Question

A metallic wire of electrical resistance 40 \( \Omega \) is bent in the form of a square loop. The resistance between any two diagonally opposite corners is ....... \( \Omega \).

Hint:

When finding resistance in series or parallel, remember that resistances in series simply add, while those in parallel follow the reciprocal rule.

Answer 1

Correct Answer: 10

Step 1: Understanding the problem.
The wire is bent into the shape of a square loop. If the resistance of the wire is 40 \( \Omega \) and we need to find the resistance between two diagonally opposite corners, we need to divide the total resistance by the number of resistances in the path between the corners.
Step 2: Calculation.
Since the wire is bent into a square, there are 4 equal segments, each contributing to the total resistance. The resistance between any two diagonally opposite corners is the sum of the two segments along the diagonal, which is half of the total resistance. Therefore, the resistance between two diagonally opposite corners is: \[ \frac{40}{2} = 20 \, \Omega \] Step 3: Conclusion.
The resistance between any two diagonally opposite corners is 20 \( \Omega \).