Derive the expression for Joule's heating effect of current.....
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JOULE'S HEATING EFFECT
ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴊᴏᴜʟᴇꜱ ʟᴀᴡ ᴏꜰ ʜᴇᴀᴛɪɴɢ, ᴡʜᴇɴ ᴀ ᴄᴜʀʀᴇɴᴛ ɪ ꜰʟᴏᴡꜱ ᴛʜʀᴏᴜɢʜ ᴀ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ʀ ᴛʜᴇɴ :
ʜᴇᴀᴛ ᴘʀᴏᴅᴜᴄᴇᴅ ɪꜱ :
(ɪ) ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ꜱQᴜᴀʀᴇ ᴏꜰ ᴄᴜʀʀᴇɴᴛ ꜰᴏʀ ᴀ ɢɪᴠᴇɴ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ
(ɪɪ) ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ᴏꜰ ɢɪᴠᴇɴ ᴄɪʀᴄᴜɪᴛ.
(ɪɪɪ) ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴛɪᴍᴇ ꜰᴏʀ ᴡʜɪᴄʜ ᴛʜᴇ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ꜰʟᴏᴡꜱ ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ʀᴇꜱɪꜱᴛᴏʀ.
So eqⁿ is
ʟᴇᴛ ᴜꜱ ᴄᴏɴꜱɪᴅᴇʀ ᴀ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ʀ , ɪɴ ᴡʜɪᴄʜ ɪ ᴀᴍᴏᴜɴᴛ ᴏꜰ ᴄᴜʀʀᴇɴᴛ ꜰʟᴏᴡꜱ.
ᴡᴏʀᴋ ᴍᴜꜱᴛ ʙᴇ ᴅᴏɴᴇ ʙʏ ᴄᴜʀʀᴇɴᴛ ᴛᴏ ᴍᴏᴠᴇ ᴄᴏɴᴛɪɴᴜᴏᴜꜱʟʏ.
ᴡ=Qx ᴠ
ʙᴜᴛ Q=ɪxᴛ
ᴡ=ɪxᴠxᴛ
ʙᴜᴛ ꜰʀᴏᴍ ᴏʜᴍꜱ ʟᴀᴡ: ᴠ=ɪʀ
ᴀꜱꜱᴜᴍɪɴɢ ᴛʜᴇ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ᴇɴᴇʀɢʏ ᴄᴏɴꜱᴜᴍᴇᴅ ɪꜱ ᴄᴏɴᴠᴇʀᴛᴇᴅ ɪɴᴛᴏ ʜᴇᴀᴛ ᴇɴᴇʀɢʏ .
ᴡᴇ ᴡʀɪᴛᴇ ᴡᴏʀᴋ ᴅᴏɴᴇ ᴀꜱ ʜᴇᴀᴛ ᴘʀᴏᴅᴜᴄᴇᴅ.
so
❶ ɪɴ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ʜᴇᴀᴛᴇʀꜱ.
❷ ɪɴ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ɪʀᴏɴ
❸ ɪɴ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ꜰᴜꜱᴇ ᴡɪʀᴇ
❹ ɪɴ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ʙᴜʟʙ
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