Question

Plzzzz solve the problem​

Answer 1

GIVEN :-

A ᴡɪʀᴇ ᴏғ ʀᴇsɪsᴛᴀɴᴄᴇ R ɪs ʙᴇɴᴛ ɪɴ ғᴏʀᴍ ᴏғ ᴀ ᴄʟᴏsᴇᴅ ᴄɪʀᴄʟᴇ .

TO FIND :-

Tʜᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ᴀᴄʀᴏss ᴀ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴄɪʀᴄʟᴇ .

SOLUTION :-

➪ sᴇᴇ ᴛʜᴇ ᴀᴛᴛᴀᴄʜᴍᴇɴᴛ ғɪɢᴜʀᴇ .

✯ As ᴡᴇ ᴄᴀɴ sᴇᴇ ᴛʜᴀᴛ ᴛʜᴇ ᴘᴏɪɴᴛ A ᴀɴᴅ B ᴅɪᴠɪᴅᴇs ᴛʜᴇ ᴄɪʀᴄʟᴇ ɪɴ ᴛᴡᴏ ᴇǫᴜᴀʟ ᴘᴀʀᴛs .

✯ Hᴇɴᴄᴇ, ɪғ ᴡᴇ ғʟᴏᴡ ᴀ ᴄᴜʀʀᴇɴᴛ ғʀᴏᴍ ᴘᴏɪɴᴛ A ᴛᴏ B ɪᴛ ᴡɪʟʟ ᴘᴀssᴇs ғʀᴏᴍ AOB ᴀɴᴅ ACB, ᴡʜᴇʀᴇ O ᴀɴᴅ B ᴀʀᴇ ᴘᴏɪɴᴛs ᴏɴ ᴛᴡᴏ ᴀʀᴄs, ᴛʜᴇʀᴇғᴏʀᴇ ᴛʜᴇ ᴄᴏɴɴᴇᴄᴛɪᴏɴ ᴡɪʟʟ ʟᴏᴏᴋ ʟɪᴋᴇ ᴛʜɪs, ɪ.ᴇ. Pᴀʀᴀʟʟᴇʟ-ᴄᴏɴɴᴇᴄᴛɪᴏɴ .

✯ Hᴇɴᴄᴇ, ᴇғғᴇᴄᴛɪᴠᴇ ᴏʀ ɴᴇᴛ ʀᴇsɪsᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴀɴʏ ᴘᴏɪɴᴛ ᴡɪʟʟ ʙᴇ,

$\huge\red\star$$\bf\green{\dfrac{1}{R_{eq}}\:=\:\dfrac{1}{R_1}\:+\:\dfrac{1}{R_2}\:}$

$\rm{:\implies\:\dfrac{1}{R_{eq}}\:=\:\dfrac{1}{R/2}\:+\:\dfrac{1}{R/2}\:}$

$\rm{:\implies\:\dfrac{1}{R_{eq}}\:=\:\dfrac{2}{R}\:+\:\dfrac{2}{R}\:}$

$\rm{:\implies\:\dfrac{1}{R_{eq}}\:=\:2\times{\dfrac{2}{R}}\:}$

$\rm{:\implies\:\dfrac{1}{R_{eq}}\:=\:\dfrac{4}{R}\:}$

$\bf\purple{:\implies\:R_{eq}\:=\:\dfrac{R}{4}\:\Omega\:}$

$\huge\red\therefore$ Tʜᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ᴀᴄʀᴏss ᴀ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴄɪʀᴄʟᴇ ɪs $\bf\pink{\dfrac{R}{4}\:\Omega\:}$ .

Answer 2

Answer:

Given, resistance of wire is R

when, it is bend in a form of circle then

the resistance across its diameter is ---

1/R' = 1/R/2 + 1/R/2

=> 1/R' = 2/R + 2/R

=> 1/R' = 4/R

=> R' = R/4

hence, the resistance across the diameter of circle is R/4.

hope this helps you