Question

a wire of resistance 10 ohm is bent to form a close the circle. what is the resistance across a diameter of the circle

Answer 1

it is 2.5 ohms as

the resistance of straight wire = 10 ohm

when it is bent in the form of a closed circle, the wires will be connected in parallel. Also, the length will be half, so resistance will also become half,

so resisteance of each part connected in parallel will be 5 ohms.

Now, resistance in parallel combination, 1/R = 1/R1 + 1/R2

1/R=1/5 + 1/5

1/R=2/5

R=5/2=2.5

Answer 2

The resistance across a diameter of the circle is 2.5 ohms.

Explanation:

It is given that, a wire of resistance 10 ohm is bent to form a close the circle. We need to find the resistance across a diameter of the circle.

When it is bent, the ends of the diameter are considered then the resistor will get split up into  and they will be now in parallel. The equivalent is given by :

$\dfrac{1}{R}=\dfrac{1}{5}+\dfrac{1}{5}\\\\R=2.5\ \Omega$

So, the resistance across a diameter of the circle is 2.5 ohms. Hence, this is the required solution.

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