Question

Derive the expression for Joule's heating effect of current.. No Spam Ans !!!

Answer 1

Derivation:

let us consider a resistance R , in which I amount of current flows.

Work must be done by current to move continuously.

W=Qx V

BUT Q=IXt

W=IxVxt

but from ohms law: V=IR

W=I²Rt

assuming the electrical energy consumed is converted into heat energy .

we write workdone as Heat  produced

so 

H=I²Rt

hence derived 

Answer 2

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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 $\bold{\huge{\red{H=I^2Rt}}}$

$\bold{\huge{\boxed{\pink{DERIVATION}}}}$

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

$\bold{\huge{\red{W=I^2Rt}}}$

ᴀꜱꜱᴜᴍɪɴɢ ᴛʜᴇ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ᴇɴᴇʀɢʏ ᴄᴏɴꜱᴜᴍᴇᴅ ɪꜱ ᴄᴏɴᴠᴇʀᴛᴇᴅ ɪɴᴛᴏ ʜᴇᴀᴛ ᴇɴᴇʀɢʏ .

ᴡᴇ ᴡʀɪᴛᴇ ᴡᴏʀᴋ ᴅᴏɴᴇ ᴀꜱ ʜᴇᴀᴛ  ᴘʀᴏᴅᴜᴄᴇᴅ.

so $\bold{\underline{\huge{\red{H=I^2Rt}}}}$

$\bold{\huge{\boxed{\pink{APPLICATION}}}}$

❶ ɪɴ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ʜᴇᴀᴛᴇʀꜱ.

❷ ɪɴ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ɪʀᴏɴ

❸ ɪɴ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ꜰᴜꜱᴇ ᴡɪʀᴇ

❹ ɪɴ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ʙᴜʟʙ

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