Four wires each of the same length, diameter and material are connected to form a square. If the resistance of each wire is R, then equivalent resistance across the opposite corners is :

The equivalent resistance across the opposite corners of a square formed by four resistors of resistance R can be calculated as follows:

Step 1: Identify the configuration of the resistors. In this case, the resistors are arranged in a square, which is a combination of parallel and series circuits.

Step 2: Calculate the equivalent resistance of the parallel circuit. Two resistors (R) are in parallel along each side of the square. The equivalent resistance (Rp) of resistors in a parallel circuit is given by the formula 1/Rp = 1/R1 + 1/R2. Since R1 = R2 = R, the formula becomes 1/Rp = 1/R + 1/R = 2/R. Solving for Rp gives Rp = R/2.

Step 3: Calculate the equivalent resistance of the series circuit. The equivalent resistance (Rs) of resistors in a series circuit is simply the sum of the resistances. In this case, Rs = Rp + Rp = R/2 + R/2 = R.

So, the equivalent resistance across the opposite corners of the square is R.