. In configuration $1$(triangle), it is an equilateral triangle and a voltage V is applied to corners A and B. In configuration $2$(circle), it is bent in the form of a circle, and the potential V is applied at diametrically opposite points P and Q. The ratio of the power dissipated in configuration $1$ to configuration $2$ is?

• A. $2/3$
• B. $9/8$
• C. $5/4$
• D. $7/8$

Answer 1

Answer: (B)

$9/8$

In configuration 1:
Let us consider that the resistance of the uniform metallic wire is R.
Then, AB is parallel to (AC and BC).
Therefore, R equivalent =
Power1 = V²/R equivalent =
In configuration 2:
Let us consider that the resistance of the uniform metallic wire is R.
Then, PQ and QP are parallel.
Therefore, R equivalent =
Power2 = V²/R equivalent =
Hence, ratio of power1 and power2 = 9/8