Question

 A piece of wire of resistance R is cut into five equal parts. These parts are then connected in series. If the equivalent resistance of this combination is R’, then the ratio R/R’ is:​

Answer 1

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✒ ᴀɴsᴡᴇʀ:-

⛄ ʀ/ʀ' = 25

✒ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

⛄ʟᴇᴛ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ʀᴇsɪsᴛᴀɴᴄᴇ ʀ ʙᴇ ʟ.

ʟᴇᴛ ᴛʜᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ᴏғ ᴇᴀᴄʜ ᴘᴀʀᴛ ᴀғᴛᴇʀ ᴄᴜᴛᴛɪɴɢ ʙᴇ ʀs.

∵ ᴛʜᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ɪs ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ʀᴇsɪsᴛᴏʀ,

ʀs = ʀ/5 .....→ (ɪ)

ғᴏʀ ᴛʜᴇ ʀᴇsɪsᴛᴏʀs ɪɴ ᴘᴀʀᴀʟʟᴇʟ,

1/ʀ' = 1/ʀ1 + 1/ʀ2 + 1/ʀ3 + 1/ʀ4 + 1/ʀ5

⇒ʀ' = ʀs/5 .....→ (ɪɪ)

ɴᴏᴡ, ғʀᴏᴍ (ɪ) ᴀɴᴅ (ɪɪ),

ʀ' = ʀ/25

⇒ʀ/ʀ' = 25

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