A wire of resistance 8 Ω is bent into a circle. Find the resistance across the diameter.

As in this question we have to calculate net resistance across the diameter of the circle and we are given with the resistance of the wire across it’s free ends which is 8 ohm.

If we remember our previous questions in which we have calculate net resistance, we will know that the given points are whom across there is potential difference and these two points will not merge and form one-point, potential difference at one point is different from another point that is A and B have different potential.

But the potential difference across each resistor is same as they have same ending points A and B.

So, we are at conclusion, that the two resistors are parallel to each other and we can calculate the net resistance now, as the resistance of the full wire across it’s free ends is 8 ohm, So by the relation

We can say that by dividing the length to half of the original keeping other things constant which they are in this question, the resistance will reduce to half of the original, that is now the resistance of the two parallel wires is 4 ohm instead of 8 ohm.

R_t = 2 ohm, is the resistance across A and B (the diameter).