Question

A wire of resistance 4ohm is bent to form a circle

Answer 1

Answer:

Resistance will be Same

Answer 2

Complete Question :-

ᴀ ᴡɪʀᴇ ᴏғ ʀᴇsɪsᴛᴀɴᴄᴇ 4 ᴏʜᴍ ɪs ʙᴇɴᴛ ᴛᴏ ғᴏʀᴍ ᴀ ᴄɪʀᴄʟᴇ ᴡʜᴀᴛ ɪs ᴛʜᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛᴡᴏ ᴅɪᴀᴍᴇᴛʀɪᴄᴀʟʟʏ ᴏᴘᴘᴏsɪᴛᴇ ᴇɴᴅs

Solution :-

ʀᴇsɪsᴛᴀɴᴄᴇ =ʀ=4ᴏʜᴍs

ʟᴇᴛ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴄɪʀᴄʟᴇ ʙᴇ ᴀʙ.

ᴛʜᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ᴏғ ᴜᴘᴘᴇʀ ᴘᴀʀᴛ ᴡɪʟʟ ʙᴇ 2ʀ ᴀɴᴅ ʟᴏᴡᴇʀ ᴘᴀʀᴛ ᴏғ ᴄɪʀᴄʟᴇ ᴡɪʟʟ ʙᴇ 2ʀ

ᴛʜᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ᴡɪʟʟ ʙᴇ ɪɴ ᴘᴀʀᴀʟʟᴇʟ.

$\orange{R1=R2=2R}$

$\dfrac{1}{Rp}=\dfrac{1}{R1}+\dfrac{1}{R2}$

$=> \dfrac{1}{2R}+\dfrac{1}{2R}$

$=> \dfrac{2}{2R}$

$\dfrac{1}{Rp}=\dfrac{1}{R}$

∴ ʀᴘ=ʀ ᴏʜᴍs 

∴ ʀᴇsɪsᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛᴡᴏ ᴅɪᴀᴍᴇᴛʀɪᴄᴀʟʟʏ ᴏᴘᴘᴏsɪᴛᴇ ᴇɴᴅs ɪs ʀ  ᴏʜᴍs