Question

A circular conductor is made of a
uniform wire of resistance 2 X10-3
ohm/metre and the diameter of this
circular conductor is 2 metres. Then
the resistance measured between the endsof the diameter is (in ohms)​

Answer 1

$\huge\underline\blue{\sf Answer:}$

Resistance measured between the endsof the diameter is $\large\underline{\sf π×10^{-3}ohm}$

$\huge\underline\blue{\sf Solution:}$

$\large\underline\pink{\sf Given: }$

• Resistance per metres = $\sf{2×10^{-3}ohm/m}$

• Diameter of circular conductor (d)=2 metres

$\large\underline\pink{\sf To\:Find: }$

• Resistance measured between the endsof the diameter is =?

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The length can be calculated as

$\large{\boxed{\sf L=π×D }}$

where D is given diameter of 2 m.

Hence ,

$\large{\sf Lenght (L)=2π }$

Therefore,

$\implies{\sf Resistance (R)=2×10^{-3}×2π}$

$\large\implies{\sf R=4×10^{-3}ohm}$

Now when the resistance is measured between ends of any diameter,

it can be seen as parallel connection of two resistances R/2 each (R being the total resistance of the entire loop). So the resistance between two end points of a diameter will be R/4

i.e

$\large{\sf π×10^{-3}ohm }$

Therefore, resistance measured between the endsof the diameter is $\large\underline{\sf π×10^{-3}ohm}$