Question

a wire of resistance 10 ohm is bent to form a closed circle. what is the resistance across a Diameter of the circle. pls explain tye ans to me.

Answer 1

Consider the circular wire to be made up of two semi circular wires each of resistance 5 Ω with their diameter along AB.

Now the question is, if you connect a battery across AB, what will be the equivalent resistance across the two points.

If you observe, you will find that the two semicircular wires are parallel to each other. 
 
In parallel connection, $R_{eq} = R_{1} R_{2} /( R_{1} + R_{2} )$
∴ $R_{eq} = 2.5$ Ω

Answer 2

When a wire of Any resitance bent into a circle...Then observe the Semicircles...Each semicircle shows up resistance half of the original resistance...And if we want to find the resistance across the ends of the diameter , firstly we have check the connection of resistances whether connected in parallel or in series...See snap

From snap...we see that Resistance acrooss the diameter is
Resistance across the ends of diameter
= Resitance / No. of Resistance ( Use when Resistances are identical )
=( R/ 2 ) / 2
= R / 4
= 10 / 4 ( since R = 10 Ohm.)
=2.5 Ohm