Question

A wire of given material having length L and area of cross-section A has a resistance of 4 ohm.What would be the resistance of another wire of same material having length L/2 and area of cross-section 2A?

Answer 1

Refer to the attachment

Answer 2

ʙʏ ᴛʜᴇ ғᴏʀᴍᴜʟᴀ ᴏғ ʀᴇsɪsᴛᴀɴᴄᴇ:

ʀ=(σ) ʟ/ᴀ

ʜᴇʀᴇ σ ɪs ʀᴇsɪsᴛɪᴠɪᴛʏ, ʟ ɪs ʟᴇɴɢᴛʜ ᴏғ ᴡɪʀᴇ ᴀɴᴅ ᴀ ɪs ᴀʀᴇᴀ ᴏғ ᴄʀᴏss sᴇᴄᴛɪᴏɴ

ɢɪᴠᴇɴ. σ1=σ2. ______ᴇϙ 1

ғᴏʀ ғɪʀsᴛ ᴍᴀᴛᴇʀɪᴀʟ ʀ1=σ1 ʟ/ᴀ.

ᴡᴇ ᴄᴀɴ ᴡʀɪᴛᴇ.. σ1=ʀ1ᴀ/ʟ

σ1=4ᴀ/ʟ.

ғᴏʀ sᴇᴄᴏɴᴅ ᴍᴀᴛᴇʀɪᴀʟ σ2 = ʀ2.4ᴀ/ʟ

ғʀᴏᴍ ᴇϙ1. 4ᴀ/ʟ=ʀ24ᴀ/ʟ

ʀ2=0.